**2.5. Irradiation**

**2. Mathematical modelling of PV system**

62 Fuzzy Logic Based in Optimization Methods and Control Systems and Its Applications

*V* = \_\_\_\_\_\_\_\_\_\_ *NKT*

**2.2. Light-generated current (radiation)**

IL = \_\_\_G

where G is the radiation (W/m2

**2.3. Reverse saturation current**

**2.4. Short-circuit current**

circuit-situation: V = 0.

Io = Ior ∗ ( T⁄ Tref)3 exp((

Iorn = \_\_\_\_\_\_\_\_ Isc

Ish = IL − Io((exp(QV−IR \_s

1.5, and Eg is the band gap for silicon 1.10 eV.

**2.1. Open-circuit voltage**

The following mathematical models of electrical characteristics are considered to design

The open-circuit voltage, VOC, is the extreme voltage offered from a PV cell, and this happens at zero current. The open-circuit voltage links to the amount of forward bias on the PV cell

where V is the open-circuit voltage, N is diode ideality constant, K is the Boltzmann constant (1.381\*10^-23 J/K), T is temperature in Kelvin, Q is electron charge (1.602\*10^-19 c), IL is the

ILref is the photoelectric current under standard condition 0.15 A, TCref is module temperature under standard condition 298 K, αISC is the temperature coefficient of the short-circuit

where Io is the reverse saturated current, Ior is the saturation current, N is the ideality factor

Ish = IL. It is the extreme value of the current produced by a PV cell. It is formed by the short

QE \_\_\_\_g KN )∗( \_\_1 Tr −\_\_1

+ 1 Volt (1)

∗ (ILref + αIsc(Tc − Tc ref)) (2)

T)) (3)

exp(Vocn ⁄ NVtn) (4)

NKT ) − 1)) (5)

,

), Gref is the radiation under standard condition 1000 W/m2

*Q in I L* − *I* \_\_\_\_*o I o*

light-generated current same as Iph (A), and Io is the saturation diode current (A).

Gref

current (A/K) = 0.0065/K, and IL is the light-generated current (radiation).

20 kW photovoltaic module and simulated using MATLAB environment:

due to the bias of the PV cell junction with the light-generated current [5, 6]:

G = radiation W/m2 (**Figures 1** and **2**).

**Figure 1.** PV—Voltage vs. current characteristics.

**Figure 2.** PV—Power vs. voltage characteristics.


*5.2. Classification and Decision-Making*

For most human activity recognition studies, the classification to discriminate the di fferent types of activities using the extracted features is a critical step. Due to the complexity in human gesture, posture, and daily activities, how to descriminiate them with certain accuracy using di fferent mathematical models becomes a research focus. The classification can be classified into two categories:

1. Threshold-based method—Threshold can be eaisly used to obtain many simple gestures, postures, and motions. For example, fall detection, hand shaking, and static standing can be recognized using the acceleration threshold calculated using equation *aTH* = - *a*2 *x* + *a*2 *y* + *a*2 *z* , and walking or running can be recognized using Doppler frquency shift thresholds.

Due to the superior performance of machine learning and deep learning techniques, many tool libraries—such as MATLAB machine learning toolbox, pandas, and scikit-learn [105]—for di fferent development environments are available, which makes the implementation of the classification quite convenient. The di fferent machine learning techniques will continually be considered the dominant tool for classification for various sensor data based human activity recognition.


**Enhancing Capacity Building for Urban Transformation as a Means to Close the Planning–Implementation Gap in Europe and China**

by Susanne Meyer, Christoph Brodnik, Gudrun Haindlmaier, Hans-Martin Neumann, Daiva Jakutyte-Walangitang, Jianming Cai, Yan Han and Jing Lin

Building socially integrative cities is high on the European Agenda, and it has also become one of the top priorities of the Chinese government's commitment to fostering sustainable urbanisation and the development of smart cities. However, there is a gap between these aspirations, reflected in strategic documents and urban plans, and the actual realisation of these aspirations in practice. Against this background, this research explores and illustrates innovative approaches in European and Chinese smart city projects that have contributed to a better alignment of city planning and implementation. In doing so, the paper draws on the transformative capacity concepts and operationalises them for the city planning and implementation context. Equipped with this framework, the research showcases a selection of the most innovative approaches that European and Chinese smart city projects have successfully employed. Furthermore, the paper analyses the

dimensions in which these approaches have helped to build capacities that can foster urban transformation. Based on the analysis, the paper reflects on further research that is needed to systematically understand innovative approaches and tools to learn to replicate in other cities, and the paper outlines policy recommendations to foster transformative capacities in cities.


