# Active coating of a water drop by an oil film using a MHz-frequency surface
acoustic wave

Avital Reizman  Department of Chemical Engineering, Technion Israel Institute
of Technology, Haifa, Israel.  Amihai Horesh  Institute of Agricultural
Engineering, Agricultural Research Organization, Volcani Center, Israel.  Lou
Kondic  Applied Mathematics, New Jersey Institute of Technology, NA, United
States.  Ofer Manor<EMAIL_ADDRESS>Department of Chemical Engineering,
Technion Israel Institute of Technology, Haifa, Israel.

###### Abstract

We employ a millimeter-scale piezoelectric acoustic actuator, which generates
MHz-frequency surface acoustic waves (SAWs) in a solid substrate, to actively
coat a drop of water by a macroscopic film of silicon oil as a paradigm for a
small scale and low power coating system. We build upon previous studies on
SAW induced dynamic wetting of a solid substrate, also known as the
acoustowetting phenomena, to actively drive a model low surface-energy liquid
– silicon oil – coat a model liquid object – a sessile drop of water. The oil
film spreads along the path of the propagating SAW and comes in contact with
the drop, which is placed in its path. The intensity of the SAW determines the
rate and the extent to which a macroscopically thick film of oil will climb
over the drop to partially or fully cover its surface. The dynamic wetting of
the drop by the oil film is governed by a balance between acoustic, capillary,
and gravitational contributions. Introducing a water drop as an object to be
coated indicates the opportunity to coat liquid phase objects by employing
SAWs and demonstrates that oil films which are actuated by SAWs may traverse
curved objects and liquid surfaces.

Figure 1: A side view illustration of the experiment, where (a) we place a
silicon oil film and a water drop atop a horizontal surface acoustic wave
(SAW) actuator, comprising a piezoelectric lithium niobate (LN) substrate
patterned with interdigitated electrodes (IDTs) and a SAW absorber (on the far
side of the actuator) to eliminate reflections. (b) The SAW, propagating in
the $x$ direction, generates spatiotemporal deformations in the solid surface
in the $z$ direction, where red (green) illustrates the deformations above
(below) the surface plane at rest, given at a specific time. (c) The
experimental snapshots present the dynamic wetting of the solid substrate and
the water drop by the oil film under SAW excitation (view from above).

##  I Introduction

Millimeter-scale piezoelectric acoustic actuators of MHz-frequency surface
acoustic waves (SAWs) have increased in popularity in previous years for
manipulating micro to nano-liter liquids and particulates therein.
(miansari2016acoustic, ; pothuri2019rapid, ; horesh2017enhanced, ;
horesh2020stabilizing, ) The actuators are piezoelectric substrates
specifically designed to generate SAWs upon the application of a sinusoidal
electrical signal, which supports electromechanical resonance in the
substrate. The piezoelectric effect in the substrate of the actuator linearly
transforms the electrical signal to a nanoscale oscillating mechanical
vibration of maximum amplitude near the surface of the devices – SAW.
(filipiak2021surface, ) SAW actuators are scalable in size, may be powered by
a pocket size source, and are devoid of moving parts, (liu2022acoustofluidic,
; zhang2021manipulation, ; zhang2021powerful, ; shilton2015rapid, ) and hence
are attractive for introducing low power and portable strategies for SAW
actuated unit operations. Lithium-niobate (LN) based
actuators,(white1965direct, ) known for their high pyroelectricity and
chemically inert surface, have been showing great promise for microfluidics
and small scale manufacturing. These actuators are well known to manipulate
and control millimeter to micrometer thick layers of liquid. In particular
they support the dynamic wetting (coating) of the actuator substrate by oil
(rezk2012unique, ; rezk2014double, ) or water solutions.
(altshuler2015spreading, ; altshuler2016free, ) However, using the actuators
for coating objects, the spreading of liquid films by the SAW must endure
geometrically structured objects. We demonstrate the application of a LN based
SAW actuator for the active coating – encapsulating – of a model liquid object
– a drop of water – by a macroscopic layer of a model coating liquid – silicon
oil – as a paradigm for using a SAW actuator for coating objects.

