*3.1. Dielectrophoretic Immobilization of Living Yeast Cells*  After applying 20 Vpp at 1 MHz, obvious cell immobilization was observed. Cell entrapment started a few seconds after cell suspension had reached the IDEs. Trapping started at the electrode edges, where the electric field gradient intensity was increased. Figure 9 demonstrates the cell trapping performance of different IDE geometries at three time intervals. Cell polarization effect in a non-uniform electric field led to dipole-dipole interaction and forming of pearl chains of cells [21]. As shown in Figure 9, the number of immobilized yeast cells is strongly dependent on the geometrical ratio of the IDEs. The number of immobilized yeast cells is reduced with increasing IDEs geometrical ratio. Cell entrapment reaches its highest efficiency by using IDEs with the largest finger width (45 µm) and smallest gap spacing (5 µm) between adjacent fingers. Furthermore, immobilization of cells using IDEs with higher geometrical ratios is challenging. This is due to the fact that the entrapped cells desorb from the IDEs with greater S/W ratios throughout the immobilization process. In addition, it is observed that increasing an electrode width, with a constant spacing size, expand the number of entrapped cells. These optical observations are in line with the simulation results presented in Figure 10. Finite element modeling (FEM) simulations support the impact of geometrical parameters on the DEP effect. The probability of immobilizing cells increases with reduced geometrical (spacing to width) ratios of the IDEs. Figure 10 illustrates the impact of various geometry ratios on the immobilization probability (IP) of yeast cells. The immobilization probability is defined After applying 20 Vpp at 1 MHz, obvious cell immobilization was observed. Cell entrapment started a few seconds after cell suspension had reached the IDEs. Trapping started at the electrode edges, where the electric field gradient intensity was increased. Figure 9 demonstrates the cell trapping performance of different IDE geometries at three time intervals. Cell polarization effect in a non-uniform electric field led to dipole-dipole interaction and forming of pearl chains of cells [21]. As shown in Figure 9, the number of immobilized yeast cells is strongly dependent on the geometrical ratio of the IDEs. The number of immobilized yeast cells is reduced with increasing IDEs geometrical ratio. Cell entrapment reaches its highest efficiency by using IDEs with the largest finger width (45 µm) and smallest gap spacing (5 µm) between adjacent fingers. Furthermore, immobilization of cells using IDEs with higher geometrical ratios is challenging. This is due to the fact that the entrapped cells desorb from the IDEs with greater S/W ratios throughout the immobilization process. In addition, it is observed that increasing an electrode width, with a constant spacing size, expand the number of entrapped cells. These optical observations are in line with the simulation results presented in Figure 10. Finite element modeling (FEM) simulations support the impact of geometrical parameters on the DEP effect. The probability of immobilizing cells increases with reduced geometrical (spacing to width) ratios of the IDEs. Figure 10 illustrates the impact of various geometry ratios on the immobilization probability (IP) of yeast cells. The immobilization probability is defined by the number of trapped cells to the total number of cells suspended in the fluidic medium.

by the number of trapped cells to the total number of cells suspended in the fluidic medium.

**Figure 9.** *Cont*.

*Micromachines* **2020**, *11*, x FOR PEER REVIEW 11 of 17

: 0.1 0.25 0.4 0.6 1 1.3 After 1 min

After 3 min

௦ :݅ݐܽݎ ௪

− **Figure 9.** Micrographs of the immobilized yeast cells as a function of IDEs geometry (spacing to width ratios) at three time intervals of 1 min, 3 min, and 6 min. Immobilization conditions: 20 Vpp, 1 MHz, 1 µm·s −1 flow rate. 1 µm·s−1 flow rate.

**Figure 10.** Calculated impact of IDE's spacing to width ratio on the immobilization of yeast cells. Finite element modeling (FEM) for the dielectrophoretic immobilization of yeast cells was performed **Figure 10.** Calculated impact of IDE's spacing to width ratio on the immobilization of yeast cells. Finite element modeling (FEM) for the dielectrophoretic immobilization of yeast cells was performed at 20 Vpp and 1 MHz.

at 20 Vpp and 1 MHz.

Increasing the IDEs ratio reversely impacts the IP. Furthermore, it can be seen that by keeping the spacing constant at 20 µm, there has been a steady decline in IP with decreasing width (at ratios of 0.6, 1, and 1.3). Therefore, it can be concluded that the DEP efficiency is highly influenced by IDE's Increasing the IDEs ratio reversely impacts the IP. Furthermore, it can be seen that by keeping the spacing constant at 20 µm, there has been a steady decline in IP with decreasing width (at ratios of 0.6, 1, and 1.3). Therefore, it can be concluded that the DEP efficiency is highly influenced by IDE's dimensional ratio (S/W). As illustrated in Figure 11, experimental results indicate that smaller IDE ratios reduce the required peak voltages for DEP immobilization. *Micromachines* **2020**, *11*, x FOR PEER REVIEW 12 of 17 dimensional ratio (S/W). As illustrated in Figure 11, experimental results indicate that smaller IDE ratios reduce the required peak voltages for DEP immobilization.

**Figure 11.** Minimum DEP driving voltage for the immobilization of yeast cells as function of spacing to width ratio, according to experimental data. **Figure 11.** Minimum DEP driving voltage for the immobilization of yeast cells as function of spacing to width ratio, according to experimental data.

(**a**) ݂ ≤ 700 kHz (**b**) 700 kHz < ݂ < 9 MHz (**c**) 9 MHz ≤ ݂ **Figure 12.** Frequency dependency of cell immobilization at 20 Vpp and a flow rate of 1 µm s−1. (**a**) High desorption rate of immobilized yeast cells; (**b**) Very high cell immobilization rate and very low

At frequencies between 700 kHz and 900 kHz and between 7 MHz and 9 MHz, the immobilization stability of cells mainly dropped, and with the passage of the time immobilized cells

desorption rate of immobilized cells; (**c**) High desorption rate of immobilized cells.

was raised and thus more cells were attracted to the electrodes.

to nDEP.

For the largest IDE dimensional ratio, the required voltage values were roughly twice as much

According to the experimental results, live cells can be trapped in a frequency range between 700 kHz and 9 MHz. Using frequencies above 10 MHz and below 300 kHz cells experience a repulsive force, which results in significant desorption of the immobilized cells from the electrodes. Figure 12 shows the frequency dependency of cell entrapment at 20 Vpp. In the frequency range between 900 kHz and 6 MHz, desorption rates are very low. Desorption rates increase drastically at lower frequencies (݂ ≤ 300 kHz) due to weak pDEP and at higher frequencies (10 MHz ≤ ݂) due to width ratio, according to experimental data.

For the largest IDE dimensional ratio, the required voltage values were roughly twice as much as the required value for the smallest IDE ratio. In addition, cell trapping was increased drastically with an increasing voltage trend. By increasing the gradient of the electric potential, the DEP force was raised and thus more cells were attracted to the electrodes. as the required value for the smallest IDE ratio. In addition, cell trapping was increased drastically with an increasing voltage trend. By increasing the gradient of the electric potential, the DEP force was raised and thus more cells were attracted to the electrodes. According to the experimental results, live cells can be trapped in a frequency range between 700 kHz and 9 MHz. Using frequencies above 10 MHz and below 300 kHz cells experience a

**Figure 11.** Minimum DEP driving voltage for the immobilization of yeast cells as function of spacing

For the largest IDE dimensional ratio, the required voltage values were roughly twice as much

*Micromachines* **2020**, *11*, x FOR PEER REVIEW 12 of 17

dimensional ratio (S/W). As illustrated in Figure 11, experimental results indicate that smaller IDE

ratios reduce the required peak voltages for DEP immobilization.

According to the experimental results, live cells can be trapped in a frequency range between 700 kHz and 9 MHz. Using frequencies above 10 MHz and below 300 kHz cells experience a repulsive force, which results in significant desorption of the immobilized cells from the electrodes. Figure 12 shows the frequency dependency of cell entrapment at 20 Vpp. In the frequency range between 900 kHz and 6 MHz, desorption rates are very low. Desorption rates increase drastically at lower frequencies (*fo* ≤ 300 kHz) due to weak pDEP and at higher frequencies (10 MHz ≤ *fo*) due to nDEP. repulsive force, which results in significant desorption of the immobilized cells from the electrodes. Figure 12 shows the frequency dependency of cell entrapment at 20 Vpp. In the frequency range between 900 kHz and 6 MHz, desorption rates are very low. Desorption rates increase drastically at lower frequencies (݂ ≤ 300 kHz) due to weak pDEP and at higher frequencies (10 MHz ≤ ݂) due to nDEP.

(**a**) ݂ ≤ 700 kHz (**b**) 700 kHz < ݂ < 9 MHz (**c**) 9 MHz ≤ ݂

**Figure 12.** Frequency dependency of cell immobilization at 20 Vpp and a flow rate of 1 µm s−1. (**a**) High desorption rate of immobilized yeast cells; (**b**) Very high cell immobilization rate and very low desorption rate of immobilized cells; (**c**) High desorption rate of immobilized cells. **Figure 12.** Frequency dependency of cell immobilization at 20 Vpp and a flow rate of 1 µm s−1 . (**a**) High desorption rate of immobilized yeast cells; (**b**) Very high cell immobilization rate and very low desorption rate of immobilized cells; (**c**) High desorption rate of immobilized cells.

*Micromachines* **2020**, *11*, x FOR PEER REVIEW 13 of 17

At frequencies between 700 kHz and 900 kHz and between 7 MHz and 9 MHz, the immobilization stability of cells mainly dropped, and with the passage of the time immobilized cells At frequencies between 700 kHz and 900 kHz and between 7 MHz and 9 MHz, the immobilization stability of cells mainly dropped, and with the passage of the time immobilized cells gradually tend to desorb from the electrodes. Figure 13 illustrates the weak immobilization as a result of imposing an AC voltage of 9 Vpp at 8 MHz. gradually tend to desorb from the electrodes. Figure 13 illustrates the weak immobilization as a result of imposing an AC voltage of 9 Vpp at 8 MHz.

**Figure 13.** An example of weak immobilization at 8 MHz (9 ܸ, and 1 µm·s−1): (**a**) Immobilization of cells after 2 min, and (**b**) 3 min, partial desorption of trapped cells from the IDEs. **Figure 13.** An example of weak immobilization at 8 MHz (9 *Vpp*, and 1 µm·s −1 ): (**a**) Immobilization of cells after 2 min, and (**b**) 3 min, partial desorption of trapped cells from the IDEs.

experimentally evaluated values of fc could be caused by the simplicity of the used model in terms

of cell wall, membrane, cytoplasm, and nucleus size.

for further investigations and analyses.

*3.2. Dielectrophoretic Separation of Live and Dead Yeast Cells*

The experimental results are in agreement with the simulation (see Figure 7), the yeast cells are

In order to differentiate between live and dead yeast cells, the impact of the AC frequency on the trajectory of live and dead cells was investigated experimentally and simulated using COMSOL. On the basis of the simulation shown in Figure 7, the DEP response of live and dead cells is significantly different at high frequencies [16]. Yeast cells subject to some modifications when they expose to heat shock. Such modifications could include a reduction in size and alterations to the dielectric properties of the cell. Due to the heat shock, intercellular water is reduced, and yeast cell experience water stress. This results in the wrinkling of the cell membrane and reduction in the cell diameter, which is associated with the shrinkage of the entire yeast cell [52–54]. The fc of dead yeasts occurs at ~1.45 MHz because dead cells lose their viability due to an impaired membrane. Their cytoplasmic conductivity is decreased while their membrane conductivity is increased. An impaired membrane of a dead cell polarized differently when it is exposed to an electric field. Thus, due to these dielectric discrepancies, responses of live and dead cells to the fringing electric field are dissimilar [16,21,55]. Our experimental results demonstrate that dead cells experienced an attractive force between 40 kHz and 1.45 MHz and can be trapped at the IDEs between 60 kHz and 1.45 MHz.

Taking into account the distinct DEP responses of live and dead yeast cells at specific frequency ranges, preliminary demonstrations of the separation were performed. The concept was also simulated using COMSOL Multiphysics. Our simulation results were reasonably consistent with experimental results. Figure 14a shows a snapshot image for the separation of dead cells from live cells, where live cells immobilized at the IDEs at 3 MHz and 20 Vpp. In contrast, separation of live cells from dead ones, when dead cells immobilized at the electrodes at 90 kHz and 20 Vpp, is shown in Figure 14b. Therefore, separation of live and dead cells using the proposed method is achievable. Furthermore, the desorbed dead or live cells can be collected at the outlet of the microfluidic channel

At lower frequencies (<40 kHz), no DEP response was observed for dead yeasts.

The experimental results are in agreement with the simulation (see Figure 7), the yeast cells are forced by pDEP at frequencies lower than 10 MHz. However, fc was found to be 10 MHz, whereas the simulated prediction of fc is about 45 MHz. The large difference between the simulated and the experimentally evaluated values of fc could be caused by the simplicity of the used model in terms of cell wall, membrane, cytoplasm, and nucleus size.

