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Research in the field of wettability has attracted tremendous attention from both fundamental and applied points of view. This chapter gives a deep insight into different kinds of surface wettability and various models used to explain the spreading of a droplet on a solid surface. The importance of surface physical and chemical properties in determining the surface wettability behaviour is outlined. The significance of various measurable parameters such as equilibrium water contact angle and contact angle hysteresis that determine the wettability nature of a surface, whether it is hydrophilic or hydrophobic, is discussed in detail. In addition, various approaches adopted to measure these parameters are also discussed. The chapter concludes with a section on superhydrophobicity, mentioning the major fabrication techniques currently being adopted and various application areas.

In Nature, living organisms transform themselves so as to attain their optimum form of existence to adapt to their environment through the process of evolution. Darwin’s theory of natural selection and survival of the fittest explains the evolution of species1 and the surface wettability of a whole species is engineered to outperform in its environment. The self-cleaning nature of the lotus leaf, the water-harvesting efficiency of the Stenocara desert beetle, the slippery surface of the Nepenthes pitcher plant, oleophobic fish scales, etc., exemplify the surface engineering efficacy of Nature.2–8 The diverse wettability of these surfaces is attributed to both the chemical and the topographic properties of the surface.9 

Mimicking Nature to tackle human problems is referred to as biomimicry or biomimetics. The word biomimetics is derived from the Greek words “bios” and “mimesis” meaning “life” and “imitation”, respectively.10 A similar term in engineering is “bionics”, used by Jack Steel for the first time, and means imitating or copying Nature.11 The multifunctional properties of naturally occurring surfaces such as plant and animal surfaces originate from their unique chemical and topographic features. Figure 1.1 shows some of the naturally occurring surfaces that are extensively used in the field of biomimetics or bionics to mimic the surface wettability behaviour.12 The upsurge in research on biomimicking of the ubiquitous wettability behaviour of various naturally occurring surfaces stems largely from their large-scale applications in diverse areas, ranging from industry to the biomedical field. Bio-inspired surfaces are showing their potential in diverse areas including self-cleaning, water harvesting, water repellency, antibacterial, drag and friction reduction, anti-reflection, anti-corrosion, anti-fouling, structural coloration, thermal insulation, biosensing, etc.13–23 

Figure 1.1

Special wettabilities in Nature. Reproduced from ref. 12, https://doi.org/10.3390/ma9020116, under the terms of the CC BY 4.0 license, https://creativecommons.org/licenses/by/4.0/.

Figure 1.1

Special wettabilities in Nature. Reproduced from ref. 12, https://doi.org/10.3390/ma9020116, under the terms of the CC BY 4.0 license, https://creativecommons.org/licenses/by/4.0/.

Close modal
Surface wettability, which can be defined as the attraction of the liquid phase to a given solid surface, is mainly governed by the surface energy of the platform and the surface tension of the liquid. A droplet on a flat surface can attain a cap-like shape and the phenomenon behind the formation of the spherical shape of the liquid droplet is surface tension.24 Surface tension is an effect that arises because of the net force experienced by the molecules on the liquid surface. This tension acts in such a way that it reduces the surface area of the droplet and provides additional energy to the surface molecules. Therefore, as the number of molecules on the surface increases, the surface tension also increases, and the drop tries to achieve the minimum surface area by taking a spherical shape of minimum energy. The cohesive force, which is the attraction between like molecules, and the adhesive force, which is the attraction between unlike molecules, together determine the wetting behaviour of a surface. In an equilibrium state, the curvature of a droplet dispensed on the surface reflects the pressure difference at the liquid–air interface and the surface tension force. The Young–Laplace equation expresses the relation between the pressure difference between two phases (∆P) and the surface tension (γ) as25 
ΔP=γ(1R1+1R2)
(1.1)
where R1 and R2 are the radius of curvature in the orthogonal direction of the surface as shown in Figure 1.2 
Figure 1.2

Laplace pressure and surface tension force acting on a droplet.