Coating a substrate, whether solid or liquid, is a fundamental process in the
manufacturing industry. It is an endemic process in the production of
automotive, electronic, medical and aerospace components alongside many
others, traversing the manufacturing of aeroplanes and satellites down to the
manufacturing of humble pens and pencils (fotovvati2019coating, ). Among the
coating techniques found in industry one may count physical vapor deposition
(hassan2018antimicrobial, ; abbas2019fabrication, ) in which the coating
material is evaporated from a solid or liquid source and then delivered as a
vapor onto a substrate, where it condenses; chemical vapor deposition
(mittal2021nanofabrication, ; hong2020chemical, ), where the coating of the
substrate is via a chemical surface reaction with a vapor phase;
electrodeposition (walsh2020electrodeposition, ;
szeptycka2016electrodeposition, ; pu2020electrodeposition, ), where electrical
potential is employed for the attraction of the coating materials in the form
of ions or particulates to a charged substrate or via an electrochemical
reaction at the surface of a charged substrate in contact with a precursor
fluid; Sol-gel coating (KLEIN198045, ), which is a wet-chemical process for
introducing a glassy or ceramic coating; spray coating (tejero2019beyond, ;
wang2021spray, ; WANG2010127, ; coatings1010017, ), where a fast-moving flow
of compressed air is steered into a stream of liquid coating and serves as a
vector for transporting the coating to the target surface; and dip coating
(salles2019electrochromic, ; singh2020functionalization, ; byrnes2017pipeline,
), where a coating liquid is put in direct contact with the target surface as
in the happy blade approach or by dipping the target surface in a reservoir of
a coating liquid. Dip coating as well as spray coating techniques are further
employed to coat substrates by multiple immiscible liquid films
(belden_multilayer_2017, ; derflinger_multilayer_2009, ;
grunlan_multilayer_2012, ). In particular, coating of one liquid film by
another is an intriguing problem when accounting for the dynamic and often
unstable nature of the interface between the two coating liquid films
(horiuchi_simultaneous_2015, ; larsson_nonuniformities_2021, ).

Lately, it was demonstrated that SAWs may be employed for precise and low
power coating of small surfaces by oil films as a paradigm for coating objects
of lateral length scales of millimeters to centimeters. (rezk2012unique, ;
rezk2014double, ) In particular, vibration in a substrate in the form of a
surface acoustic wave (SAW), undergoing frequencies comparable to the HF and
VHF radio frequency range, may invoke the continuous spreading of sub
micrometer to hundreds of micrometer thick films of a fully wetting silicon
oil along or opposite the path of the propagating SAW. Partially wetting water
films under similar excitation were also found to undergo similar coating
flows. (altshuler2015spreading, ; altshuler2016free, ) However, in the latter
case, capillary stresses had to be reduced to a level below that of the
acoustic stresses in the film to render dynamic wetting; otherwise capillary
stresses arrest the coating flow.

There are several mechanisms by which SAW actuates the dynamic wetting of
substrates by liquid films. (manor_dynamics_2015, ; morozov_vibration-
driven_2018, ) Briefly, A SAW in a solid substrate leaks ultrasonic waves of
the same frequency and of a wavelength $\lambda_{l}$ into the nearby fluid.
The ratio between $\lambda_{l}$ and the thickness of the film
(shiokawa_liquid_1989, ) determines the specific mechanism that governs film
dynamics. In previous studies on micron and tens of micron thick liquid films
and SAW frequency of $20$-$40$ MHz, (rezk2012unique, ; rezk2014double, ;
manor_dynamics_2015, ; morozov_vibration-driven_2018, ) the thicknesses of the
film were smaller than $\lambda_{l}$. The governing mechanism for the
actuation of film dynamics was found to be the Stokes drift
(Schlichting:1932p447, ; Rayleigh, ) of liquid mass due to the convection of
momentum in an acoustic boundary layer flow near the solid substrate.

We consider oil films that are hundreds of micron thick and a SAW frequency of
20 MHz. In this case, the thickness of the film is greater than the wavelength
of the acoustic leakage ($\lambda_{l}\approx 80~{}\mu$m). The dominant
acoustic streaming mechanism is Eckart Streaming. Flow is predominantly
generated by the attenuation of the SAW in the actuator (shiokawa_liquid_1989,
). The Attenuation of SAW spatially alters the intensity of the acoustic
leakage in the liquid and hence generates Reynolds stress variations, i.e.,
net body force therein. The Reynolds stress in the liquid film brings about
the spreading of the film on the surface of the actuator and hence the dynamic
wetting of the actuator along the path of the SAW.