*2.2. Behavior*

The behavior of single tester males towards two Di2 headless target flies (a male and a female) was measured over a 5 min period. All flies were isolated 0–4 h after eclosion under CO2 anaesthesia. A few minutes prior to the test, anaesthetized target flies were decapitated with a razor blade (cleaned with ethanol between each sex). In all courtship tests, we used headless flies which do not copulate: therefore, decapitation allows courtship duration to be standardized. Moreover, some tests were performed under red light (25W with a Kodak safe-light filter no. 1) under which flies are virtually blind. In these conditions, most behavioral, visual and acoustic variables associated with the object fly are removed, this enhancing the behavioral e ffect of pheromones [55,56]. Only upright headless flies were used for the test. Tester males were individually aspirated (without anaesthesia) under a watch glass used as an observation chamber (1.6 cm3). After 5 min, the two headless target flies were simultaneously introduced and the courtship index (CI) toward each target was measured (CIf = courtship towards female flies; CIm = courtship towards male flies). CI corresponds to the fraction of the time spent courting relative to the total amount of time multiplied by 100. We only took in account male active courtship (wing vibration, licking and attempting copulation; the very brief episodes of tapping behavior were rarely seen under red light and thus was not included in the CI calculation). No qualitative di fference was noted between the di fferent courtship sequences shown by the di fferent tester male genotypes. The discrimination measure was based on the comparison between CIf and CIm for each genotype and condition used. *n* > 30. Locomotor activity, resulting of the cumulation of the activity of single flies, was measured during five periods of 10 s (total of 50 s), over five minutes (*n* > 24). All tests took place 1–5 h after lights on, in a room at 24 ± 0.5 ◦C with 65 ± 5% humidity. Tests were performed over several days to randomize the experimental variation of uncontrolled environmental parameters.


**Abstract**

Vapor condensation is a ubiquitous phase change phenomenon in nature, as well as widely exploited in various industrial applications such as power generation, water treatment and harvesting, heating and cooling, environmental control, and thermal management of electronics. Condensation performance is highly dependent on the interfacial transport and its enhancement promises considerable savings in energy and resources. Recent advances in micro/nano-fabrication and surface chemistry modification techniques have not only enabled exciting interfacial phenomenon and condensation enhancement but also furthered the fundamental understanding of interfacial wetting and transport. In this chapter, we present an overview of dropwise condensation heat transfer with a focus on improving droplet behaviors through surface design and modification. We briefly summarize the basics of interfacial wetting and droplet dynamics in condensation process, discuss the underlying mechanisms of droplet manipulation for condensation enhancement, and introduce some emerging works to illustrate the power of surface modification. Finally, we conclude this chapter by providing the perspectives for future surface design in the field of condensation enhancement.

**Keywords:** condensation, micro/nanostructures, droplet, wetting, nucleation, heat transfer enhancement

### **1. Introduction**

Condensation heat transfer has been at the forefront of both fundamental and engineering research due to its significance in many conventional and emerging industrial applications. For example, vapor condensation has been widely exploited for thermal management of high-power systems to maintain adequate performance and system reliability, such as advanced lasers, light-emitting diodes, radars, microprocessors, electrical machines, and power inverters [1, 2]. Meanwhile, the thermal efficiency of steam cycles, responsible for a major fraction of electricity production, is highly dependent on the heat transfer performance of vapor condensation [3]. Furthermore, condensation performance strongly influences the energy and infrastructure costs of water treatment and desalination technologies, which is becoming increasingly important due to water scarcity and world population growth [4]. Recent advances in condensation processes on the micro/nanostructured surfaces have also enabled many emerging applications in water and energy systems, such as atmospheric water harvesting [5], solar steam generation [6, 7], humidity control of building environment [8], droplet-jumping-induced gas

absorption [9], jumping-droplet electronics cooling [10, 11], and jumping-droplet electrostatic energy harvesting [12]. More natural phenomena and emerging applications in the field can be found in **Figure 1**.