### *3.2. Dielectrophoretic Separation of Live and Dead Yeast Cells*

In order to differentiate between live and dead yeast cells, the impact of the AC frequency on the trajectory of live and dead cells was investigated experimentally and simulated using COMSOL. On the basis of the simulation shown in Figure 7, the DEP response of live and dead cells is significantly different at high frequencies [16]. Yeast cells subject to some modifications when they expose to heat shock. Such modifications could include a reduction in size and alterations to the dielectric properties of the cell. Due to the heat shock, intercellular water is reduced, and yeast cell experience water stress. This results in the wrinkling of the cell membrane and reduction in the cell diameter, which is associated with the shrinkage of the entire yeast cell [52–54]. The fc of dead yeasts occurs at ~1.45 MHz because dead cells lose their viability due to an impaired membrane. Their cytoplasmic conductivity is decreased while their membrane conductivity is increased. An impaired membrane of a dead cell polarized differently when it is exposed to an electric field. Thus, due to these dielectric discrepancies, responses of live and dead cells to the fringing electric field are dissimilar [16,21,55]. Our experimental results demonstrate that dead cells experienced an attractive force between 40 kHz and 1.45 MHz and can be trapped at the IDEs between 60 kHz and 1.45 MHz. At lower frequencies (<40 kHz), no DEP response was observed for dead yeasts.

Taking into account the distinct DEP responses of live and dead yeast cells at specific frequency ranges, preliminary demonstrations of the separation were performed. The concept was also simulated using COMSOL Multiphysics. Our simulation results were reasonably consistent with experimental results. Figure 14a shows a snapshot image for the separation of dead cells from live cells, where live cells immobilized at the IDEs at 3 MHz and 20 Vpp. In contrast, separation of live cells from dead ones, when dead cells immobilized at the electrodes at 90 kHz and 20 Vpp, is shown in Figure 14b. Therefore, separation of live and dead cells using the proposed method is achievable. Furthermore, the desorbed dead or live cells can be collected at the outlet of the microfluidic channel for further investigations and analyses. *Micromachines* **2020**, *11*, x FOR PEER REVIEW 14 of 17 Figure 15 demonstrates how DEP can be used diversely to isolate specific cells from a mixture of cells using the distinct DEP behavior of live and dead yeast cells. Keeping the signal frequency constant at 3 MHz, dead cells were separated from live cells, which were simultaneously immobilizing at the IDEs (Figure 15a). The opposite situation happens when a signal frequency in the range of 70 kHz ≤ ݂ ≤ 100 kHz is applied to the system (Figure 15b).

live cells, and (**b**) vice versa as a function of frequency.

**4. Conclusions**

the simulation.

(**a**) pDEP at 3 MHz (**b**) pDEP at 90 kHz

**Figure 14.** Separation of live and dead cells based on DEP characteristics. (**a**) Immobilize of live cells at the IDEs, while dead ones repel from the IDEs and leave the microfluidic channel at 20 Vpp, and (**b**) Immobilization of dead yeast cells at the IDEs. ). **Figure 14.** Separation of live and dead cells based on DEP characteristics. (**a**) Immobilize of live cells at the IDEs, while dead ones repel from the IDEs and leave the microfluidic channel at 20 Vpp, and (**b**) Immobilization of dead yeast cells at the IDEs).

(**a**) DEP at 3 MHz

(**b**) DEP at 90 kHz **Figure 15.**  The device has been used to differentiate between live and dead yeast cells based on the selective DEP forces, pDEP and nDEP. IDEs with various geometrical parameters were studied. The effect of DEP force on the trajectory of yeast cells as functions of voltage, frequency, flow-rate, and IDE geometry was studied experimentally. Besides, finite element modeling was used to predict the trajectories of the cells. Experimental and simulation results demonstrate that based on the specific properties of cells, the microfluidic device can be used to immobilize and separate specific cells by varying the AC frequency. It was found that the experimental results are in agreement with

Figure 15 demonstrates how DEP can be used diversely to isolate specific cells from a mixture of cells using the distinct DEP behavior of live and dead yeast cells. Keeping the signal frequency constant at 3 MHz, dead cells were separated from live cells, which were simultaneously immobilizing at the IDEs (Figure 15a). The opposite situation happens when a signal frequency in the range of 70 kHz ≤ *fo* ≤ 100 kHz is applied to the system (Figure 15b). (**a**) pDEP at 3 MHz (**b**) pDEP at 90 kHz **Figure 14.** Separation of live and dead cells based on DEP characteristics. (**a**) Immobilize of live cells at the IDEs, while dead ones repel from the IDEs and leave the microfluidic channel at 20 Vpp, and (**b**) Immobilization of dead yeast cells at the IDEs. ).

*Micromachines* **2020**, *11*, x FOR PEER REVIEW 14 of 17

the range of 70 kHz ≤ ݂ ≤ 100 kHz is applied to the system (Figure 15b).

Figure 15 demonstrates how DEP can be used diversely to isolate specific cells from a mixture of cells using the distinct DEP behavior of live and dead yeast cells. Keeping the signal frequency constant at 3 MHz, dead cells were separated from live cells, which were simultaneously immobilizing at the IDEs (Figure 15a). The opposite situation happens when a signal frequency in

**Figure 15.** Simulated DEP separation of live and dead yeast cells: (**a**) Separation of dead cells from live cells, and (**b**) vice versa as a function of frequency. **Figure 15.** Simulated DEP separation of live and dead yeast cells: (**a**) Separation of dead cells from live cells, and (**b**) vice versa as a function of frequency.

#### **4. Conclusions 4. Conclusions**

A silicon-based CMOS integrated microfluidic device for immobilization of live and dead yeast cells via DEP was investigated. The device has been used to differentiate between live and dead yeast cells based on the selective DEP forces, pDEP and nDEP. IDEs with various geometrical parameters were studied. The effect of DEP force on the trajectory of yeast cells as functions of voltage, frequency, flow-rate, and IDE geometry was studied experimentally. Besides, finite element modeling was used to predict the trajectories of the cells. Experimental and simulation results demonstrate that based on the specific properties of cells, the microfluidic device can be used to immobilize and separate specific cells by varying the AC frequency. It was found that the experimental results are in agreement with the simulation. A silicon-based CMOS integrated microfluidic device for immobilization of live and dead yeast cells via DEP was investigated. The device has been used to differentiate between live and dead yeast cells based on the selective DEP forces, pDEP and nDEP. IDEs with various geometrical parameters were studied. The effect of DEP force on the trajectory of yeast cells as functions of voltage, frequency, flow-rate, and IDE geometry was studied experimentally. Besides, finite element modeling was used to predict the trajectories of the cells. Experimental and simulation results demonstrate that based on the specific properties of cells, the microfluidic device can be used to immobilize and separate specific cells by varying the AC frequency. It was found that the experimental results are in agreement with the simulation.

**Author Contributions:** Methodology, H.M.E.; Validation, H.M.E.; Software, H.M.E., and P.S.Z.; Formal analysis, H.M.E., R.H., and C.W.; Data curation, H.M.E.; Writing—Original draft preparation, H.M.E.; Writing—Review and editing, H.M.E., P.S.Z., R.H. and C.W.; Supervision, C.W.; Funding acquisition, C.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Brandenburg Ministry of Science, Research, and Cultural Affairs for the project within the StaF program in Germany. The publication of this article was funded by the Open Access Fund of the Leibniz Association.

**Acknowledgments:** The authors would like to thank the technology department of IHP for the fabrication of the sensor chip. The authors would like to thank Rita Winkler for the fabrication of the manifold.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

*Article*

## **Driving Waveform Design of Electrowetting Displays Based on an Exponential Function for a Stable Grayscale and a Short Driving Time**

**Zichuan Yi 1 , Zhenyu Huang 2,3, \*, Shufa Lai 3 , Wenyao He 2 , Li Wang 2,3 , Feng Chi 1 , Chongfu Zhang 1 , Lingling Shui 1,2 and Guofu Zhou 2,3**

Received: 8 February 2020; Accepted: 12 March 2020; Published: 16 March 2020

**Abstract:** The traditional driving waveform of the electrowetting display (EWD) has many disadvantages, such as the large oscillation of the target grayscale aperture ratio and a long time for achieving grayscale. Therefore, a driving waveform based on the exponential function was proposed in this study. First, the maximum driving voltage value of 30 V was obtained by testing the hysteresis curve of the EWD pixel unit. Secondly, the influence of the time constant on the driving waveform was analyzed, and the optimal time constant of the exponential function was designed by testing the performance of the aperture ratio. Lastly, an EWD panel was used to test the driving effect of the exponential-function-driving waveform. The experimental results showed that a stable grayscale and a short driving time could be realized when the appropriate time constant value was designed for driving EWDs. The aperture ratio oscillation range of the gray scale could be reduced within 0.95%, and the driving time of a stable grayscale was reduced by 30% compared with the traditional driving waveform.

**Keywords:** electrowetting display; driving waveform; aperture ratio; exponential function; time constant

#### **1. Introduction**

In recent years, display technology has been widely used in all aspects of daily life [1,2]. In 2003, Hayes et al. proposed the EWD structure based on the principle of ink electrowetting [3], which has the advantages of low power consumption, high reflectivity, high contrast, and fast response speed. As one of new display technologies [4], increasingly more attention has been paid to EWDs. However, EWD technology has not been industrialized, and its driving technology is one of the limiting factors.

Grayscale is displayed in EWDs by applying a voltage sequence, called as driving waveform, which is used to control the form of colored ink in a pixel [5]. The ratio of a pixel area not covered by the ink to a whole pixel area is the aperture ratio, which can reflect the performance of EWDs [6]. Because the ink is divided into several parts, called the ink dispersion [7], the ink coverage area is constantly changing in the process of providing a fixed grayscale display. Therefore, an oscillation of the aperture ratio can be formed, which can reduce the number of grayscale levels and the

visual experience of users. At present, some problems with EWDs are being solved, such as ink dispersion [8], charge capture [9,10], hysteresis [11], ink reflow [12], and large oscillations of the aperture ratio [13]. We have used industrial electrophoretic electronic display driver chips to drive TFT (thin-film transistor) EWDs and a four-level gray scale was realized using a PWM (pulse-width modulation) driving waveform [14]. However, the ink in the EWD pixel has obvious shrinkage and the oscillation range of the aperture ratio is relatively large due to a high switching frequency of the voltage in PWM, which has a bad effect when aiming to display stable grayscales [15]. In addition, by comparing the duty cycle of different PWMs, we found that the smaller the duty cycle of the PWM, the larger the oscillation range of the aperture ratio in the EWDs was [13]; in contrast, the larger the duty ratio, the smaller the oscillation range, which provides a reference for the driving waveform design of stable grayscales. Based on a PWM driving waveform, where the starting point of a driving waveform is set to 10 V as a maintained voltage, the optimized design of the maintained voltage and its timing can reduce the ink breakage, which can reduce the oscillation range of aperture ratio effectively; however, its driving time is extended [16]. At the same time, by optimizing the slope of the driving waveforms to control movement state of the ink in EWDs, the ink dispersion can be improved and the reflectivity can effectively be increased. However, the driving waveform increases the oscillation range of the aperture ratio and lengthens the driving time [17]. However, the damped oscillation of an electrowetting liquid drop can be optimized by changing the rising speed of the driving waveform, and the transition between the under-damping state and the over-damping state in the electrowetting lens is realized [18], which provides a reference direction for optimizing the driving waveform of the EWDs.

In order to display a stable grayscale and reduce the driving time in EWDs, an exponential-function-driving waveform was proposed in this study. By testing the impact of different time-constant values, we set parameters of the exponential function when designing the driving waveform. Compared with traditional driving waveforms, the exponential-function-driving waveform had a better driving performance.

### **2. Driving Principle of the EWD**

### *2.1. Model of the EWD*

The EWD was mainly composed of a glass substrate, indium tin oxide glass (ITO), hydrophobic insulation layer, pixel wall, conductive liquid (NaCl solution), colored ink, and so on [19,20], as shown in Figure 1.

**Figure 1.** Structure of a pixel in electrowetting displays (EWDs). ITO: Indium tin oxide.

The ink is laid between a NaCl solution and a hydrophobic insulation layer when no voltage is applied, and the NaCl solution does not contact the hydrophobic insulation layer directly. Then, the color of ink is displayed, and the pixel is in the "off" state, as shown in Figure 2a. The interfacial tension between the NaCl solution and the hydrophobic insulation layer is changed by an electric field force when a certain amplitude of voltage is applied between the upper and lower electrodes. At this time, the NaCl solution contacts with the hydrophobic insulating layer directly, and the ink is pushed away. Then, the pixel shows the white substrate, and the pixel is in the "on" state, as shown in Figure 2b. The ink can be spread on the hydrophobic insulating layer again when the voltage is removed such that the pixel can be continuously switched between "on" and "off " [21].

**Figure 2.** Ink state in an EWD pixel. (**a**) The pixel is "off" and the whole pixel is covered by ink such that the color of the ink is reflected. (**b**) The pixel is "on" and the ink is pushed into a corner of the pixel such that the white substrate is reflected.

For typical submillimeter-scale EWD pixels, the main driving forces of the ink movement are the interface tension and electrostatic force. The interface boundary is usually described using the Young–Lippmann equation [22,23], as shown in Equation (1):

$$\cos\theta = \cos\theta\_0 + \frac{1}{2}\frac{\varepsilon\_0 \varepsilon\_{FP}}{d\gamma\_{OW}}\mathcal{U}^2\tag{1}$$

*θ θ ε ε γ* In Equation (1), θ is the contact angle of the Lippmann, and θ0 is the equilibrium contact angle between the NaCl solution and the hydrophobic insulating layer. ε*0* represents the dielectric constant of the vacuum, ε*FP* represents dielectric constant of the hydrophobic insulating layer, *d* represents thickness of the hydrophobic insulating layer, *U* represents the driving voltage of the pixel, and γ*OW* represents the interfacial tension between the ink and the NaCl solution.