The capability of a liquid film, actuated by a SAW, to dynamically wet a solid
substrate and to overcome a textured substrate or coat a solid or liquid
object atop the SAW actuator was not studied to date, albeit it was used for
SAW based PCR systems on a chip B412712A , where it appears that the coating
of small water drops by oil was governed by capillary effects. Here, we
consider the problem of using a SAW to actuate the coating of a liquid object
by a low surface energy coating. For this endeavor, we employ a model
experimental system in which we employ a SAW actuator to coat a water drop by
a macroscopic layer of silicon oil. The water drop is a model liquid obstacle,
which we place in the path of the silicon oil film. The film dynamically wets
the solid substrate under the action of the propagating SAW therein and
partially or fully climbs over the drop upon contact.

Our goal is to realize the physical conditions that support the active coating
of a water drop by a macroscopic layer of oil film. We briefly describe our
experimental procedure in Experiment, give our results alongside a dedicated
discussion in Results and Discussion, and summarize and conclude our work in
Summary and Conclusion.

Figure 2: Time-lapse of (side view) images, which portray the dynamic wetting
of a sessile drop (right) by a silicone oil film (left) under SAW intensities
of (a) SDA$\sim 4.0$ Å, where the oil film partially coat the drop, and (b)
SDA$\sim$ $9.3$ Å, where the oil film fully coat the drop. Initially (t=$0$
s), we show the moment of contact between oil and water; at following times,
we demonstrate the coating of the water drop by the oil film which spreads to
the right. The light exposure is different between the sections. Figure 3:
Time-lapse of (side view) images, which portray the dynamic wetting of a
sessile drop (right) by a silicone oil film (left) in the absence of an
acoustic wave. Initially (t=$0$ s), we show the moment of contact between oil
and water; at following times, we demonstrate the partial wetting of the water
drop by the oil film, where the system appears to obtain steady state at
$t=30$s.

##  II Experiment

We fabricated an actuator – a SAW device – by using photolithography to place
interdigiated electrodes (IDTs), comprising $5$ nm titanium as adhesion layer
and $1$ $\mu$m aluminum, atop a piezoelectric 128∘ y-cut lithium niobate
($\text{LiNbO}_{\text{3}}$) substrate. The actuator generates a $20$ MHz-
frequency Rayleigh type SAW in the solid substrate.

Fig 1 illustrates the use of a SAW actuator for coating a water drop: We
initially placed A $3.0$ $\pm$ $0.05$ $\mu$L sessile drop of deionized (DI)
water and a puddle of a 100 cSt viscous silicone oil (SIGMA-ALDRICH, Merck)
atop a SAW actuator. Upon the application of power to the actuator, the SAW of
a wavelength of $200~{}\mu$m propagates at a phase velocity of
(kushibiki1999accurate, ) 3880 m/s away from the electrodes near the upper
surface of the actuator (which faces the two liquids). Firstly encountering
the silicon oil film, the SAW leak ultrasonic waves of a wavelength of
approximately $\lambda_{l}\approx 80~{}\mu$m into the oil phase. The
ultrasonic waves generate Reynolds stress and Eckart streaming in the
$100-200~{}\mu$m thick oil film of a nominal dynamic viscosity of 100 cSt and
nominal surface tension of 20 mN/m at room temperature. The SAW actuates the
dynamic wetting of the substrate by the oil film toward the drop. As the
actuated oil film comes in contact with the sessile drop, which is pinned to
the solid substrate by capillary stresses (altshuler2015spreading, ), it
climbs over the drop to partially or fully coat its surface. The level to
which the oil film climbs over the drop is found dependent on the normal
surface displacement amplitude of the SAW (SDA). We give in Supporting
Information graphs which connect the SAW to the voltage, which we generate
using our signal generator (R&s SMB100A microwave signal generator) and apply
to an 5X amplifier (Model A10150, Tabor Electronics Ltd.) and then to the SAW
devices. Moreover, To capture the film dynamics, We used a side-view camera
(Data Physics; OCA 15Pro) and a top-view USB camera (Dino-Lite).

The SAW imposes comparable lateral and transverse harmonic displacement in
time and space in the LN substrate. The displacement amplitude is proportional
to the voltage, i.e., to the square root of the power applied to the actuator.
We measured the (normal) surface displacement amplitude (SDA) of the SAW at
the spatial region of interest on the LN substrate; specifically, we measured
the displacement at the initial location between the oil and water drop for
each experiment. For the measurement, we used a scanning laser Doppler
vibrometer (MSA-500, Polytech) for each input voltage level and verified that
the SAW is a propagating wave. To avoid the presence of a standing SAW on the
actuators, we placed a layer of wet paper (Kimberly-Clark Professional :
KIMWIPES Ex-L) at the far side of the actuators (opposite side to the IDTs) as
wave absorbers. Moreover, in a bare SAW device, the attenuation length of the
$20$ MHz-frequency SAW is approximately $1$ meter. This translates to
negligible attenuation on our device, which is a couple of centimeters long.
Under the oil film and water drop, the SAW should attenuate appreciably
however to lesser extent than the attenuation level of the SAW under half-
space of water or oil. In this case the attenuation length of the 20 MHz-
frequency SAW is approximately 1 millimeter. (doi:10.1063/1.1754894, ) Hence,
the actual position of the drop on the SAW device may introduce a change to
the height in which the oil film climbs atop the drop. To reduce variability
in the experiment, we kept the position of the drop and oil film on the SAW
device the same during our different experiments, i.e., 3 mm away from the
IDT.