Vapor preferentially condenses on a solid substrate rather than directly homogeneous nucleation in the vapor phase due to the smaller energy barrier [13]. Once vapor condensation occurs on a solid substrate, the wetting of liquid condensate, determined by surface topography and chemical compositions, plays a key role in heat transfer performance as it is involved in the whole cycle of nucleation, growth, and departure of a liquid phase [14]. Dropwise condensation on a hydrophobic surface, where the gravity-driven droplet roll-off frequently refresh the surface, has an order of magnitude higher heat transfer efficiency than that of filmwise condensation on a hydrophilic surface, where a continuously thickening liquid film covers on the condensing surface [15]. Dropwise condensation is an intrinsically multi-scale energy transfer process, involving the initial formation of droplets at a length scale at a few nanometers, then growth and coalescence, and final droplet departure/shedding of at the millimeter scale, as shown in **Figure 2**. Besides, each sub-process of condensation has different preferred wettability for accelerating the whole cycle of condensed droplets, for example, easier initial nucleation on a hydrophilic substrate with low energy barrier, and faster surface refreshing on a hydrophobic surface with low surface adhesion [16–19]. Thus, the requirements on the surface topography and chemical compositions are dynamically varying from the initial nucleation to final droplet departure.

prevent the nucleation-induced flooding, some emerging techniques, for example, hybrid surfaces with wettability contrast and slippery liquid-infused porous (SLIP) surfaces, have been proposed to manipulate droplet behaviors in condensation process. For example, the different wettability on a hybrid surface can spatially control initial nucleation, addressing the random nucleation on a uniform surface [18, 19, 27]. On a SLIP surface, the lubricating fluid is immiscible with liquid condensate while preferentially wets the micro/nanostructures on the substrate, creating a lubricating fluid layer between the substrate and condensed droplets to

*Multiscale characteristics of dropwise condensation and differential preference on wettability for various subprocesses. Droplet cycle from nucleation to departure has the characteristic length scales from a few nanometers to several millimeters and the preferred wettability from hydrophilicity to hydrophobicity.*

Given the importance of surface structures and wettability on condensation processes, intensive efforts have been devoted to understanding the physics of dropwise condensation and to developing various micro/nanostructures and functional coatings to control droplet behaviors. In this chapter, we present an overview

Wetting behavior of liquid condensate on the substrate is critical in condensation process. For a smooth surface without roughness, a droplet forms an intrinsic contact angle, defined as the angle between the solid-liquid and liquid-vapor interfaces within the liquid (**Figure 3**). The intrinsic contact angle *θ* is a force balance at

where *σ*lv, *σ*sv, and *σ*sl are the liquid-vapor, solid-vapor, and solid-liquid interfacial tensions, respectively. On a real surface with roughness, there is a contact angle

*σ*lv cos *θ* ¼ *σ*sv � *σ*sl (1)

the tri-phase contact line, which can be described by the Young equation,

of the advance in dropwise condensation with a focus on improving droplet dynamics by surface modification. We briefly summarize the surface fabrication and modification, introduce droplet nucleation and size distribution in dropwise condensation, discuss the underlying mechanisms of droplet manipulation using micro/nanostructures, and introduce some typical works to illustrate the power of surface modification. We also discuss several emerging strategies to enhance condensation that could break the limit of conventional dropwise condensation. Finally, we conclude this chapter by providing the perspectives for future surface

reduce surface adhesion for high droplet mobility [5, 28–30].

*Advances in Dropwise Condensation: Dancing Droplets DOI: http://dx.doi.org/10.5772/intechopen.92689*

design in the field of condensation enhancement.

**2. Basics of dropwise condensation**

**Figure 2.**

**231**

Despite that superhydrophobic surfaces with micro/nanostructures can further promote surface refreshing with spectacular water repellency, for example, selfpropelled droplet jumping, the presence of vapor layer within the micro/ nanostructures that is beneficial for reduce solid-liquid adhesion, brings in an additional thermal resistance to hinder droplet growth [20, 21]. Even worse is that the nucleation of nanoscale droplets within micro/nanostructures can cause unwanted pinned states of condensed droplets, which can lead to flooding phenomenon and ultimately heat transfer degradation of superhydrophobic surfaces [22–26]. To

#### **Figure 1.**

*Condensation phenomenon in nature and daily lives, and its applications in various conventional and emerging industrial systems. The high efficiency of vapor condensation heat transfer is critical in water and energy fields.*