Figure 1.2

Laplace pressure and surface tension force acting on a droplet.

Close modal
.
The gravitational force acting on the droplet tries to distort its spherical shape. As the volume of the droplet increases, the effect of gravitational force also increases. To ensure a negligible effect of gravitational force on the droplet, the size of the droplet is compared with the capillary length Lc:26 
Lc=γlvρg
(1.2)

where γlv, ρ and g are the surface tension, the density of the liquid and acceleration due to gravity, respectively. Under ambient conditions, the capillary length of water is ∼2.7 mm and the gravitational deformation of the water droplet is insignificant if the size of the droplet is below this characteristic length scale.27 

When a droplet rests on a solid surface, in addition to the surface tension (γlv) two more interfaces, solid–vapour and solid–liquid, and corresponding interfacial tensions, γsv and γsl, become relevant.28,29 The shape of the droplet on a smooth, flat surface is determined by the balance between these three interfacial forces. Hence the condition for the droplet spreading on such a surface can be defined with the spreading power S, given by
S=γsv(γsl+γlv)
(1.3)

It is defined as the free energy difference between the solid in the air and the solid in contact with the flat, thick liquid layer. When S > 0, the droplet spontaneously spreads over the surface and attains the situation of total wetting. For S < 0, the droplet partially wets the surface and remains on the surface with an equilibrium shape.29 

The fundamental theory of wettability science begins with Young’s equation, which was proposed by Thomas Young in 1805.30 For a droplet placed on an ideal surface (Figure 1.3a), i.e. an isotropic, chemically homogeneous, non-reactive and non-deformed, atomically flat, solid surface, the contact angle can be determined with Young’s equation:
cosθ=γsvγslγlv
(1.4)

where γsv, γsl and γlv are the solid–vapour, solid–liquid and liquid–vapour interfacial tensions, respectively, and θ is the equilibrium contact angle or Young’s contact angle. According to Young’s equation, a droplet on the aforementioned surface has an inevitable tendency to reach the lowest energy with a balanced state and the interaction among the three interfaces determines the equilibrium contact angle. For the complete wetting state, γsv > γsl + γlv, the force balance cannot be achieved. In the case of partial wetting and non-wetting cases, 0 < cos θ < 1 and −1 < cos θ < 0, respectively.31 The experimentally measured value of the equilibrium water contact angle (WCA) determines whether the surface is water loving (hydrophilic) or water hating (hydrophobic). Conventionally, a hydrophilic surface is a surface upon which a water droplet makes a contact angle of <90°. If the WCA is >90° but <150°, the surface is called hydrophobic, whereas a surface that exhibits a WCA of >150° is termed a superhydrophobic surface. Complete wetting, characterized by a WCA of ∼0°, occurs for liquids with an extremely low surface tension or a surface with very high surface energy.32 In the case of hydrophilic surfaces, γsl < γsv, the reverse is true for hydrophobic surfaces. However, it should be noted that the classification of the substrate as the hydrophilic–hydrophobic boundary at a WCA of 90° is a matter of debate. Based on the attraction–repulsion forces of chemistry, Berg et al. suggested that the boundary between hydrophilic and hydrophobic lies at around 65°.33 In reality, Young’s model is a simplified mathematical model to explain the wettability of a surface and the model often fails to describe the wettability of a surface that has surface heterogeneity and roughness. In a practical scenario, surface heterogeneity and roughness play an important role in determining surface wettability. The influence of macroscopic roughness on wettability is taken into account theoretically in two further different models: the Wenzel and Cassie–Baxter models.

Figure 1.3

(a) Young’s, (b) Wenzel and (c) Cassie–Baxter models of wetting.

Figure 1.3

(a) Young’s, (b) Wenzel and (c) Cassie–Baxter models of wetting.