It can be seen from Equation (1) that the contact angle of the NaCl solution on the surface of the hydrophobic insulating layer can be controlled by changing the electric potential. That is to say, due to the change of electric potential energy, the surface performance of the hydrophobic insulating layer is changed, which produces a change of the conductive liquid contact angle on the hydrophobic insulating layer surface [24]. With an increase of the electric potential, the interface tension between the hydrophobic insulation layer and the NaCl solution becomes larger, the contact angle can also become larger, and the voltage difference breaks the balanced state. At this time, the NaCl solution is in direct contact with the hydrophobic insulation layer and the colored ink is pushed to a corner of the pixel to expose the white substrate. The area ratio of the exposed white substrate is called the aperture ratio, which can directly represents the reflectivity of EWDs [25], where the expression is shown in Equation (2):

$$\mathbf{A} = \left[1 - \left(\frac{S\_{oil}}{S\_{pix}}\right)\right] \times 100\% \tag{2}$$

where A is the aperture ratio, *Soil* is the area of ink when it is pushed to a corner of a pixel, and the area of a whole pixel is *Spix*.

#### *2.2. Design Principle of an Exponential-Function-Driving Waveform*

The exponential-function-driving waveform expression is shown in Equation (3):

$$\mathcal{U} = \mathcal{U}\_0 \times \left(1 - e^{-\frac{\mathcal{U}}{\dagger}}\right) \tag{3}$$

where *U* represents the real-time voltage of a driving waveform; *U0* represents the maximum voltage in a driving waveform, which is a fixed value; *t* represents driving time; and τ represents the time constant of the exponential function. We can analyze the influence of τ on the exponential-function-driving waveform by changing its value.

We take the derivative of Equation (3) to obtain Equation (4):

$$
\mathcal{U}'(t) = \frac{\mathcal{U}\_0}{\tau} e^{-\frac{t}{\tau}}.\tag{4}
$$

When τ = 1 ms:

$$\begin{cases} \mathcal{U}'(t) = \mathcal{U}\_0 e^{-t} \\ \mathcal{U}'(1) = \mathcal{U}\_0 e^{-1}, \quad \mathcal{U}'(2) = \mathcal{U}\_0 e^{-2} \\ \mathcal{U}'(3) = \mathcal{U}\_0 e^{-3}, \quad \mathcal{U}'(4) = \mathcal{U}\_0 e^{-4} \end{cases} \tag{5}$$

When τ = 6 ms:

$$\begin{cases} \mathcal{U}'(t) = \mathcal{U}\_0 e^{-\frac{1}{6}} \\ \mathcal{U}'(1) = \mathcal{U}\_0 e^{-\frac{1}{6}}, \quad \mathcal{U}'(2) = \mathcal{U}\_0 e^{-\frac{1}{3}} \\ \mathcal{U}'(3) = \mathcal{U}\_0 e^{-\frac{1}{2}}, \quad \mathcal{U}'(4) = \mathcal{U}\_0 e^{-\frac{2}{3}} \end{cases} \tag{6}$$

In Equations (5) and (6), *U*0 is a fixed value. Therefore, the change rate of the derivative in an exponential function is determined by τ, which is used to change the rising speed of driving waveforms.

#### **3. Design of the Exponential-Function-Driving Waveform**

#### *3.1. Maximum Voltage of the Driving Waveform*

EWD has the characteristic of displaying hysteresis in the pixel [26,27]. In the rising-voltage stage, the ink area could be reduced slightly between 9 V and 16 V, but its aperture ratio was too small, and the pixel was not opened. However, the aperture ratio could be increased to about 50% when the voltage reached 17 V. At this time, the pixel was in an "on" state. Therefore, 17 V was the threshold voltage of a pixel. Then, the aperture ratio could reach the maximum value when the voltage was increased to 30 V. In the falling-voltage stage, the aperture ratio could be closed to 0 when the voltage was reduced to 5 V. Hence, the aperture ratio of the pixels was different between the rising-voltage stage and the falling-voltage stage at the same voltage value, as shown in Figure 3. In addition, it is easy to break through the hydrophobic insulation layer if the voltage is too high, which can cause damage to the EWD pixels [28]. Therefore, the maximum voltage of the driving waveform was set as 30 V.

**Figure 3.** Rising-voltage stage and falling-voltage stage of the hysteresis curve in EWDs.

#### *3.2. Time Constant of the Exponential Function*

*τ τ τ τ τ τ τ τ* ≤ *τ* ≤ By taking the derivative of the exponential function, the derivative value at each time point can be obtained. Furthermore, it can be changed by using different time constants τ. The smaller the value of τ, the greater the variation of the exponential function derivative when the frequency and the maximum voltage *U0* are fixed. On the contrary, the larger the value of τ, the smaller the exponential function derivative change is. Therefore, the voltage-rising speed can be controlled by changing the derivative, which can be used to control the oscillation range of the aperture ratio for stable grayscales and reduce the driving time. As shown in Figure 4, the exponential function with τ = 1 ms was the steepest one, whereas the exponential function with τ = 6 ms was the smoothest one. The exponential function was close to PWM due to its fast voltage-rising speed when τ < 1 ms, and it could not reach the maximum driving voltage in a driving cycle due to its slow voltage-rising speed if τ > 6 ms at the same time. Therefore, the value of τ was in the range of 1 ms ≤ τ ≤ 6 ms. *τ τ τ τ τ τ τ τ* ≤ *τ* ≤

*τ* **Figure 4.** Exponential functions with different *τ*τ values.

Ink in the pixel can be pushed toward corners using a conductive NaCl solution by applying a driving voltage to EWDs when a grayscale needs to be displayed. However, the ink may be divided into several parts in this process; this phenomenon is called ink dispersion [29]. With the increase of the driving time, some smaller inks can gradually move closer to the larger one, as shown in Figure 5. In this process, the grayscale is unstable until all the ink is in one corner of a pixel.

**Figure 5.** The ink formation change process in the driving process of a pixel.

∆ Therefore, there is an oscillation phenomenon of the aperture ratio in all driving processes, which has a bad effect when aiming to display stable grayscales. The aperture ratio of the pixel decreased from 77% to 76%, and then increased to 77%, where the oscillation range of the aperture ratio is expressed as ∆*R* in this paper. In addition, the driving time for a stable grayscale is expressed as *ST*, where a complete driving process is shown in Figure 6. ∆ ∆

*τ* ∆ **Figure 6.** The aperture ratio change process when a driving waveform is applied to the EWD.

*τ τ τ* ∆ *τ τ* Then, the relationship between τ and ∆*R* can be tested by using the exponential-function-driving waveform to drive the EWD, and the same method can be used to test the relationship between τ and *ST*. In the testing, the value range of τ was from 1 ms to 6 ms, where the relationship curves are shown in Figure 7. *τ* ∆ *τ τ*

*τ* ∆ *τ τ* ∆ *τ τ* ∆ *τ* **Figure 7.** The relationship among parameters of the exponential-function-driving waveform. (**a**) The relationship between τ and ∆*R*. (**b**) The relationship between τ and the stable time.

As shown in Figure 7a, with the increase of τ, ∆*R* reached the minimum value of 0.95% when τ = 2 ms. Furthermore, ∆*R* reached the maximum value of 1.25% when τ = 4 ms. As shown in Figure 7b, with the increase of τ, the ST reached the minimum value of 8 s when τ = 4 ms, where the maximum *ST* was 18 s when τ = 2 ms.

#### **4. Experimental Results and Discussion**

#### *4.1. Testing System*

In order to test the effect of driving waveforms, we developed an experimental platform to record the aperture ratio and the driving process to measure the oscillation range of the aperture ratio and the driving time of the grayscales. The driving system consisted of a computer, a waveform generator and a high-voltage amplifier, which were used to edit the driving waveform for the EWD. The testing system consisted of a microscope and a high-speed camera. Relevant equipment information is shown in Table 1. Furthermore, an EWD panel was used in the experiment, where its parameters are shown in Table 2.

In the EWD panel, the hydrophobic insulation layer was not resistant to a high voltage, and the withstand voltage value was under 40 V. The hydrophobic layer material was Teflon AF1600, and its solution was FC-43, which is a fluorocarbon solvent from the 3M company (Maplewood, MN, USA); the pixel wall grid material was transparent polyimide; the ITO glass substrate came from Shenzhen Laibao Hi Tech Co., Ltd. (Shenzhen, China); the glass thickness was 0.7 mm and the impedance is 100 Ω/cm2 ; and the electrolyte solution was NaCl with a concentration of 1 × 10−4 mol/L. Deionized water was obtained using an ultra-pure ultraviolet water purification system.

In the testing process, the driving waveform was edited using MATLAB (Mathworks, Natick, MA, USA) and ArbExpress software (V3.4, Tektronix, Beaverton, OR, USA), and then it was sent to the signal generator via a serial port. Since the maximum output voltage of the signal generator was 5 V, the EWD could not be driven by the signal generator directly. Therefore, the signal generator should be connected with a high-voltage amplifier for outputting the driving voltage. In addition, an industrial camera was used to record the ink state of the EWD in real time using a microscope. The microscope could magnify the pixel 200 times and the resolution of the industrial camera was 1920 × 1080. The real-time picture of a pixel could be captured every 50 ms and the aperture ratio of the pixels could be calculated for each picture using binary processing. Therefore, the relationship between the aperture ratio and the time could be obtained. During the experiment, the surrounding temperature was 25 ◦C and the humidity was 60%. Next, two comparative experiments are shown as follows.

#### *4.2. Oscillation Range of the Aperture Ratio*

Two traditional driving waveforms were used to analyze and compare the oscillation range ∆*R*. In the design of the traditional PWM driving waveform, the maximum voltage was still set to 30 V, and its duty cycle was changed from 50% to 90%, as shown in Figure 8a. The smaller the duty cycle, the smaller the ratio of the maximum voltage in an entire driving cycle. ∆ ∆

The testing results of ∆*R* in PWM are shown in Figure 8b; as the duty cycle increased, ∆*R* decreased. The ∆*R* was as high as 6.1% when the duty cycle was at 50%, and the ∆*R* was reduced to 1.4% when the duty cycle was at 90%, which met the requirement for stable grayscales. However, the ink in a pixel reflowed when the duty cycle was larger than 90% and the pixel could be closed at this time [14,30]. Therefore, this situation was meaningless for the experiment. ∆ ∆ ∆ ∆ ∆ ∆

△ **Figure 8.** The pulse width modulation (PWM) driving waveform and its aperture ratio performance [14,30]. (**a**) The PWM driving waveform with different duty cycles. (**b**) Relationship between the duty cycle and ∆*R*. △

∆ ∆ ∆ In the contrast experiment of slope-driving waveforms, the maximum driving voltage was set to 30 V and the slope value range of driving waveforms was from 3 V/ms to 10 V/ms, as shown in Figure 9a, where *K* is the slope [17,31]. Furthermore, the relationship between *K* and ∆*R* is shown in Figure 9b, where the maximum value of ∆*R* was 2.2% when *K* was 3 V/ms; the minimum value of ∆*R* was 0.3% when *K* was 10 V/ms. ∆ ∆ ∆

∆ ∆ **Figure 9.** Slope-driving waveform and its aperture ratio performance [17,31]. (**a**) Slope-driving waveform with different *K* values. (**b**) Relationship between *K* and ∆*R*.

∆ ∆ ∆ ∆ ∆ ∆ In order to compare ∆*R* among three kinds of driving waveforms, the parameters of three driving waveforms were optimized to obtain the minimum value of ∆*R*. The minimum ∆*R* of the PWM

∆

∆

was 1.4% when the duty cycle was 90%, the minimum ∆*R* of the slope-driving waveforms was 0.3% when *K* was 10 V/ms, and the minimum ∆*R* of the exponential-function-driving waveform was 0.95 when τ was 2 ms. As shown in Figure 10, the PWM could cause a large grayscale oscillation but the slope-driving waveform and the exponential-function-driving waveform could solve the problem. As a result, more levels of the grayscale display could be achieved. ∆ *τ*

*τ* **Figure 10.** Aperture ratio response of different driving waveforms. (**a**) PWM with a duty cycle of 90% [14,30]. (**b**) Slope-driving waveform with *K* = 10 V/ms [17,31]. (**c**) Exponential function with τ = 2 ms.

#### *4.3. Driving Time of a Stable Grayscale*

∆ ∆ In the PWM driving waveform, ∆*R* was 1.4% when the duty cycle was 90%, and its *ST* for stable grayscales was 19 s. Furthermore, ∆*R* values of other duty cycle PWM waveforms were greater than 3%; therefore, the PWM driving waveform with a 90% duty cycle was the best one. In the slope-driving waveform, the *ST* could reach the minimum value when *K* was 5 V/ms, as shown in Figure 11.

In the exponential-function-driving waveform, *ST* was the shortest when τ was 4 ms. As shown in Figure 12, the *ST* of the PWM driving waveform was 19 s. Furthermore, the *ST* of the slope-driving waveform could be shortened to 10.5 s. However, the *ST* of the exponential-function-driving waveform was the shortest with 8 s when τ was 4 ms. Therefore, the driving time for stable grayscales could be reduced by using the exponential-function-driving waveform, and the oscillation of the aperture ratio

**Figure 11.** The relationship between *ST* and the slope of the driving waveform.

*τ* **Figure 12.** Driving time for the stable grayscale display of different driving waveforms. (**a**) The PWM with a duty cycle of 90% [14,30]. (**b**) The slope-driving waveform with *K* = 5 V/ms [17,31]. (**c**) The exponential function with τ = 4 ms.

*τ*

### **5. Conclusions**

In order to reduce the oscillation of the aperture ratio and the driving time for stable grayscales in pixels, an exponential-function-driving waveform was proposed for improving the performance of EWDs. Then, the time constant of the exponential function was optimized by testing the driving process of the aperture ratio. The results showed that the grayscale oscillation could be controlled in a certain range by using the exponential-function-driving waveform when its time constant was 2 ms, which could be used to reduce the flicker of EWDs. In addition, the shortest driving time of the stable grayscale could be obtained by using the proposed driving waveform when its time constant was 4 ms, which could improve the static display performance of EWDs.