*Advances in Dropwise Condensation: Dancing Droplets DOI: http://dx.doi.org/10.5772/intechopen.92689*

**Figure 2.**

absorption [9], jumping-droplet electronics cooling [10, 11], and jumping-droplet electrostatic energy harvesting [12]. More natural phenomena and emerging appli-

Vapor preferentially condenses on a solid substrate rather than directly homogeneous nucleation in the vapor phase due to the smaller energy barrier [13]. Once vapor condensation occurs on a solid substrate, the wetting of liquid condensate, determined by surface topography and chemical compositions, plays a key role in heat transfer performance as it is involved in the whole cycle of nucleation, growth, and departure of a liquid phase [14]. Dropwise condensation on a hydrophobic surface, where the gravity-driven droplet roll-off frequently refresh the surface, has an order of magnitude higher heat transfer efficiency than that of filmwise condensation on a hydrophilic surface, where a continuously thickening liquid film covers on the condensing surface [15]. Dropwise condensation is an intrinsically multi-scale energy transfer process, involving the initial formation of droplets at a length scale at a few nanometers, then growth and coalescence, and final droplet departure/shedding of at the millimeter scale, as shown in **Figure 2**. Besides, each sub-process of condensation has different preferred wettability for accelerating the whole cycle of condensed droplets, for example, easier initial nucleation on a hydrophilic substrate with low energy barrier, and faster surface refreshing on a hydrophobic surface with low surface adhesion [16–19]. Thus, the requirements on the surface topography and chemical compositions are dynamically varying from

Despite that superhydrophobic surfaces with micro/nanostructures can further promote surface refreshing with spectacular water repellency, for example, selfpropelled droplet jumping, the presence of vapor layer within the micro/

nanostructures that is beneficial for reduce solid-liquid adhesion, brings in an additional thermal resistance to hinder droplet growth [20, 21]. Even worse is that the nucleation of nanoscale droplets within micro/nanostructures can cause unwanted pinned states of condensed droplets, which can lead to flooding phenomenon and ultimately heat transfer degradation of superhydrophobic surfaces [22–26]. To

*Condensation phenomenon in nature and daily lives, and its applications in various conventional and emerging industrial systems. The high efficiency of vapor condensation heat transfer is critical in water and energy fields.*

cations in the field can be found in **Figure 1**.

*21st Century Surface Science - a Handbook*

the initial nucleation to final droplet departure.

**Figure 1.**

**230**

*Multiscale characteristics of dropwise condensation and differential preference on wettability for various subprocesses. Droplet cycle from nucleation to departure has the characteristic length scales from a few nanometers to several millimeters and the preferred wettability from hydrophilicity to hydrophobicity.*

prevent the nucleation-induced flooding, some emerging techniques, for example, hybrid surfaces with wettability contrast and slippery liquid-infused porous (SLIP) surfaces, have been proposed to manipulate droplet behaviors in condensation process. For example, the different wettability on a hybrid surface can spatially control initial nucleation, addressing the random nucleation on a uniform surface [18, 19, 27]. On a SLIP surface, the lubricating fluid is immiscible with liquid condensate while preferentially wets the micro/nanostructures on the substrate, creating a lubricating fluid layer between the substrate and condensed droplets to reduce surface adhesion for high droplet mobility [5, 28–30].

Given the importance of surface structures and wettability on condensation processes, intensive efforts have been devoted to understanding the physics of dropwise condensation and to developing various micro/nanostructures and functional coatings to control droplet behaviors. In this chapter, we present an overview of the advance in dropwise condensation with a focus on improving droplet dynamics by surface modification. We briefly summarize the surface fabrication and modification, introduce droplet nucleation and size distribution in dropwise condensation, discuss the underlying mechanisms of droplet manipulation using micro/nanostructures, and introduce some typical works to illustrate the power of surface modification. We also discuss several emerging strategies to enhance condensation that could break the limit of conventional dropwise condensation. Finally, we conclude this chapter by providing the perspectives for future surface design in the field of condensation enhancement.