Prior to each experiment, we rinsed the actuator under toluene, acetone,
2-propanol, ethanol (Bio-Lab Ltd.) for $20$ s and finally under HPLC water
(HPLC plus, Sigma-Aldrich). We then used Pogo pins (BC201403AD, Interconnect
Devices, INC.) to connect the IDTs on the actuator to a signal generator (R&S
SMB100A) and a signal amplifier (A10150, Tabor Electronics Ltd.). The SAW was
generated by imposing different levels of a continuous sinusoidal input
voltage at a fixed frequency of $20$ MHz. Moreover, initially, we examined the
rate of water evaporation from the drop in the absence of silicon oil by
monitoring the drop height over the time of the experiments which later on
included oil. The change in the drop height in these measurements was found
negligible. We then conducted a parametric study of the coating of water drops
by silicon oil atop the SAW actuator.

##  III Results and Discussion

We introduce representative time lapse images showing the partial and full
coating of a water drop by oil film in Fig 2. The figure shows a side view of
the experiment for two representative cases. Fig 2 (a) illustrates the partial
coating dynamics of a water drop by oil film for a SAW normal displacement
amplitude at the surface of the actuator (SDA) of $\sim$ $7.0$ $\pm$ 0.59 Å,
and Fig. 2 (b) illustrates the full coating dynamics for an SDA of $\sim$
$9.3$ $\pm$ $0.59$ Å. In both cases, we show the initially separated oil film
(left) and water drop (right), and then time laps of the climb of the
macroscopic oil film over the drop. The oil film partially coat the water drop
when actuated by SAW of the lower SDA value, leaving the upper part of the
drop devoid of a macroscopic oil film (although it may be coated by a
molecular layer of oil due to capillary stresses). The oil film fully coats
the water drop by a layer of a macroscopic thickness when actuated by a SAW of
the greater SDA value. The climb height of the oil over the drop is known to
be the result of acoustic, capillary, and gravitational stresses in the
therein. (horesh2019acoustogravitational, ) Corresponding movies of the
experiment are given in Supporting Information.

To evaluate the contribution of the SAW to the coating process, we further
give time lapse images of the interaction of the oil film and a water drop on
our actuator, but in the absence of SAW (no power is applied to the actuator)
in Fig 3. The figure demonstrates that in the absence of SAW, the oil slowly
and spontaneously spreads across the LN surface due to its low surface
tension. Once encountering the water drop, the macroscopic oil climbs to a
finite height, partially coating the drop. This is quantified in Fig 4, where
the oil film climbs over the drops in our experiment to $\psi$=$0.42$ $\pm$
$0.04$ of the drop heights of $h_{i}=1.05$ $\pm$ $0.02$ mm in our experiments.
The climb height in this case is associated with a balance between capillary
and gravitational stresses in the oil film;(xue2020marangoni, ) here
$\psi\equiv h_{\text{c}}/h_{\text{i}}$ represents the ratio between the
measured height to which the oil film climbs over the water drop,
$h_{\text{c}}$, and the height of the water drop prior to SAW excitation
$h_{\text{i}}$. The latter appears to remain the same throughout the
experiment. As a note, in our experiments, the volume of the drops is
$3.00\pm$0.05$~{}\mu$L and the height of the water drops is $h_{i}$= $0.88$
$\pm$ $0.02$ mm. The main reason for variations in drop heights between
different experiments is most likely the three phase contact angle hysteresis.
The hysteresis renders the height of a drop dependent on the specifics of
placing the latter on the actuator surface. (mittal_guide_2009, ) Increasing
the applied power to the SAW, leads to an increase in $\psi$. SAW induced
Reynolds stress in the oil film modifies the previously mentioned equilibrium
and supports a greater climb height of the oil film.
(horesh2019acoustogravitational, ) Above an SDA threshold of approximately
$\sim$ $8.0$ Å, we observe that the macroscopic oil film fully covers the drop
in most experiments.