**Author Contributions:** Z.Y. and S.L. designed this project. Z.H. and Z.Y. carried out most of the experiments and data analysis. W.H. and L.W. performed part of the experiments and helped with discussions during manuscript preparation. F.C. and L.S. contributed to the data analysis and correction. C.Z. and G.Z. gave suggestions on project management and provided helpful discussions on the experimental results. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Guangdong Basic and Applied Basic Research Foundation (no. 2020A1515010420), the Key Research Platforms and Research Projects in Universities and Colleges of Guangdong Provincial Department of Education (no. 2018KQNCX334), the Zhongshan Innovative Research Team Program (no.<PHONE_NUMBER>97886), the Guangdong Government Funding (no. 2014A010103024), the Zhongshan Institute high-level talent scientific research startup fund project (no. 416YKQ04), the Project for Innovation Team of Guangdong University (no. 2018KCXTD033), and the National Key R&D Program of China (nos. 2018YFB0407100-02 and 2016YFB0401502).

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## **Driving Waveform Design of Electrophoretic Display Based on Optimized Particle Activation for a Rapid Response Speed**

**Wenyao He 1,2 , Zichuan Yi 1, \* , Shitao Shen 2 , Zhenyu Huang 2,3 , Linwei Liu 2,3 , Taiyuan Zhang 2,3 , Wei Li 2,3 , Li Wang 2,3 , Lingling Shui 1,2 , Chongfu Zhang 1 and Guofu Zhou 2,3**

Received: 3 April 2020; Accepted: 13 May 2020; Published: 14 May 2020

**Abstract:** Electrophoretic displays (EPDs) have excellent paper-like display features, but their response speed is as long as hundreds of milliseconds. This is particularly important when optimizing the driving waveform for improving the response speed. Hence, a driving waveform design based on the optimization of particle activation was proposed by analyzing the electrophoresis performance of particles in EPD pixels. The particle activation in the driving waveform was divided into two phases: the improving particle activity phase and the uniform reference grayscale phase. First, according to the motion characteristics of particles in improving the particle activity phase, the real-time EPD brightness value can be obtained by an optical testing device. Secondly, the derivative of the EPD brightness curve was used to obtain the inflection point, and the inflection point was used as the duration of improving particle activity phase. Thirdly, the brightness curve of the uniform reference grayscale phase was studied to set the driving duration for obtaining a white reference grayscale. Finally, a set of four-level grayscale driving waveform was designed and validated in a commercial E-ink EPD. The experimental results showed that the proposed driving waveform can cause a reduction by 180 ms in improving particle activity phase and 120 ms in uniform reference grayscale phase effectively, and a unified reference grayscale can be achieved in uniform reference grayscale phase at the same time.

**Keywords:** electrophoretic display; driving waveform; particle activation; response speed; reference grayscale

#### **1. Introduction**

Electrophoretic display (EPD) technology has been a research topic of interest for many years due to its wide market potential [1]. As a paper-like display technology, EPDs have the advantages of paper-like display effect, ultra-low power consumption, and being readable under bright light [2,3]. In recent years, EPDs have been widely used in e-books, electronic labels, and smart watches, amongst others [4,5]. The grayscale display of an EPD depends on the distribution of black and white particles in a microcapsule, which can be driven by voltage timing applied on the pixel, and the voltage timing is called the driving waveform. As a core part of EPDs, the length of the driving waveform can affect

the response speed of EPDs directly. Therefore, it is of great significance to improve the response speed and reduce visibility of the ghost image of EPDs by optimizing the driving waveform design [6].

Currently, the driving waveform is divided into three phases: erase original image phase, particle activation phase, and new image phase [7]. In driving processes, the photoelectric properties of the microcapsule system are nonlinear, and it is difficult to form a grayscale display accurately [8]. A lot of time is required to unify the spatial position of particles for driving to a target grayscale, and this process takes hundreds of milliseconds, or even one second [9]. The erase original image phase can obtain a stable state which is in a white or black state. The new image phase is used for driving the EPD to a new grayscale [10]. When a particle has been kept at the same state for a long period, the mobility of charged particles becomes much lower than others. The particle activity can be improved by driving the panel several times between two optical extremes (black/white extremes states) in the particle activation phase [11,12]. In EPDs, the distribution of individual black or white particles is random, so it is necessary to find a relatively stable grayscale as a reference grayscale. The white grayscale is usually used as the reference grayscale, and the display of other grayscale are obtained by using the white grayscale as the driving start point. This driving mode has been used up to now, and plays an important role in EPD products [13]. However, the particle activation phase is longer than the other two phases and has a significant impact on the response speed of EPDs. In order to optimize the activation phase, the particle activation can be optimized by a high-frequency voltage mode, but it is difficult to obtain a stable reference grayscale and the driving duration can reach 960 ms [14]. Some scholars have removed the particle activation phase and added a response latency to eliminate the original image, but the reference grayscale uniformity cannot be obtained, resulting in ghosting after writing new images many times [15]. At the same time, some short waveforms have been proposed, which were divided into three phases: zero voltage bias phase, high-frequency activation phase, and driving phase [16,17], but with reduced display quality of EPDs [18,19].

By analyzing the electrophoresis performance of particles, a driving waveform design of EPDs based on optimized particle activation phase for a rapid response speed was proposed in this study. The activation phase of the driving waveform was divided into the improving particle activity phase and the uniform reference grayscale phase. In one phase, the derivative of the EPD brightness curve was used to obtain the inflection point, which was used as the duration of improving particle activity phase. In the other phase, the brightness curve of the uniform reference grayscale phase was studied to set the driving duration for obtaining a white reference grayscale. Currently, the designed waveforms have been validated in commercial E-ink EPDs. This can shorten the driving duration, improve the response speed, and reduce visibility of the ghost image effectively.

#### **2. System Design Principle**

#### *2.1. Display Principle*

The motion and distribution of electrophoretic particles in microcapsules is very complex [20]. The trajectories of charged particles interfere with each other, and the attraction and repulsion among particles exist at the same time [21]. During a grayscale display process in EPDs, the spatial position of the particles contained in the microcapsule determines the grayscale value in a pixel. The positively charged black particles can move toward the common electrode by the force of the electric field when a positive voltage is applied to the pixel electrode, and the negatively charged white particles can move toward the pixel electrode such that the display observed by the human eye is black, as shown in Figure 1 [22]. When all of the black particles are driven to the common electrode, the state is referred to as the black extreme state. The white particles move to the common electrode when a negative voltage is applied to the pixel electrode, and the display observed by the human eye is white [23]. When all of white particles have been driven to the common electrode, the state is referred to as the white extreme state. The voltage sequence applied on pixels is called the driving waveform, and its quality directly

determines the display effect of EPDs. The internal electrophoretic particles cannot be displaced when the electric field is not applied to the pixel, which is referred to as bistability EPDs [24].

**Figure 1.** Schematic of an electrophoretic display (EPD) structure. The bottom is the pixel electrode, the middle is the microcapsule which includes a neutral electrophoresis suspension and white and black electrophoretic particles, while the top is the common electrode. The spatial position of particles cannot be changed after the removal of the pixel electrode voltage, which is referred to as bistability.

With the driving of the electric field, the charged particles are subjected to electric field forces as Equation (1):

$$F\_c = q \times E \tag{1}$$

where *Fc* is an electric field force, *q* is the charge of a particle, and *E* is the electric field intensity. The particle motion is hampered by Stokes forces when particles are driven in the liquid, and the expression is shown in Equation (2):

$$Fd = 6\pi\mu\nu r\tag{2}$$

6π μ where *Fd* is Stokes force, µ is liquid viscosity coefficient, *v* is the motion relative rate between particles and fluids, and *r* is sphere particle diameter. In addition, the number of charges which are carried by a particle is 50–100 when the particle radius is within 1 µm. The materials in microcapsules include insulating oil, electrophoretic particles, and density balancing agent [25]. The parameters related to electrophoretic phenomena are particles mass and zeta potential, dielectric properties, viscosity, and electric field strength of the insulating oil. The particles can be driven and are in an accelerated motion state when the electric field force is greater than the Stokes force, and the combined force is shown in Equation (3):

$$F = Fc - Fd = m\frac{dv}{dt} \tag{3}$$

where *m* is the mass of a particle and *dv dt* is the acceleration. The differential equation of Equation (3) is shown as Equation (4) [26]:

$$vi = \frac{qE}{6\pi\mu V} [1 \pm \exp(-\frac{6\pi\mu V}{m}t)] \tag{4}$$

where *vi* is the velocity of a particle, which is proportional to the electric field strength. The particle's motion distance can be obtained by Equation (5):

6

π

6

π

$$s = v i \times t \tag{5}$$

where *t* is the particle's driving time and *s* is the particle's motion distance, which can be reflected by the change in EPD reflectivity. According to the CIELab (International Committee on Illuminate Lab color space) standard, the relationship between brightness and reflectivity can be calculated as Equation (6):

$$L^\* = 116 \times (\sqrt[3]{\frac{R}{R0}}) - 16\tag{6}$$

where *R* is the reflectivity of an EPD, *R*0 is the reference standard of 100% reflectivity, and *L* ∗ is the brightness of the EPD. The brightness value error of EPDs are mainly caused by the ghost image [27], as shown in Equation (7) [28]: 0 \*

3 0 116 ( ) 16

\*

$$
\Delta L^\*\_{\text{GS}(n)} = L^\*\_{\text{GS}(n), \text{Max}} - L^\*\_{\text{GS}(n), \text{Min}} \tag{7}
$$

where ∆*L* ∗ *GS*(*n*) is the ghost value, *L* ∗ *GS*(*n*),*Max* is the maximum brightness value of EPDs, *L* ∗ *GS*(*n*),*Min* is the minimum brightness value of EPDs, and *n* is the grayscale level. The uniformity of the grayscale needs to be detected when the image is refreshed. By using the gray differential statistics, a grayscale image is expressed as a function *H*(*x*, *y*), and (*x*, *y*) is a point in the image. (*x* + ∆*x*, *y* + ∆*y*) is the adjacent point of (*x*,*y*), and the gray difference between the two points is shown as Equation (8): \* ( ) \* ( ), \* ( ), (, ) (, ) (, ) (, )

$$H\_{\Delta}(\mathbf{x}, y) = H(\mathbf{x}, y) - H(\mathbf{x} + \Delta \mathbf{x}, y + \Delta y) \tag{8}$$

where *H*∆ is the grayscale difference. The probability of getting each grayscale differential is *p*(*i*). Equation (9) is used to calculate the texture feature value entropy *e* in a grayscale image, and texture is a phenomenon of nonuniform grayscale display in an EPD. The nonuniformity of the texture in the grayscale image is reflected, and the smaller the value, the more even the texture in the grayscale image, where the expression is shown in Equation (9): ( )

$$e = -\sum\_{i=0}^{n} p(i) \log\_2[p(i)]\tag{9}$$

#### *2.2. Design Principles for Driving Waveforms*

The characteristics of conventional driving waveform are shown in Figure 2. It is usually divided into three phases: erase the image, activation phase, and new image phase. The driving durations of three phases are 240, 480, and 240 ms, respectively.

**Figure 2.** A typical EPD conventional driving waveform contains three phases for image updating. The T1 phase is used as improving particle activity phase and the T2 phase is used as uniform reference grayscale phase in the activation phase. The image in T1 is erased in T2.

In the original image, the particle spatial position in each pixel is different. Hence, there are different grayscale values in each pixel when the driving voltage is the same as each other. It's easy to form a ghost image, and the EPD can be driven to a uniform optical extremes states (black or white extremes states) for eliminating ghost images, which is called as the erase the image phase.

In addition, the longer a pixel remains in the same state, the lower the mobility of charged particles, which can hinder the driving of a new grayscale in EPDs. By driving the display several times between two optical extremes, it can improve the activity of particles and further eliminate ghosts, and this phase is called as particle activation phase. In this study, the particle activation phase was divided into two phases: improving particle activity phase and uniform reference grayscale phase (white extreme state). The main function of the improving particle activity phase is to increase particle activity, which can improve the particle driving speed. Then, the main function of the uniform reference grayscale phase is to unify a reference grayscale, so as to ensure that particles can drive to a same spatial position form different initial grayscale before new image phase.

In the new image phase, the target grayscale is produced in the end of pulse sequence. Different driving voltages with different driving durations are applied to different pixels for driving different grayscale. These three phases are combined into a complete driving waveform, and the n-level grayscale requires n2 driving waveforms, then multilevel grayscale driving waveforms are combined into a lookup table [29]. In the display process, the driving waveform can be called by the driver system according to different initial grayscale and target grayscale.

#### **3. Design of the Activation Phase in Driving Waveforms**

The particle motion characteristics in the improving particle activity phase were studied by us according to the change of display brightness value. The inflection point of particles brightness was obtained by solving the first derivative of the brightness curve, which was the duration of the improving particle activity phase. The driving duration for the uniform reference grayscale phase was then studied to shorten the driving waveform.

#### *3.1. Response Time Characteristics of the Improving Particle Activity Phase*

The brightness changes in improving particle activity phase of driving waveforms for a four-level grayscale were measured, and black (B), dark gray (DG), light gray (LG), and white (W) were set as the initial grayscale, as shown in Figure 3.

**Figure 3.** Brightness change curve of the improving particle activity phase at different initial grayscale. (**a**) The brightness curve of the T1. (**b**) The driving waveform used in measurements.