### **2. Basics of dropwise condensation**

Wetting behavior of liquid condensate on the substrate is critical in condensation process. For a smooth surface without roughness, a droplet forms an intrinsic contact angle, defined as the angle between the solid-liquid and liquid-vapor interfaces within the liquid (**Figure 3**). The intrinsic contact angle *θ* is a force balance at the tri-phase contact line, which can be described by the Young equation,

$$
\sigma\_{\rm lv} \cos \theta = \sigma\_{\rm sv} - \sigma\_{\rm sl} \tag{1}
$$

where *σ*lv, *σ*sv, and *σ*sl are the liquid-vapor, solid-vapor, and solid-liquid interfacial tensions, respectively. On a real surface with roughness, there is a contact angle

#### **Figure 3.**

*Wetting states of a droplet on the smooth and structured surfaces. Intrinsic contact angle of a droplet on a smooth surface and apparent contact angle of a droplet in Wenzel and Cassie states on a structured surface.*

hysteresis for an incipient droplet motion Δ*θ*, defined as the difference between advancing contact angle *θ*adv and receding contact angle *θ*rec. When a water contact angle on a surface is typically smaller or larger than 90°, the surface is defined as hydrophilic or hydrophobic, respectively. Further introducing the roughness, for example, micro/nanostructures, can increase surface hydrophobicity to superhydrophobicity, defined with a contact angle larger than 150° and a contact angle hysteresis smaller than 5° [31].

During condensation process, the wetting of condensed droplets on a rough surface can be differentiated into the highly pinned Wenzel state with large adhesion and suspended Cassie state with high mobility. Both Wenzel and Cassie states can be understood as a global energy minimization of a droplet. On such a surface with roughness *r* defined as the ratio of the total surface area to projected area, the apparent contact angle of a droplet in Wenzel state can be expressed as,

$$r\cos\theta\_W = r\cos\theta\tag{2}$$

where *J*0 is a kinetic constant. Once a droplet nucleates on the surface, it grows by direct vapor-to-liquid condensation on the droplet surface. During initial growth without coalescence, droplets grow with an expected radius as a function of time as,

*R* ¼ *t*

layer to the droplet surface. The mass transfer flux can be expressed as,

*Advances in Dropwise Condensation: Dancing Droplets DOI: http://dx.doi.org/10.5772/intechopen.92689*

*w* ¼ *D*12

boundary layer. Here, the boundary layer thickness can be related to the free-stream velocity *U*, the kinematic viscosity *μ*, and the Schmidt number,

Sc = *μ/D*12, by

where *α* is the power-law exponent, which ranges from 0 to 1 depending on the surface property, surface subcooling, and vapor conditions. If non-condensable gas (NCG) is present in the vapor, a mass transfer boundary layer will be established near the solid surface, resulting in vapor molecules diffusion through the boundary

> *pr* � *ps* � �

where *D*12 is the diffusion constant of vapor molecules in the gas. *p*r and *p*s are the vapor pressure and saturation pressure, respectively. *δ*0 is the thickness of the

*δ*0 ¼ ð Þ *xμ=U* 1*=*2

When a droplet grows large enough to contact with adjacent droplets, they merge and speed up droplet growth, stabilizing the surface coverage to a constant value, known as the self-similarity in dropwise condensation [14, 15, 17, 33, 34]. On

removed by the gravity-driven shedding. Droplet departure radius *r*max can thus be estimated by the force balance between the surface tension and gravity [35],

*π* 2 � 3 cos *θ* þ cos 3 ð Þ*θ*

Once the droplets begin to departure from the surface driven by the gravity, other droplets in the path of droplet departure can be effectively swept by coalescence, refreshing the condensing surface. New small droplets then re-nucleate, grow, and coalescence on the fresh surface, which is responsible for the highefficiency heat transfer performance of dropwise condensation [36, 37]. Compared with the time scale of initial nucleation, the duration of droplet growth, coalescence, and departure usually dominates the whole cycle [1, 37]. Increasing apparent contact angle *θ* and decreasing contact angle hysteresis (*θ*adv � *θ*rec) can effectively

Understanding the cycle of condensed droplets on a solid surface, a classical model was proposed by Le Fevre and Rose to predict dropwise condensation heat transfer where the heat transfer through individual droplet is calculated first and the average heat flux is then obtained by integrating over all the distributed droplets

where *q*d is the heat flux through an individual droplet and *N* is the droplet size distribution on the surface. Subsequently, corresponding modifications of dropwise

� �1*=*2

a vertical or inclined hydrophobic surface, condensed droplets are generally

*r*max ¼ 6c cos ð Þ *θ*rec � cos *θ*adv sin *θ*

reduce droplet departure size for accelerating surface refreshing.