Figure 4: SAW intensity (SDA) variations of the oil film height ($h_{c}$) to
drop height ($h_{i}$) ratio, $\psi\equiv h_{c}/h_{i}$, which indicates the
level of climb of the oil film over the drop, showing a approximately linear
trend. Note that for $\psi<1$, the oil does not reach the top of the drop, and
for $\psi>1$, the oil film extends over the top of the drop, fully coating the
latter; the line is a guide to the eye. The characteristic errors are:
$\psi=\pm$ $0.04$ and SDA = $\pm$ $0.73$ Å.  Figure 5: We show the time to
reach steady state ($\tau$) against the intensity of the SAW. From the moment
the oil film touches the drop to the moment the oil film attains a steady
state height for SDA$<\sim$ $8.0$ Å, or reaches the top of the drop for
SDA$>\sim$ $8.0$ Å. A decaying trend is observed. the line is a guide to the
eye. The characteristic errors are: $\tau=\pm$ $0.02$ s and SDA = $\pm$ $0.73$
Å.

To give an indication of the dynamics of the coating process, we show in Fig.
5 the influence of the SAW intensity (SDA) on the time, $\tau$, in which the
oil film climbs over the drop. We define $\tau$ as the time that passes from
the moment of contact between the oil film and the drop to the time in which
the oil film reaches a steady state height (when it does not reach the top of
the drop) or to the moment it reaches the full height of the drop. In
particular, a drop may be partially or fully coated by the oil film at time
$\tau$. The system reaches a steady state when the oil film partially coats
the water drop for approximately SDA$<8.0$ Å. The oil film fully coat the drop
for approximately SDA$>8.0$ Å.

In the figure, we demonstrate the slow climb of the oil film atop the drop in
the absence of the SAW (SDA=0) and the remarkable reduction of the value of
$\tau$ in the presence of the SAW (SDA$>0$). Moreover, in Fig. 6, we connect
$\tau$ and the steady state height of climb of the oil film, $\psi$. The
figure indicates a reciprocal connection between the two quantities. That is,
increasing the acoustic intensity (SDA) results in shorter time of climb to a
greater height of the drop.

Figure 6:  We show the time to reach steady state ($\tau$) against the ratio
between the climb height of oil film and the original height of the water
drop. Each point on the graph represents a different experiment at different
intensity of the SAW as follows (from left to right): $0.0$, $2.0$, $4.0$,
$4.0$, $6.0$, $4.0$, $8.0$, $6.0$, $6.0$, $9.5$, $8.0$, $9.3$, $8.0$ Å.
Relative height of oil climb, $\psi$, variations of the coating time, $\tau$,
indicating an inverse relationship, which is mediated through the magnitude of
the SAW intensity (SDA), where the line is a guide to the eye. The
characteristic errors are: $\psi=\pm 0.04$ and $\tau=\pm 0.02$ s.

##  IV Summary and Conclusion

Here we demonstrate the application of a millimeter size LN based acoustic
actuator, which generates a MHz-frequency SAW, to support the active coating
of a sessile water drop by a silicone oil film. The difference in the surface
energy of the two liquids results in different responses of the two liquids to
the SAW. The low surface energy oil dynamically wets the solid substrate and
the water drop. The high surface energy water drop keeps sessile. Hence the
oil and water system makes a well defined and ideal case to explore the SAW
induced dynamic wetting of a non planar object and in particular a liquid
object.

In the absence of SAWs, the oil dynamically wets the LN surface. Upon contact
between the oil film and the water drop, the macroscopic oil film partially
climbs atop the drop as a result of a gravitational-capillary stress balance.
Gravitational and capillary contributions to the climb arrest the motion of
the macroscopic oil film when it reaches a partial height of the drops in our
experiments.

Upon introducing a propagating SAW in the LN substrate, the oil film
dynamically wets the substrate along the path of the SAW. Once the oil film
makes contact with the drop, it climbs over the surface of the latter. The
intensity (SDA) of the SAW determines the extent of the drop coverage by oil.
Greater levels of SDA results in greater coverage of the drop surface. Above
an SDA threshold of $8.0$ Å, we observe that the oil film fully coat the drops
in our experiments.

##  V Acknowledgement

We are grateful for the support of this study by the Israel Science
Foundation, grant number $441$/$20$ and by the United States Israel Binational
Science Foundation, grant number $2020174$.

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