The initial brightness values of the four different initial grayscale are not the same, but the brightness values can be closed together after the image erasure phase in the driving waveform (the phase before T1). Hence, when the measuring area is T1 phase, the brightness value is consistent. The motion speed of particles is directly proportional to the change speed of the display brightness value. The motion of particles is shown as the brightness change of EPDs. In Figure 3a, it can be seen

that the brightness value decreases gradually, and the speed of the decrease rate increased and then decreased, so the motion speed of particles was increased and then decreased. In order to calculate the change of particles motion speed, the first order derivative was carried out for each curve, as shown in Figure 4.

**Figure 4.** First order derivative curve of brightness value in improving particle activity phase. "B", "DG", "LG", and "W" indicate different initial grayscale in the driving waveform.

As can be seen, the change rate of the EPD brightness was the highest when the time was 40–60 ms, when the particle motion had a highest speed. Thus, the particle activity was highest when the driving duration of T1 was 40–60 ms, which was conducive for driving effect in the next phase.

#### *3.2. Response Time Characteristics of the Uniform Reference Grayscale Phase*

The brightness change value of T2 was measured when the white grayscale was set as the initial grayscale. As shown in Figure 5, the driving duration of T1 was 40, 45, 50, 55, and 60 ms, respectively.

**Figure 5.** The influence of T1 timing on T2. (**a**) The brightness curve of T2. (**b**) The driving waveform used in the measurement.

As shown in Figure 5a, the time required for reaching the reference grayscale is 120 ms when T1 is 40, 45, 50, 55, and 60 ms. In the conventional driving waveform, the time required for reaching the reference grayscale is 220 ms. The change in brightness value of T2 is shown in Table 1.

**Table 1.** Change value of EPD brightness in T2.

The initial brightness of the EPD was more than 30 nits, when the T1 was 40, 45, 50, and 55 ms respectively, which showed that the EPD cannot reach optical extremes (black or white states) when the driving duration of 40, 45, 50, and 55 ms was applied continuously in T1, and it was not conducive to the particle driving in the next phase [30]. Therefore, 40, 45, 50, and 55 ms were not suitable for setting as the duration of T1. The driving duration to stable reference grayscale was 120 ms when T1 was 60 ms, and the driving duration to a stable reference grayscale was 220 ms when T1 was 240 ms in the conventional driving waveform, which showed that it was easier to obtain a stable reference grayscale with the uniform reference grayscale phase than the conventional driving waveform. The curve of brightness when T1 was 60 ms and the conventional driving waveform are shown in Figure 6.

**Figure 6.** Brightness curves at different initial grayscale. (**a**) The brightness curve of T2. (**b**) The driving waveform used in this measurement.

#### *3.3. Four-Level Grayscale Driving Waveform Design*

In this paper, a four-level grayscale driving waveform was taken as an example to test the performance of the driving waveform. The proposed driving waveform was divided into three phases. The first phase was used for erasing the original image. The negative voltage duration of 240, 80, 40, and 0 ms were used to drive EPDs continuously when the initial grayscale was "B", "DG", "LG", and "W", respectively. The grayscale of the original image was driven to white. The second phase was the particle activation phase. A positive voltage of 60 ms was adopted to drive the particle for getting an activation state, and a negative voltage duration of 120 ms was adopted to drive the particle to form a unified reference grayscale according to the driving waveform design of the activation phase. The third phase was used to display a new grayscale. The positive voltage duration of 240, 80, 40, and 0 ms were used to obtain target grayscale of "B", "DG", "LG", and "W", respectively, and the uniform white reference grayscale was driven to target grayscale, as shown in Figure 7.

**Figure 7.** A four-level grayscale driving waveform set. X is displayed as an original grayscale, and Y can be displayed when the EPD has been driven by the driving waveform.

### **4. Experimental Results and Discussion**

### *4.1. Testing System*

Microcapsule EPDs (ED060SC7, 6.0 inch, screen resolution is 600 × 800) produced by E-ink (Holding Inc., Hsinchu, Taiwan) were introduced for the experiments in this study. The experimental equipment comprised mainly into two parts: the driving waveform editing system and the brightness data acquisition system. A driving waveform design can be completed by the computer software LabVIEW (LabVIEW10.0.1f3, National Instruments, Austin, TX, USA). The brightness data acquisition system was composed of a driving power supply, a closed lab case, two light sources, a camera, and a temperature controller, as shown in Figure 8. The details of the EPD and the temperature controller are shown in Figure 9.

**Figure 8.** Optical testing device for EPDs. Camera was ADIMEC-1600m. Light sources were Brilliantline 12V 20W 36D Halogen. Temperature controller was Julabo FP25-ME. The power supply was an Agilent 3161A three-way output power supply.

**Figure 9.** The details of the EPD and the temperature controller. Temperature controller was Julabo FP25-ME.

A closed lab case was designed to prevent the interference from external light and ensure uniform lighting across the EPD surface. Two light sources were used as the external light source for the data acquisition system. In a confined space, the light environment provided by internal light sources was relatively stable, which provided good comparability for testing the driving effect of driving waveforms. In addition, the electrophoretic motion of particles in an EPD system is easily affected by temperature [31,32], so the experiment temperature was set at 25 ◦C.

The data acquisition system can test the brightness value of EPDs. Firstly, the data acquisition system is initialized, camera parameters are set, and the data acquisition system is calibrated effectively. Then, the system is idled for awaiting calibration results, and the waveform binary file is loaded into the driving system. The system can measure the brightness automatically and export the measurement data. The flow chart of data acquisition is shown in Figure 10.

**Figure 10.** The flow chart of data acquisition. Calibration includes the effective number of measurement area blocks, the international white and black reference grayscale reflectance. The measurement mode includes single measurement and multiple measurement.

LabVIEW, a software development platform of NI, was applied as a waveform editing system, and the driving waveform can be edited by G language of graphical programming. The waveform editing interface is shown in Figure 11 The designed driving waveform can be converted into a binary file and downloaded directly to the driver circuit.

− **Figure 11.** Waveform editing interface. A black grid indicates that a 20 ms positive voltage of +15 V is applied to the pixel electrode, a white grid indicates that a 20 ms negative voltage of −15 V is applied to the pixel electrode, and the rest states are 0 V. −

### *4.2. Timing Comparison of Driving Waveforms*

In different initial grayscale, it only takes 120 ms from the uniform reference grayscale to the white reference grayscale, which is 100 ms less than the conventional driving waveform, whose improving particle activity phase is 60 ms. The activation phase waveform of the proposed driving waveform and the conventional driving waveform is shown in Figure 12.

**Figure 12.** Driving timing comparison of activation phases in driving waveforms, and each vertical line represents 20 ms. In the proposed waveform, T1 is 60 ms and T2 is 120 ms. In the conventional waveform, T1 is 240 ms and T2 is 240 ms.

It can be seen that the activation phase in the proposed driving waveform was shortened by 180 ms, and the uniform reference grayscale phase was shortened by 120 ms. The overall proposed driving waveform was shortened by 300 ms compared to the conventional driving waveform.

#### *4.3. Performance Testing*

The conventional driving waveform and the proposed driving waveform were used to drive EPDs to the white state. The results show that the proposed driving waveform can increase the white grayscale by 2.7, as shown in Figure 13.

**Figure 13.** Comparison of the white reference grayscale. (**a**) An EPD was driven to white grayscale by the conventional driving waveform. (**b**) An EPD was driven to white grayscale with the proposed driving waveform.

Then, the proposed driving waveform was used to verify the image quality through several experiments. Firstly, a picture "E" was loaded in an EPD, and the proposed driving waveform and the conventional driving waveform were each used to drive it to the white grayscale, so as to explore visibility of the ghost image of each driving waveform, as shown in Figure 14.

**Figure 14.** Visibility of the ghost image comparison between the proposed driving waveform and the conventional driving waveform. (**a**) Original image. (**b**) Driving effects of the proposed driving waveform. (**c**) Driving effects of the conventional waveform.

Figure 14a is an original image with a white background and a black font. When it was driven to full white by the proposed driving waveform, the background brightness value of the image was 64.9 nits, and the shadow brightness value was 62.5 nits, so the ghost image brightness was 2.4 nits, as shown in Figure 14b. When it was refreshed to full white by the conventional driving waveform, the background brightness value of the image was 64.5 nits and the shadow brightness value was

58.7 nits, so the ghost image brightness was 5.8 nits, as shown in Figure 14c. Hence, the proposed driving waveform can reduce visibility of the ghost image by 57%.

The uniformity of the grayscale was analyzed by calculating the change rate of entropy value and the gray value. As shown in Table 2, the proposed driving waveform was used to an EPD, and it can be driven the original image to full white, and the change rates of the entropy value and the gray value were −6.3% and −79.7%, respectively. Then, the conventional waveform was used to test related data, and the change rates of entropy value and gray value were −5.78% and −79.32% respectively. Hence, the proposed driving waveform can reduce the image grayscale texture by 0.52% and improve the image grayscale uniformity by 0.38%. Hence, the proposed driving waveform can optimize the activation phase without affecting the image grayscale quality and reduce the driving duration of 300 ms. − − − −

**Table 2.** The change of entropy and gray value.

In addition, the conventional driving waveform has serious flicker when updating an image, especially in the refresh process of B-W. There are three phases in this process: In the erase the image phase, the original image is erased from black to full white. In the particle activation phase, the image needs to be driven to full black and then to full white. In the new image phase, the image is erased from white to full black. The human eye can feel a flicker due to the high contrast switch between black and white, as shown in Figure 15a. However, the proposed driving waveform cannot drive the EPD to full black in the activation phase, so the switching intensity of EPDs can be decreased, resulting in the decrease of the flicker, as shown in Figure 15b.

(**a**)

**Figure 15.** *Cont.*

(**b**)

**Figure 15.** The change curve of EPD brightness. (**a**) When the EPD was driven by the conventional driving waveform. (**b**) When the EPD was driven by the proposed driving waveform.

The extreme values of the brightness curve in the activation phase were 66.4, 18.1, and 67.8 nits, respectively, when the EPD was driven by the conventional waveform, so flickers with the intensity of 48.3 and 49.6 nits were respectively formed. When the EPD was driven by the proposed driving waveform, the extreme values of the brightness curve in the activation phase was 66.9, 32.5, and 69.9 nits, respectively, so flickers with the intensity of 34.4 and 37.4 nits were respectively formed. Therefore, the proposed driving waveform can reduce the flicker intensity by 28.8% and 24.6%, and the overall flicker intensity by 26.7%, as shown in Table 3.

**Table 3.** The change in flicker intensity.

#### **5. Conclusions**

In this study, a fast response driving waveform for EPDs based on optimized activation phase was proposed by analyzing the characteristics of EPDs. The duration of the driving waveform can be effectively shortened by 300 ms compared to the conventional driving waveform, and the reference white grayscale can be increased by 2.7 at the same time. In addition, it can reduce visibility of the ghost image by 57%, which can improve display quality, and the flicker intensity can be reduced by 26.7% for enhancing the visual experience of human eyes.

**Author Contributions:** Z.Y. and W.H. designed this project. W.H. and Z.Y. carried out most of the experiments and data analysis. Z.H. and S.S. performed part of the experiments and helped with discussions during manuscript preparation. L.L. and T.Z. contributed to the data analysis and correction. L.W., C.Z., W.L., L.S. and G.Z. gave suggestions on project management and provided helpful discussions on the experimental results. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Guangdong Basic and Applied Basic Research Foundation (no. 2020A1515010420), the Key Research Platforms and Research Projects in Universities and Colleges of Guangdong Provincial Department of Education (no. 2018KQNCX334), the Zhongshan Innovative Research Team Program (no.<PHONE_NUMBER>97886), the Zhongshan Institute high-level talent scientific research startup fund project (no. 416YKQ04), the Project for Innovation Team of Guangdong University (no. 2018KCXTD033), and the National Key R&D Program of China (no. 2018YFB0407100-02).

**Conflicts of Interest:** The authors declare no conflicts of interest.

### **References**

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Review* **High-Sensitivity in Dielectrophoresis Separations**

#### **Benjamin G. Hawkins \* , Nelson Lai and David S. Clague**

Biomedical Engineering Department, California Polytechnic State University, San Luis Obispo, CA 93407, USA<EMAIL_ADDRESS>(N.L<EMAIL_ADDRESS>(D.S.C.)

**\*** Correspondence<EMAIL_ADDRESS>Tel.: +1-805-756-6203

Received: 19 February 2020; Accepted: 26 March 2020; Published: 9 April 2020

**Abstract:** The applications of dielectrophoretic (DEP) techniques for the manipulation of cells in a label-free fashion within microfluidic systems continue to grow. However, a limited number of methods exist for making highly sensitive separations that can isolate subtle phenotypic differences within a population of cells. This paper explores efforts to leverage that most compelling aspect of DEP—an actuation force that depends on particle electrical properties—in the background of phenotypic variations in cell size. Several promising approaches, centering around the application of multiple electric fields with spatially mapped magnitude and/or frequencies, are expanding the capability of DEP cell separation.

**Keywords:** dielectrophoresis; microfluidics; cell separation

#### **1. Introduction**

Dielectrophoresis (DEP) is in the process of growing from a developmental technology to an integrated research tool. A testament to this is the number of research articles that continue to demonstrate novel device designs and separations. There are number of excellent recent review articles that establish a clear foundation in the theory [1], technologies [2,3], and applications [4–6]. With many preeminent researchers, an active research portfolio, and strong surveys of the field, there is little need at this time for a broad survey of DEP theory and applications; instead, this review focuses specifically on high-performance techniques that aim to achieve highly sensitive separations and overcome some of the traditional challenges found in DEP applications. For completeness and context, however, a short summary of the foundational physics and assumptions that are integrated in the oft-cited governing equations for DEP are presented here.