*q* ¼

ð*r*max *r*min

on the condensing surface [38].

**233**

*α* (7)

*δ*0*RT* (8)

*CSc*1*=*3 (9)

*σ*lv *ρ*l*g*

*q*dð Þ*r N r*ð Þd*r* (11)

(10)

For a droplet in Cassie state on a rough surface, the apparent contact angle is defined by,

$$\cos \theta\_{\mathbb{C}} = \rho(\cos \theta + 1) - 1 \tag{3}$$

Nucleation is the first step in dropwise condensation to create a new solid-liquid interface, followed by droplet growth and shedding [16]. The critical nucleation radius *r*min is determined by both liquid properties and surface subcooling and it can be given by the classical nucleation equation [32],

$$r\_{\min} = \frac{2\sigma\_{\rm lb}T}{\rho\_{\rm l}h\_{\rm fg}\Delta T} \tag{4}$$

where *ρ*l and *h*fg are the liquid density and latent heat of the vapor-to-liquid phase transition, respectively. The energy barrier Δ*G*e for droplet formation on a substrate should be overcome to activate the nucleation process [19],

$$
\Delta G\_{\text{e}} = \frac{\pi \sigma\_{\text{lv}} r\_{\text{min}}^2 (2 - 3 \cos \theta + \cos^3 \theta)}{3} \tag{5}
$$

Compared to a hydrophobic surface with a larger contact angle *θ*, vapor nucleation occurs more easily on a hydrophilic surface with a smaller intrinsic contact angle. The intrinsic wettability of a surface also has a strong effect on the nucleation rate *J* via the inverse exponential dependence on Δ*G*e [19],

$$J = J\_0 \exp\left(-\frac{\Delta G\_\text{e}}{kT}\right) = J\_0 \exp\left(-\frac{\pi \sigma\_{\text{lv}} r\_{\text{min}}^2 (2 - 3\cos\theta + \cos^3\theta)}{kT}\right) \tag{6}$$

where *J*0 is a kinetic constant. Once a droplet nucleates on the surface, it grows by direct vapor-to-liquid condensation on the droplet surface. During initial growth without coalescence, droplets grow with an expected radius as a function of time as,

$$R = t^a \tag{7}$$

where *α* is the power-law exponent, which ranges from 0 to 1 depending on the surface property, surface subcooling, and vapor conditions. If non-condensable gas (NCG) is present in the vapor, a mass transfer boundary layer will be established near the solid surface, resulting in vapor molecules diffusion through the boundary layer to the droplet surface. The mass transfer flux can be expressed as,

$$w = D\_{12} \frac{(p\_r - p\_s)}{\delta\_0 RT} \tag{8}$$

where *D*12 is the diffusion constant of vapor molecules in the gas. *p*r and *p*s are the vapor pressure and saturation pressure, respectively. *δ*0 is the thickness of the boundary layer. Here, the boundary layer thickness can be related to the free-stream velocity *U*, the kinematic viscosity *μ*, and the Schmidt number, Sc = *μ/D*12, by

$$\delta\_0 = \frac{\left(\varkappa\mu/U\right)^{1/2}}{\mathrm{CSc}^{1/3}}\tag{9}$$

When a droplet grows large enough to contact with adjacent droplets, they merge and speed up droplet growth, stabilizing the surface coverage to a constant value, known as the self-similarity in dropwise condensation [14, 15, 17, 33, 34]. On a vertical or inclined hydrophobic surface, condensed droplets are generally removed by the gravity-driven shedding. Droplet departure radius *r*max can thus be estimated by the force balance between the surface tension and gravity [35],

$$r\_{\text{max}} = \left(\frac{6\mathbf{c}(\cos\theta\_{\text{rec}} - \cos\theta\_{\text{adv}})\sin\theta}{\pi(2 - 3\cos\theta + \cos^3\theta)} \frac{\sigma\_{\text{lv}}}{\rho\mathbf{g}}\right)^{1/2} \tag{10}$$

Once the droplets begin to departure from the surface driven by the gravity, other droplets in the path of droplet departure can be effectively swept by coalescence, refreshing the condensing surface. New small droplets then re-nucleate, grow, and coalescence on the fresh surface, which is responsible for the highefficiency heat transfer performance of dropwise condensation [36, 37]. Compared with the time scale of initial nucleation, the duration of droplet growth, coalescence, and departure usually dominates the whole cycle [1, 37]. Increasing apparent contact angle *θ* and decreasing contact angle hysteresis (*θ*adv � *θ*rec) can effectively reduce droplet departure size for accelerating surface refreshing.