DEP is the transport of polarizable particles in response to an externally applied electric field. Actuation is achieved by application of a non-uniform electric field which simultaneously induces polarization and exerts force on the interface between two electrically dissimilar media. In general, the DEP force can be written in terms of Maxwell's Stress Tensor, ~ ~ *T*:

$$\vec{F}\_{\rm DEP} = \iiint\_{V} (\nabla \cdot \vec{\vec{T}})dV\tag{1}$$

$$
\vec{T} = \epsilon \vec{E} \vec{E} + \frac{1}{\mu} \vec{B} \vec{B} - \frac{1}{2} \left( \epsilon \vec{E} \cdot \vec{E} + \frac{1}{\mu} \vec{B} \cdot \vec{B} \right) \vec{I},\tag{2}
$$

where ~ *E* is the electric field, ~ *B* is the magnetic field, ~ *n* is the unit normal to a surface over which we are integrating to calculate the total force, *ǫ* is the material permittivity, *µ* is the material permeability, and ~ ~ *I* is the identity tensor. Equation (2) is an expression of the volumetric electromagnetic force on an object with non-uniform electrical properties. Though the DEP force can be generated by static or time-varying fields, the applications of interest here—those that achieve some form of separation that is sensitive to particle electrical properties—typically employ harmonic (sinusoidal) electric fields with

frequencies that allow a quasi-static approximation. The force observed is the result of time-averaging the DEP force equation [7]:

$$
\langle \vec{F}\_{\rm DEP} \rangle = \iiint\_{V} (\nabla \cdot \langle \vec{\vec{T}} \rangle)dV \tag{3}
$$

$$
\langle \vec{T} \rangle = \frac{1}{4} \Re(\varepsilon) \left( \vec{E} \vec{E}^\* + \vec{E}^\* \vec{E} - |\vec{E}|^2 \vec{I} \right),
\tag{4}
$$

where ~*E* ∗ is the complex conjugate of the electric field. An accurate model for the force on a particle would be based on the volume integral of divergences of the MST within the particle. Application of the divergence theorem and assumption of locally homogeneous electrical properties allows replacement of Equation (4) with:

$$
\langle \vec{F}\_{DEP} \rangle = \iint\_A (\langle \vec{T} \rangle \cdot \vec{n}) dA\_\prime \tag{5}
$$

where ~*n* is the unit vector normal to a surface at the interface between two media with homogeneous, but dissimilar, electrical properties and indicates that DEP force is generated at teh interfaces between materials. This simplification provides the basis for the multi-shell models employed by most researchers in the field.

#### *Approximations*

With the application of several approximations, the expression for ~*FDEP* can be simplified to the form presented in most applications in literature:

$$
\langle \vec{F}\_{\rm DEP} \rangle = \pi \epsilon\_m a^3 \Re \left( \vec{f}\_{\rm CM} \right) \nabla \left( \vec{E} \cdot \vec{E} \right), \tag{6}
$$

where ˜ *fCM* is the complex Clausius-Mossotti factor and *a* is the particle radius. ˜ *fCM* depends on the complex permittivity, *ǫ*˜ of material on either side of the interface under consideration:

$$f\_{CM} = \frac{\mathfrak{E}\_p - \mathfrak{E}\_m}{\mathfrak{E}\_p + 2\mathfrak{E}\_m} \tag{7}$$

$$
\vec{\epsilon} = \epsilon - j\frac{\sigma}{\omega'} \tag{8}
$$

where *ǫ* is the electrical permittivity, *σ* is the electrical conductivity, and *ω* is the frequency of the applied electric field in radians/second. ℜ( ˜ *fCM*) varies from −0.5 to 1.0; the point where ℜ( ˜ *fCM*) = 0 is termed the "cross-over frequency" and here notated as *fCM*,0. The approximations that lead to Equation (6) should be carefully examined for a given application:

#### **2. Sensitivity**

Here, we consider the effects of variability among the major components of a multi-shell model for a subjected to a DEP force. To examine the sensitivity of the magnitude of the DEP force to changes in cellular components, we consider the magnitude of the DEP force normalized by the squared field gradient, which we define as Γ*DEP*:

$$\Gamma\_{DEP} \equiv \left(\frac{\vec{F}\_{DEP}}{\nabla(\vec{E}\cdot\vec{E})}\right) = \pi a^3 \varepsilon\_m \Re\left(\tilde{f}\_{\mathbb{C}M}\right). \tag{9}$$

We consider a 4-shell, spherical cell with parameters reported by Rohani, et al. [9] and indicated in Table 1. This work is further discussed in Section 3.5. This model includes permittivity and conductivity for the cell membrane, cytoplasm, nuclear envelope, and nucleoplasm. While no definitive library exists for such parameters, a survey of available literature indicates that permittivity values vary slightly compared to conductivity values for each of these cellular compartments.

**Table 1.** Model parameters for DEP force sensitivity evaluation. These baseline values were used as a starting point and increased by 10% for permittivities and 100% for conductivities. Variation of cell radius increased the overall cell size, but did not change the thickness of any layer.

To determine the sensitivity, a MATLAB model was developed to calculate Γ*DEP* between 1 Hz and 1012 Hz for a given set of electrical model cell parameters. Values for Γ*DEP* were calculated for a 10% increase of permittivity and a 100% increase of conductivity for each compartment over 10 equally spaced intervals, for example, ∆*ε* or ∆*σ* . The average of these changes at each frequency was calculated to determine the sensitivity as a function of frequency for each parameter.

$$
\Delta F\_{DEP} = \frac{1}{N-1} \sum\_{j=1}^{N} |\Gamma\_{DEP,j} - \Gamma\_{DEP,j+1}| \tag{10}
$$

with summation over *j* representing the interval. The multishell model equation is a monotonic function for the values considered, so refinement of the intervals would yield no additional information. As shown by Rohani, et al. and others [10], media conductivity can be chosen to enhance the variation of the DEP force in response to changes in cell properties. Accordingly, MATLAB's optimization package was used to vary media conductivity between 1 µS/m and 0.2 S/m to maximize the variation of ∆*FDEP* in response to changes in a given compartment electrical parameter, independent of frequency. The optimized conductivities for each parameter are indicated in Table 2 and Figure 1.

The average sensitivity of the DEP force, ∆*FDEP*, is plotted as a function of frequency in Figure 1.

**Figure 1.** The average variation in the DEP force, ∆*FDEP*, that arises from variations in radius and other electrical parameters in a 4-shell model for HEK cells. Model parameters are given in Table 1.

**Table 2.** Optimized media conductivity values to maximize the variation in ∆*FDEP* in response to changes in cell model electrical properties.

The largest change in the DEP force is due to variation in cell radius, with other parameters contributing significantly less (by approximately a factor of 2) to the overall variation. The maximum average variation across all frequencies was considered as well (Figure 2) and shows similar results.

In order to achieve the optimized sensitivity, solutions of quite high or low conductivity are required, potentially harming or altering cell populations of interest, so the realistic limits for the relative contributions of cellular electrical properties to the overall DEP force remains significantly lower than that of cell size. This underscores the need for DEP techniques that aim to reduce the contribution of overall size variation.

Beyond the need for sensitive techniques that can reduce the influence of biological size variability, DEP techniques are needed that can distinguish between subtle variations in the magnitude of the force, rather than the cross-over frequency. For example, a model for viral vesicle inclusions in Hepatitis C infected hepatocytes is developed using a combination of multi-shell models and Maxwell's mixture theorem. As Hepatitis-C virus infection continues, vesicles containing viral bodies build up within the cytoplasm of hepatocytes. Isolation of these cells from a background of healthy hepatocytes could have significant impact on diagnosis and treatment. The results indicate that increasing viral vesicle load within the cytoplasm causes subtle variation in ℜ( ˜ *fCM*) in the pDEP frequency regime and relatively small variation in the cross-over frequency, *fCM*,0 (Figure 3) [11].

**Figure 2.** The maximum average variation in ∆*FDEP* across all frequencies that arises from variations in radius and other electrical parameters in a 4-shell model for HEK cells. Model parameters are given in Table 1.

**Figure 3.** A multi-shell model that incorporates the presence of increasing volume fraction of Hepatitus-C viral vesicles in an example ellipsoidal hepatocyte model. The primary variation that results is a change in the magnitude of pDEP at high frequencies.

In order to realize the potential of DEP to perform truly robust, repeatable, label-free separations, a collection of techniques and approaches must be developed that can successfully separate cells with subtle variations like those identified in Figure 3 independent of biological size variability.

#### **3. Approaches to Increasing Sensitivity**

In general, methods to improve the sensitivity of DEP separations introduce another force that acts in opposition to the primary actuating DEP force and also carries with it a size-dependence. In this way, if the opposing force is volume-dependent, the effects of particle size can largely be omitted. Here we consider the primary methods for generating an opposing force and characterize each method by whether it is a batch process or continuous flow, whether it is an equilibrium method or not, and whether it is a dynamic process or static. For clarity, batch processes are those that separate a population of particles once, and must be cleaned and reloaded to perform additional separation; continuous flow separations operate continuously and do not require "resetting". Equilibrium methods separate particles to a particular position where the DEP force is cancelled out by the opposing force; non-equilibrium methods have a net force on actuated particles, so they will continue to move in response. Dynamic separations are those that change the separation or actuation force during the separation process, static separations yield a single result for the separation of particles. The highest performance DEP separation will be one that achieves continuous, equilibrium separation in a dynamically adjustable manner.

#### *3.1. Gravity-Based Systems: DEP-FFF*

The first practical method to counteract the size-dependence of DEP was demonstrated by Wang, et al. [12], and used gravity to perform a combination of DEP and field flow fractionation (FFF). Subsequently, the process has been refined and separations of differentiated stem cells, [13], circulating tumor cells [14,15] and bacteria [16] have been demonstrated.

In a recent 'tour-de-force' in the application of DEP-FFF, Gascoyne and co-workers [14,17,18] demonstrated isolation of circulating tumor cells (CTCs) from blood, specifically preferentially capturing CTCs over peripheral blood mononuclear cells. This demonstration, overcoming one of the main confounding factors that reduce the purity of other separation methods, highlights the need for further development of DEP technologies. The DEP-FFF method used for capture and characterization in this suite of studies was based on the elution time in a DEP-FFF system; operating as a batch, non-equilibrium, dynamic method. In addition to CTC isolation and characterization, Waheed, et al. identified a "dielectric phenotype" factor (1/*Rφ*) that depends on the particle radius (*R*) and the degree of membrane folding (*φ*). This factor was shown to be the primary determining factor of the cell cross-over frequency, *fCM*,0 [14].

DEP-FFF suffers from a number of confounding factors, however, that limit its size-independent nature. The reliance on a pressure-driven flow field that varies significantly over the size of the typical particle leads to a drag induced torque and subsequent rotational lift force in certain flow regimes [19]. In addition to this lift effect, DEP-FFF methods lead to a equilibrium separation position that is a function of device depth, so orientation of the device to gravity is a factor and recovering separate streams from such a separation poses very challenging fabrication [20]. Separating multiple streams vertically within a microfabricated system requires multilayer device alignment, increasing design and manufacturing cost. For this reason, DEP-FFF is typically operated as a batch process, with elution time being the primary measurement.

#### *3.2. 2D Electrode Systems: Single-Field/Single-Frequency*

There are several methods that utilize DEP trapping effects to reduce the size-dependent nature of the force. In contrast to DEP-FFF, where the DEP force and fluid drag forces are orthogonal, these techniques typically involves a balance between nDEP forces and fluid drag in the same direction which reduces—but does not eliminate—the radius term. When these forces are balanced, the resulting DEP velocity is dependent on *a* 2 ,

$$i\vec{\mu}\_{DEP} = \frac{\varepsilon\_{\mathfrak{m}} a^2 \mathfrak{R}(\tilde{f}\_{CM})}{6\eta} \nabla(\vec{E} \cdot \vec{E}),\tag{11}$$

where *η* is the fluid viscosity. As a result, the approach to achieving size-independent separations using a single DEP force relies on leveraging the so-called "cross-over frequency" of DEP force. In this manner, a single field with a single frequency can be applied to a device, and particles experiencing a non-zero DEP force will be actuated, with those at the cross over frequency being unaffected. This approach has been used to separate cells from latex beads [21], bacteria from blood [22], and fluorescently-labeled cancer cells from blood [4]. Electrode configurations that are employed consist of interdigitated [23,24], castellated [25], ratchet [26] and trapezoidal [27] configurations.

There are a few limitations to this approach—(i) the dependence on the cross over frequency, (ii) the near-zero value of the DEP force near the cross over frequency, and (iii) the binary nature of the separation mechanism. In consideration of the former, many alterations to the electrical properties of particles of interest do lead to changes in the cross-over frequency, however there are many examples of more subtle changes that could be actuated via DEP that do not lead to significant changes in

cross-over frequency (see Figure 3). While the force at cross over is zero, and therefore the lack of actuation from DEP will be independent of size, the magnitude of the DEP force near the cross over frequency is small, and other size-dependent actuation forces will be potentially dominant for particles with ℜ( ˜ *fCM*) near the cross over frequency, again leading to a reduction in sensitivity and an increase in size dependence. Finally, the binary nature of this approach leads to a separation for particles that have a cross over frequency near the field frequency, and those that do not. There is no ability to separate a spectrum of particles as a function of cross-over frequency. These factors combined mean that single-field, single-frequency approaches lack sufficient resolving power to truly engage the potential of DEP for highly sensitive separations.

The concept of "iso-motive" DEP also rests within this category, with electrode configurations that generate a spatially uniform DEP force (hence "iso-motive") [28,29]. The approach counters one of the challenges to DEP—the non-uniform nature of the force—but all the above approaches lead to batch-mode separations, or continuous-flow separations that remain size-dependent.

Of particular interest for this review is the application of CMOS memory fabrication techniques to realize an addressable electrode grid in a microchannel [30]. The authors created an array of 32,768 individually addressable 11 µm-square electrodes. Bordering on hyperresolution digital microfluidics, the ability to apply an RF-frequency field to each local electrode leads to exceptionally promising platform for highly flexible separation design and testing. In contrast to many purpose-built DEP separation systems, this programmable array integrated circuit approach could be dynamically reconfigured to a wide range of separations, or tuned for a specific separation in-situ.

#### *3.3. 2D Electrode Systems: Multiple-Fields/Multiple-Frequencies*

The combination of multiple electric fields operating at the same or different frequencies holds the greatest promise for highly sensitive DEP separations. Multiple-field configurations can be split in to two major types: combined field DEP and travelling-wave DEP. Multiple, overlapping fields have been generated in planar electrode configurations and leveraged by many to accomplish various cell separations. In the combined-field separation area, work by Urdaneta and Smela showed separation of live and dead yeast cells, using different frequencies to preferentially attract each cell type to a different set of electrodes [31]. Similar techniques have been recently applied, taking advantage of multi-frequency signals (amplitude, frequency, or phase modulated) on a single electrode array to generate dissimilar DEP actuation forces on particles of interest to separate polystyrene microspheres based on size [32], algae cells based on lipid content [33], and MCF7 cancer cells from diluted blood [34]. Planar multifield configurations have also been extended to concentrate viruses, proteins, and bacteria [35].

In a thoughtful extension of DEP-FFF, Gascoyne and coworkers developed the "electrosmear" assay by spatially mapping the magnitude of the DEP force along the channel [36]. nDEP forces are generated on the bottom of a wide channel, and variations in the magnitude of the DEP force are accomplished by changing the local electric field magnitude or by changing the local electric field frequency. This, combined with the gravitational sedimentation force leads to cell adhesion to the interdigitated electrode array at locations where the nDEP force is overcome by gravity. This allows a spatial mapping of cellular DEP response to physical location on the electrode array. The electrosmear technique effectively minimizes size dependence, but because it is a temporal (batch) separation technique, it is relatively low throughput. Also, as with DEP-FFF, dependence on gravity limits the flexibility and versatility of the system.

Travelling-wave approaches leverage an electric field that is typically applied across 4 electrodes, each 90◦ out of phase with one another, leading to a field force that is based on the out of phase component of ˜ *fCM* [37,38]:

$$
\langle \vec{F}\_{\text{twDEP}} \rangle = -\frac{2\pi^2 a^2 \varepsilon\_m}{\lambda} \Re \left( f\_{\text{CM}} \right) \nabla \left( \vec{E} \cdot \vec{E} \right), \tag{12}
$$

where ℑ (· · ·) refers to the imaginary part and *λ* defines the wavelength of the twDEP field (i.e., distance between electrodes at each phase). twDEP systems have the advantage of reduced size dependence and can be applied perpendicular to the drag force and the electrode array, meaning that the twDEP field simultaneoulsy suspends and translates cells. The electrodes are actuated at a frequency corresponding to nDEP, suspending them above the array, and the difference in phase drives them transverse to the array. One of the initial applications was developed in theory by the Mezic group to demonstrate a multifield appraoch using twDEP to achieve separation [39]. twDEP methods have also been used by many and show promise as a method for size-independent cell separation [40–43]. In each case, the twDEP field is used to simultaneously levitate cells via nDEP and transport them transverse to the direction of a fluid flow field via the phase-dependent component of the twDEP force (proportional to ℑ( ˜ *fCM*). However, twDEP remains a non-equilibrium technique. In order to achieve predictable separation, careful tuning of force magnitude and flow velocity is required, or binary separation can be achieved as the equilibrium condition.

#### *3.4. 3D Electrode Systems*

Three-dimensional electrode systems refers to the use of electrodes on multiple sides of a microfluidic channel, rather than confining the electrode pattern to one side. This can mean an energized channel top with an interdigitated array on the bottom, interdigitated arrays embedded in the side of a microchannel, conductive posts, or electrodes that encompass the entire channel. Some 3D electrode systems also have incorporated multiple electric fields at different frequencies.

In a straightforward extension of the planar interdigitated electrode array, Lai, et al. used a solid conductive ITO sheet to close the top of the channel and energized an interdigitated array formed using a Ti/Al thin film on the bottom. The device successfully isolated RBCs from plasma in a serpentine channel [25]. Another example of top/bottom electrode configuration for continuous flow was demonstrated by Tada, et al. using multiple fields applied to an interdigitated array on the channel bottom with an indium-tin-oxide (ITO) coated glass top layer to generate electric field gradients spanning channel depth. The result was a device that trapped dead cells via pDEP on the channel bottom and concentrated live cells via opposing nDEP forces in the center of the channel [44]. Top-bottom electrode configurations generate gradients throughout channel depth, overcoming the challenge faced by planar configurations whose gradients do not reach sufficiently far in to the device to affect all particles. The distribution of field gradients allows for better control over their location as well, but at the cost of lower gradient magnitudes, meaning such devices require larger applied fields to achieve actuation. While top/bottom configurations offer better uniformity across channel depth, they require precise alignment if electrodes are patterned on both sides of the device, or suffer slightly non-uniform gradients across channel depth if one surface is a single electrode. Separations that leverage the top/bottom electrode configuration either rely on the cumulative effects of successive particle-gradient interactions or repulsion type interactions to manipulate particles. Applying a single field between electrodes leads to separations that depend on the equilibrium between nDEP and fluid drag forces, as shown in Equation (11). While features can be patterned to achieve better control over particle trajectories, making for more sensitive separations that can be performed in continuous flow, they remain strongly size-dependent.

Spanning the field from top to bottom of the channel has been accomplished with physical structures as well. Energized post array systems have been developed by Voldman and co-workers to achieve broad field distributions that were able to achieve single-cell trapping [45]. These traps were extruded metal posts that generated a quadrupolar DEP force field. Martinez-Duarte and co-workers have demonstrated a technique to easily generate arrays of conductive pillars by pyrolysis of SU-8 and used the resulting structures to filter bacterial cells [46,47]. This approach is highly efficient for fabrication and allows distribution of the electric field throughout the depth of the microchannel. These structures overcome the challenge of varying field magnitude across channel depth encountered in the top/bottom configurations. Conductive pillars allow control of field gradients uniformly across

channel depth without requiring precise alignment of top and bottom structures, and require lower field magnitudes. Like top/bottom electrode configurations, applying a single field leads to continuous-flow separations that rely on successive interactions or exclusion, and remain size dependent.

Electrodes have also been incorporated in to the sidewall of a channel, fashioned out of conductive PDMS [48], solder [49], and various metals [50,51]. The advantage of 3D- and sidewall electrode systems is that they distribute the electric field (and its gradient) throughout the channel. Rather than limited by proximity to a planar interdigitated electrode array on a single channel surface, placing potential and ground on opposite sides of the channel allows the DEP force to be applied further in to the fluid domain. Extending the application, electrodes on either sidewall have been developed to achieve lateral separation of a number of analytes [14,52,53]. By changing the distance between electrodes the field magnitude can be spatially mapped, and cell separation can be tuned even further, improving sensitivity and allowing for either batch or continuous separations. Without a countering, volume dependent force, however, the resulting separation is size-dependent.

A few researchers have demonstrated successful actuation of cells using 3D electrode structures and multiple field frequencies, successfully sorting particles transverse to the direction of flow and achieving a continuous flow, size-independent separation [54]. In this work, opposing nDEP and pDEP fields were applied to side-wall electrodes to separate HEK293 from N115 mouse neuroblastoma cells. The benefits of such a system are clear. The total DEP force exerted on a particle due to overlapping fields at different frequencies. Under ideal circumstances, the field applied at the sidewall exerts a force transverse to the direction of flow such that the equilibrium position of a single particle can be determined according to:

$$\sum \vec{F}\_{\rm DEP} = 2\pi \varepsilon\_m a^3 \Re \left( \vec{f}\_{\rm CM,1} \right) \nabla \left( \vec{E}\_{rms,1} \cdot \vec{E}\_{rms,1} \right) +$$

$$2\pi \varepsilon\_m a^3 \Re \left( \vec{f}\_{\rm CM,2} \right) \nabla \left( \vec{E}\_{rms,2} \cdot \vec{E}\_{rms,2} \right) = 0 \tag{13}$$

$$\frac{\nabla \left( \vec{E}\_{rms,1} \cdot \vec{E}\_{rms,1} \right)}{\nabla \left( \vec{E}\_{rms,2} \cdot \vec{E}\_{rms,2} \right)} = \frac{\Re \left( \tilde{f}\_{\text{CM},2} \right)}{\Re \left( \tilde{f}\_{\text{CM},1} \right)},\tag{14}$$

where the equilibrium lateral position of a particle subjected to fields with different frequency and magnitude occurs at the point where the ratio of squared field gradients equals the ratio of Clausius-Mossotti factors. This approach indicates four possible experimental tuning parameters—field magnitudes and field frequencies. While this approach achieves size-independence, application of the field across the channel width requires high field magnitudes or narrow channel dimensions. Furthermore, gradients between electrodes decay rapidly, meaning that a component of the applied DEP forces oppose fluid drag and potentially reintroduce a measure of size-dependence.

The furthest extension of the 3D electrode based dielectrophoresis concept was demonstrated by Kung, et al. and termed "tunnel" DEP. Researchers fabricated independent electrodes at the corners of a microchannel parallel to the direction of flow. Selective actuation of the electrodes at each corner allowed positioning of a stream of particles to an equilibrium position within the channel cross-section [55,56]. Like Wang, et al. this size-independent separation offers advantages in the form of tunability and continuous flow separation; additionally, this approach offers a second dimension of spatial control, in theory allowing the positioning of particles within the channel cross section based on DEP responses to multiple field frequencies and magnitudes. In order to achieve this level of control, however, complicated fabrication procedures must be applied and channel dimension must remain small to maintain field gradient magnitudes.

#### *3.5. Media Conductivity*

In addition to cell electrical properties, the DEP force depends on the properties of the surrounding media. Throughout it development, researchers have chosen media conductivity to allow for larger DEP force magnitudes and potential separations. Swami and co-workers have demonstrated a number of sensitive separations, isolating cells with mitochondrial structure variations [9], extracellular vesicles from pancreatic tumor cells based on invasiveness [57], and bacterial (*C*lostridium difficile) cells with altered envelope structure [58]. While the approach does not eliminate size dependence, as we show in Section 2, it can be leveraged to increase the relative contribution of particle electrical properties to variations in the resultant DEP force.

In another approach to minimize the dependence on size in cell discrimination and increase sensitivity, Voldman and coworkers developed "isodielectric focusing" which leverages the media dependence of ˜ *fCM* eliminating the majority of size dependence in a continuous flow separation [59,60]. Vahey, et al. established the isodielectric focusing technique by first creating a spatial gradient in the electrical conductivity of the media. Suspended cells then have a varying ˜ *fCM* across the gradient. Using an angled array of interdigitated electrodes to induce an nDEP force, they were able to deflect polystyrene beads and cells to a location where the nDEP force goes to 0. Particles introduced by a pressure driven flow are deflected transverse to the direction of flow—and transverse to the media conductivity gradient—by nDEP. As the local media conductivity changes, ˜ *fCM* changes and approaches 0. When ˜ *fCM* = 0, h~*FDEP*i = 0 and particles are transported by fluid flow. While this technique also minimizes size dependence and achieves continuous flow separation, it requires a conductivity gradient that is both stable and properly varies ℜ ˜ *fCM* to achieve separation. Such a stable flow and proper design of the conductivity gradient may not be achievable in all applications.

#### **4. Conclusions**

In this article, we have identified a number of approaches that variously combine 2D and 3D electrode structures, single or multiple electric field magnitudes, single or multiple electric field frequencies, and media variation strategies aimed at improving the sensitivity of label-free DEP separations to small variations in cell electrical properties. An analysis of the sensitivity of the DEP force indicates that particle size variation is potentially the largest factor, confounding efforts to isolate other variations. Therefore, we focus on efforts to increase sensitivity while also reducing or eliminating size dependence. The first counteracting force was gravity. DEP-FFF encompases these techniques and there is a deep body of work in the area. The technique has the potential to be sensitive and size-independent, but either operates in batch mode, limiting throughput, or requires significant manufacturing investment to develop a continuous flow implementation. 2D electrodes are often used to actuate DEP forces. For the most part, these techniques can be sensitive, and are easy to fabricate, but without an opposing force, are largely size dependent. 2D electrode structures where multiple field magnitudes and/or multiple field frequencies are applied overcome the size-dependent nature with a second DEP force. While eliminating the size-dependence, 2D structures offer limited control of the spatial distribution of electric field gradients. 3D electrode structures, on the other hand, distribute electric field gradients more uniformly, at the expense of slightly more involved fabrication, but without multiple fields, remain size-dependent. Combining 3D structures with multiple fields overcomes both the size-dependent nature of the DEP force as well as the challenge of controlling the spatial distribution of the electric field.

As we develop techniques that get closer and closer to isolating minute particle electrical properties, it is highly likely that our assumptions of homogeneity and isotropy will break down. The multi-shell model, in these cases, will likely not completely reflect or predict particle response. In order to more accurately model the DEP force, some have considered multipolar approximations, but the MST approach (Equation (2)), should be considered when attempting to model particle behavior and characterizing these highly sensitive separations.