Understanding the cycle of condensed droplets on a solid surface, a classical model was proposed by Le Fevre and Rose to predict dropwise condensation heat transfer where the heat transfer through individual droplet is calculated first and the average heat flux is then obtained by integrating over all the distributed droplets on the condensing surface [38].

$$q = \int\_{r\_{\rm min}}^{r\_{\rm max}} q\_{\rm d}(r) N(r) \mathrm{d}r \tag{11}$$

where *q*d is the heat flux through an individual droplet and *N* is the droplet size distribution on the surface. Subsequently, corresponding modifications of dropwise

hysteresis for an incipient droplet motion Δ*θ*, defined as the difference between advancing contact angle *θ*adv and receding contact angle *θ*rec. When a water contact angle on a surface is typically smaller or larger than 90°, the surface is defined as hydrophilic or hydrophobic, respectively. Further introducing the roughness, for

*surface and apparent contact angle of a droplet in Wenzel and Cassie states on a structured surface.*

*Wetting states of a droplet on the smooth and structured surfaces. Intrinsic contact angle of a droplet on a smooth*

superhydrophobicity, defined with a contact angle larger than 150° and a contact

During condensation process, the wetting of condensed droplets on a rough surface can be differentiated into the highly pinned Wenzel state with large adhesion and suspended Cassie state with high mobility. Both Wenzel and Cassie states can be understood as a global energy minimization of a droplet. On such a surface with roughness *r* defined as the ratio of the total surface area to projected area, the

For a droplet in Cassie state on a rough surface, the apparent contact angle is

Nucleation is the first step in dropwise condensation to create a new solid-liquid interface, followed by droplet growth and shedding [16]. The critical nucleation radius *r*min is determined by both liquid properties and surface subcooling and it can

*r*min ¼ 2*σ*lv*T*

where *ρ*l and *h*fg are the liquid density and latent heat of the vapor-to-liquid phase transition, respectively. The energy barrier Δ*G*e for droplet formation on a

Compared to a hydrophobic surface with a larger contact angle *θ*, vapor nucleation occurs more easily on a hydrophilic surface with a smaller intrinsic contact angle. The intrinsic wettability of a surface also has a strong effect on the nucleation

min 2 � 3 cos *θ* þ cos 3 ð Þ*θ*

substrate should be overcome to activate the nucleation process [19],

¼ *J*0 exp � π*σ*lv*r*2

*ΔG*e ¼ π*σ*lv*r*2

rate *J* via the inverse exponential dependence on Δ*G*e [19],

*J* ¼ *J*0 exp � *ΔG*e

**232**

*kT*  cos *θ*W ¼ *r* cos *θ* (2)

cos *θ*C ¼ *φ*ð Þ� cos *θ* þ 1 1 (3)

*ρ*l*h*fg*ΔT* (4)

3 (5)

(6)

min 2 � 3 cos *θ* þ cos 3 ð Þ*θ kT*

example, micro/nanostructures, can increase surface hydrophobicity to

apparent contact angle of a droplet in Wenzel state can be expressed as,

angle hysteresis smaller than 5° [31].

*21st Century Surface Science - a Handbook*

be given by the classical nucleation equation [32],

defined by,

**Figure 3.**

condensation heat transfer model to include more accurate expressions for the heat transfer through an individual droplet [35, 39–48] and droplet size distribution [14, 33, 39, 43, 46, 49–51] are developed, for example, the conduction resistance of the liquid droplet, the thermal resistance of a hydrophobic coating, mass transfer on the liquid–vapor interface, and the effect of interface curvature.

resistance and good chemical stability has been used to obtain stable dropwise condensation, without obvious heat transfer degradation in a 2-week measurement [56]. Another typical material is the rare-earth oxide (REO), which can be potentially used as a hydrophobic material at scale due to the development of ceramic processing techniques (**Figure 4f**) [57]. Note that the wettability of REO is reported to be intrinsically hydrophilic and the hydrophobicity of REO is due to the adsorbed hydrocarbon species [60–62]. Despite that many new functional coatings mentioned above have shown some potential to achieve dropwise condensation, a costeffective, low-thermal resistance, and robust hydrophobic coating to promote sustainable dropwise condensation has proven to be exceedingly challenging, resulting