#### **5. Future Directions**

The field of DEP cell separation continues to iterate on new device designs and configurations that take advantage of various chemical, hydrodynamic, and electrical properties of devices and analytes. The field is bustling with new proof of concept demonstrations that achieve challenging separations in useful ways. As microfabrication techniques become more and more accessible and see application to the microfluidic field in more useful ways, dielectrophoresis and electrokinetics will play a crucial role in new and novel separations that answer valuable research questions.

The biggest challenge to the field will be successfully bridging the gap between increasingly niche and narrowly focused demonstrations of a particular separation to robust and flexible separation tools that can be routinely applied in the biomedical and basic science labs. To date, DEP has not successfully bridged that gap, with DEP-FFF and the DEPTech 3DEP instrument being notable exceptions. The potential for truly label-free separations based solely on subtle variations in electrical phenotype in a robust, repeatable, and flexible platform remains a persistent challenge. Novel approaches that leverage spatially tunable electric field magnitudes and frequencies will be at the forefront of the next generation of DEP separation devices; tools and instruments that will enable groundbreaking work in the hands of a broader community of biomedical, biological, and basic science researchers.

**Author Contributions:** N.L. surveyed the literature and summarized relevant articles. D.S.C. provided valuable perspective and assisted with writing. B.G.H. completed the modeling analysis, compiled additional literature sources, and conceptualized and wrote the article. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

The following abbreviations are used in this manuscript:

### **References**

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

*Article*

## **Polarizability-Dependent Sorting of Microparticles Using Continuous-Flow Dielectrophoretic Chromatography with a Frequency Modulation Method**

#### **Jasper Giesler 1 , Georg R. Pesch 1,2, \* , Laura Weirauch 1 , Marc-Peter Schmidt 3 , Jorg Thöming 1,2 and Michael Baune 1**

Received: 7 November 2019; Accepted: 23 December 2019; Published: 28 December 2019

**Abstract:** The separation of microparticles with respect to different properties such as size and material is a research field of great interest. Dielectrophoresis, a phenomenon that is capable of addressing multiple particle properties at once, can be used to perform a chromatographic separation. However, the selectivity of current dielectrophoretic particle chromatography (DPC) techniques is limited. Here, we show a new approach for DPC based on differences in the dielectrophoretic mobilities and the crossover frequencies of polystyrene particles. Both differences are addressed by modulating the frequency of the electric field to generate positive and negative dielectrophoretic movement to achieve multiple trap-and-release cycles of the particles. A chromatographic separation of different particle sizes revealed the voltage dependency of this method. Additionally, we showed the frequency bandwidth influence on separation using one example. The DPC method developed was tested with model particles, but offers possibilities to separate a broad range of plastic and metal microparticles or cells and to overcome currently existing limitations in selectivity.

**Keywords:** dielectrophoresis (DEP); microparticles; polystyrene; chromatography; interdigitated electrodes; microfluidic; separation

#### **1. Introduction**

Separating microparticles according to specific properties such as size, material, and shape is a research area of great interest for instance in cell or biomolecule manipulation [1–5] and waste recovery [6,7]. To separate microparticles, field-flow fractionation [8], gel electrophoresis [9], and size-exclusion chromatography [10] are state-of-the-art approaches. A major drawback of these approaches is their low throughput or low selectivity for particle mixtures with similar separation properties (e.g., shape, density) below a particle size of 10 µm [11–13]. Dielectrophoresis (DEP), which is referred to as the movement of polarizable particles in an inhomogeneous electric field, offers an alternative tool to address a wide range of particles and at the same time is able to achieve relevant throughputs [14,15]. The dielectrophoretic force not only depends on one specific property of a particle, but on a variety of particle properties, such as size [16,17], permittivity, and electrical conductivity [1], allowing for multi-dimensional particle fractionation. Apart from

established DEP concepts such as field-flow fractionation [17,18], filtration [19], selective trapping (e.g., insulator-based dielectrophoresis) [20], dielectrophoretic particle chromatography (DPC) is a promising concept to achieve high throughput separation of particles. Since DPC was introduced by Washizu et al. [5], different approaches were done using selective trapping of particles [21,22], packed bed columns [23], or stepwise change of the frequency [24]. DEP chromatography proved to be very successful in isolating circulating breast tumor cells (CTCs) from blood [25] at a very low concentration. Such studies later led to the development of a clinical high throughput device to separate CTCs from blood samples [26,27]. Aldaeus et al. [28] developed an analytical model for a DPC device that was based on multiple trap and release cycles for fractionation. A related technique to manipulate micrometer sized particles is using traveling wave dielectrophoretic separators [29,30]. In these microfluidic devices, a 90◦ phase angle is present between adjacent electrodes, which changes the dielectrophoretic movement a particle experiences [31,32]. Such traveling wave systems offer versatile particle separation techniques, but are usually complex to fabricate and operate [30,33]. The other presented dielectrophoretic chromatography techniques have in common that they depend on strongly diverging polarizabilities (e.g., one type of particle showing positive dielectrophoresis, whereas the other particles show negative dielectrophoresis or exhibit no dielectrophoretic movement). This requirement limits the applicability when addressing particle mixtures with less pronounced differences in polarizability. Addressing binary (or more) mixtures in which there is heterogeneity in the two (or more) classes is even more complex, especially when the cross-over frequencies of the classes are so close that the heterogeneity causes an overlap (an example is the separation of cells according to only small differences in their expression).

Here, we introduce the novel concept of frequency modulated dielectrophoretic particle chromatography. The frequency of the applied field changes constantly to exploit small differences in the dielectrophoretic mobilities of target particles. In this technique, by switching the frequency, we switch between positive and negative dielectrophoretic movement of target particles to generate multiple trap-and-release cycles, which leads to a polarizability dependent chromatographic separation. In principle, this allows separating particles that even show only minute differences in their polarizability and to separate mixtures with heterogeneity in the classes. The simplicity of our approach allows for a simple fabrication and operation and could be easily scaled up by using different ways to introduce the electric field gradient (for example using a porous medium as demonstrated in our recent work [14]).

#### **2. Method**

#### *2.1. Theory*

In classic chromatographic processes (e.g., gas chromatography), mixtures are separated due to different interactions of the sample and stationary phase, leading to characteristic retention times for each class in the sample. In dielectrophoretic particle chromatography, the stationary phase is represented by the inhomogeneous electric field rising over interdigitated electrodes. The electrode chip forms the bottom of a microfluidic device, where a polydimethylsiloxane (PDMS) channel is used as the separation column. The microparticle suspension is injected into the flow chamber and further transported by a carrier flow. The electrodes are connected to an AC voltage source to generate a highly inhomogeneous electric field. This gives rise to a dielectrophoretic force on the particle caused by the action of the inhomogeneous field on the induced dipole (or multipole) of the particle. In the simple point-dipole approximation, the dielectrophoretic force **F**DEP can be expressed as:

$$\mathbf{F\_{DEP}} = \pi r\_\mathbf{p}^3 \varepsilon\_\mathbf{m} \text{Re}\left(\frac{\tilde{\varepsilon}\_\mathbf{p} - \tilde{\varepsilon}\_\mathbf{m}}{\tilde{\varepsilon}\_\mathbf{p} + 2\tilde{\varepsilon}\_\mathbf{m}}\right) \nabla |\mathbf{E}|^2,\tag{1}$$

with *r*p representing the particles radius, ∇|**E**| 2 the electric field gradient squared, and *ε*˜p the complex permittivity of the particles and the medium (*ε*˜m), respectively. The velocity due to dielectrophoresis, **v**DEP, in a stationary fluid can be calculated by dividing the dielectrophoretic force by the friction factor *f* ∗ :

$$\left|\mathbf{v\_{DEP}} = \mu\_{\text{DEP}} \nabla \left|\mathbf{E}\right|^2 = \frac{\pi r\_{\text{p}}^3 \varepsilon\_{\text{m}} \text{Re}\left(\frac{\varepsilon\_{\text{p}} - \varepsilon\_{\text{m}}}{\varepsilon\_{\text{p}} + 2\varepsilon\_{\text{m}}}\right) \nabla \left|\mathbf{E}\right|^2}{f^\*}. \tag{2}$$

Here, *µ*DEP is the dielectrophoretic mobility, which not only provides the direction of the movement of the microparticles, but incorporates the radius of the particles and fluid properties additionally. The direction of the DEP force can be determined by calculating the real part of the Clausius–Mossotti factor Re(*CM*):

$$\text{CM} = \frac{\mathfrak{E}\_{\text{P}} - \mathfrak{E}\_{\text{m}}}{\mathfrak{E}\_{\text{P}} + 2\mathfrak{E}\_{\text{m}}}.\tag{3}$$

The complex permittivity expands the permittivity *ε* of a material and incorporates the material's conductivity *σ* and the angular frequency *ω* of the electric field:

$$
\tilde{\varepsilon} = \varepsilon\_0 \varepsilon\_{\rm r} - i \frac{\sigma}{\omega}. \tag{4}
$$

For low frequencies, Re(*CM*) is dominated by the conductivity of the material. With increasing frequency, the permittivity becomes more important. When particles are less polarizable than the surrounding medium (Re(*CM*) < 0, negative DEP), they move against the electric field gradient and towards low field regions. On the contrary, more polarizable particles (Re(*CM*) > 0, positive DEP) are directed with the gradient towards field maxima. In the current setup, field maxima are located close to the edges of the interdigitated electrodes at the bottom, and local field minima can be found at the top of the channel. Depending on the polarization, particles are either attracted to the edges of the electrode (positive, pDEP) or to the top (negative, nDEP). Therefore, the movement direction will be strongly affected by the applied field's frequency due to the frequency dependence of Re(*CM*) (Equation (4)). Particles can become trapped in potential wells (field extrema) due to DEP and can adhere to the walls of the device when they reach them.

The conductivity of small insulating particles (such as the polystyrene particles that are used in this study as a model) is dominated by their surface conductance *K*S [34]:

$$
\sigma\_{\mathbf{p}} = \frac{2\mathbf{K\_S}}{r\_{\mathbf{p}}}.\tag{5}
$$

Usually, *K*S is assumed to be around 1 nS for polystyrene particles [35]. Equation (5) leads to a (with increasing particle diameter decreasing) net conductivity of polystyrene particles (1 µm < *d*P < 10 µm) of around 4 µS cm−1 to 40 µS cm−1 , which is higher than some low conductive DEP buffers. This allows for positive DEP manipulation at low frequencies of even electrically insulating particles, when they are smaller than a certain threshold diameter.

To evaluate the resolution of a chromatographic separation, *R*S can be calculated [28],

$$R\_s = \frac{\Delta t}{\frac{1}{2}(w\_1 + w\_2)},\tag{6}$$

with ∆*t* as the separation time between the maximum values (*I*max) of two peaks and *w*x, the width of the two residence time distributions. The width is defined as the distance in time between the half maximum values (FWHM).

#### *2.2. Device Operation*

The device proposed here, a microfluidic channel with interdigitated electrodes at the bottom of the channel (Figure 1b), uses periodic changes from pDEP to nDEP or vice versa to separate particles with respect to their polarizability. Since the polarizability of a particle directly depends on the frequency of the electric field, constant frequency changes (Equation (7)) can be used to manipulate the particles' position in the separator. To achieve a retardation, due to either nDEP or pDEP, particles are dragged out of the fast streamlines in the center of the channel to streamlines with low fluid velocity at the bottom or top. Then, when the frequency changes, the pDEP or nDEP effect is reversed, and particles are pushed back into the faster streamlines in the center of the channel. Depending on the strength of the interaction of a particle with the field (i.e., the absolute value of Equation (3)), particles with different polarizabilities experience different retardation. Unlike DEP field-flow fractionation, there is no particle equilibrium position. Here, the periodic change of frequency leads to a constant change of the particles position and, therefore, depending on the polarizability of a particle, to a different average velocity.

**Figure 1.** (**a**) Sketch of the DPC separation experiments. (**b**) Sketch of the DPC separation column. Meandering PDMS microchannel sealed by interdigitated electrodes on a glass chip. (**c**–**f**) Different possible outlet concentrations for DPC. (**c**) Without voltage, no retardation of the particles occurs, and both fractions elute at the same time. (**d**) When a voltage is applied and the frequency is fixed, the particles are trapped in the column due to DEP and will not exit the channel. If the frequency is modulated, a chromatographic separation occurs (**e**), which can be optimized by changing the frequencies and voltage (**f**).

In case a particle gets trapped in potential wells because of dielectrophoresis or adheres to the surface of the channel due to non-specific adsorption, a particle resuspension requires a force pointing away from the wall, which is in our case again DEP. Naturally, to reverse the trapping movement, particles trapped by pDEP now have to experience nDEP and vice versa (Figure 1a). Especially for particles trapped at the bottom of the channel, a resuspension via an external force becomes important, since no gravitational force contributes to their remobilization. Further, as the particles' diameter decreases, the gravitation force becomes less important and therefore may not be sufficient to resuspend small particles close to the ceiling of the channel. To achieve a retardation of the particles and consequently a chromatographic separation, it is in general not necessary to fixate particles at the bottom or ceiling. To generate an increase in retention time, particles are just required to be transported into regions of low fluid velocity, which are present at the bottom (transport via pDEP) or the ceiling (nDEP) of the channel. Apart from the approach taken here, which is to modulate the frequency to reverse the particle polarization and the DEP force vector's direction, in principle, it would also be possible to change the polarization by changing the medium's conductivity.