To further improve droplet mobility, various micro/nanostructured surfaces are developed using advanced fabrication technologies. Micro/nanostructured silicon surfaces are fabricated using both wet and dry etching methods [63]. Typically, silicon nanowires synthesized by wet etching methods are vertically aligned [64]. Due to the surface tension of water during the drying process of nanowire synthesis, a large number of micro-defects are naturally formed where the closely aligned silicon nanowires cannot individually stand but form clusters [65]. Compared with the wet etching methods, finer structure geometries can be fabricated by dry etching where the etching rate can be controlled more precisely. In addition to the nanowires with uniform diameters, conical silicon nanowires were also fabricated to promote the formation of high-mobility droplets with the auxiliary Laplace pressure difference (**Figure 5a**) [25]. To meet the need of multiple length scales in manipulating droplet growth, hierarchical silicon nanowires with both microscale and nanoscale features have been fabricated by coupling micro-patterns and nanostructures [66]. **Figure 5b** shows a hierarchical surface with parallel microgrooves that are formed by patterning silicon nanowire arrays with different lengths [67, 68]. **Figure 5c** shows another hierarchical surface, consisting of micropyramids covered by silicon nanowires [69]. Compared to the silicon, metal materials, for example, aluminum, stainless steel, and copper, have better physical and thermal properties, to be exploited for improving heat transfer such as high thermal conductivity, stability, and machinability. Among various surface fabrication

*Micro/nanostructured surfaces for condensation enhancement. (a) Conical silicon nanowire arrays [25]. (b) Microgroove silicon nanowires [67]. (c) Micro-pyramids covered by silicon nanowires [69]. (d) Gold nanowires [70]. (e) Closely spaced copper nanowire arrays [65]. (f) 3D copper nanowire networks [71]. (g) Hierarchical surface with micro-patterned copper nanowire arrays [21]. (h) Hierarchical copper mesh-*

in ubiquitous filmwise condensation in real industrial applications.

*Advances in Dropwise Condensation: Dancing Droplets DOI: http://dx.doi.org/10.5772/intechopen.92689*

**Figure 5.**

**235**

*covered structure [72].*


*3.2. PF2: Band Selection Using Genetic Algorithm (GA) and Particle Swarm Optimization (PSO)*

In this processing framework (Figure 3b), the use of the *GA* and *PSO* for the selection of the most representative wavelengths of the HS data for this particular application is proposed. The optimization algorithms are aimed to find the best combination of elements from an initial set of available elements. Normally, these algorithms are focused on reaching the global minimum of the function to be analyzed. The reduced training labeled dataset evaluated in *PF1* was employed to reduce the extremely high execution time of the SVM training procedure, due to the iterative nature of the optimization algorithms. The procedure is as follows. First, the training data are employed in the optimization algorithm, where the initial bands to be used for the classification are randomly selected. After this band selection procedure, a classification model is generated and evaluated with the test dataset, obtaining a classification result that is assessed using three custom metrics independently (*OAPenalized, FoM* and *FoMPenalized*). These metrics will be explained in detail later on in Section 3.5. After computing one of the custom metrics, its value is stored and then the procedure is iteratively executed using other bands selected by the optimization algorithm. The algorithm is executed until performs all possible combinations, returning the best metric value, or when after a high number of iterations, the metric value remains constant. Once the algorithm finishes its execution, it returns the identification of the optimal bands to obtain the best classification result.

#### 3.2.1. Genetic Algorithm (GA)

The *GA* is an optimization algorithm that mimics the process of natural selection [41]. *GA* tries to find the optimal solution (usually the global minimum) of the function to be studied. The main advantage of this algorithm is its great ability to work with a large number of variables [55,56]. The objective of this algorithm is to optimize a series of parameters (called genes) that will then be concatenated with each other, when necessary, to provide the best results (called chromosomes). In order to find these most important parameters, it is necessary to generate populations in a random manner, whose size is chosen by the user. This population allows the performance of the algorithm to be improved. Once these parameters are defined, the *GA* must perform the following steps:

Steps 2 to 6 are repeated as many times as necessary until the best solution is found [41].