Close modal
The Wenzel model, proposed in 1936, incorporated surface roughness r, which is the ratio of the actual area to the apparent area of the surface, in Young’s equation and modified it to34 
cosθw=rcosθ
(1.5)

where θw is the apparent contact angle based on the Wenzel model. According to this model, liquid droplets on the rough surface will completely wet the surface, as shown in Figure 1.3b, and also the roughness can enhance the intrinsic wettability nature of the surface. In other words, an increase in the surface roughness turns a hydrophilic/hydrophobic surface into more hydrophilic/hydrophobic. For rough surfaces, r is >1. Compared with Young’s equation, the Wenzel model explains the wettability of a rough surface; however, this model fails to explain the wettability of a heterogeneous surface, particularly one that exhibits superhydrophobic behaviour. For such surfaces, researchers often rely on the Cassie–Baxter model to explain their results.

As mentioned earlier, the Wenzel model provided a theoretical explanation of wetting on a homogeneous rough surface, and in 1944 Cassie and Baxter developed another model to understand wetting on a heterogeneous rough surface.35 In the Cassie–Baxter model of wetting, gas or air can be trapped between the structures, and this trapped air can act as a cushion for the liquid droplet, which ensures minimal contact between the liquid and the substrate (Figure 1.3c). According to this model, in addition to the solid–liquid and liquid–air interfaces, the solid–air interface also plays a role in the determination of the wettability of a surface. The apparent contact angle θCB of this model is calculated by amending Wenzel’s equation by incorporating the contributions of a two-component composite surface:
cosθCB=f1cosθ1+f2cosθ2
(1.6)
where f1 and f2 are the area fractions of the liquid area that come into contact with domains 1 and 2, respectively, and θ1 and θ2 are the corresponding intrinsic contact angles. If domain 1 is the solid surface and domain 2 is the trapped air, f1, θ1 and f2, θ2 can be replaced with fsl, θs and fla, θa, respectively. Substituting fsl + fla = 1, θs = θ and θa = 180° in eqn (1.6), the Cassie–Baxter equation becomes
cosθCB=1+fsl(1+cosθ)
(1.7)
The introduction of an additional roughness factor rf, which is the ratio of the actual wetted area to the projected area, in eqn (1.6) yields the modified Cassie–Baxter equation as
cosθCB=1+fsl(1+rfcosθ)
(1.8)
Irrespective of the initial contact angle, this model always predicts the enhancement of the hydrophobicity of the surface. When fsl = 1, the Cassie–Baxter equation matches the Wenzel equation. Even though both models can explain the wettability of a surface having a WCA of >150°, the adhesion properties of the surface differ greatly. In the Wenzel state, the penetration of the droplet into the structures offers high adhesion of the droplet, which prevents the droplet from rolling off the surface, whereas the air plastron (a thin layer of air) in the Cassie–Baxter state reduces the adhesion of the droplet compared with the Wenzel state and can support the easy removal of the droplet from the surface.36 Hence the threshold between the Wenzel and Cassie–Baxter states plays an important role in the fabrication of superhydrophobic surfaces. Comparing eqn (1.5) and (1.7), Lafuma and Quéré introduced a critical contact angle, θC, which favours the formation of air pockets at the liquid–air interface as in the equation37 
cosθC=fsl1rfsl
(1.9)

Comparison between the Wenzel state, the Cassie–Baxter state and the corresponding interfacial energies suggests that the formation of air pockets is favoured only when θ > θC. In this case, the droplet will stay on the rough grooves by entrapping the air plastrons beneath it. On the other hand, the liquid impregnates the grooves via capillary action and thus prefers to be in a superhydrophilic state.38 Due to the pinning offered by the roughness features at the three-phase contact point, the coexistence of Wenzel and Cassie–Baxter states of wetting is allowed.39 However, the Cassie–Baxter state can be transformed into the Wenzel state due to the escape of the trapped air plastron from the structures.

In practical applications, the contact angle alone cannot determine the wettability of the surface. The surface imperfections lead to the existence of multiple contact angles for a surface. In such cases, the maximum contact angle is taken as the advancing contact angle and the minimum contact angle is taken as the receding contact angle. The difference between these advancing and receding contact angles is known as contact angle hysteresis.40 The relation between the contact angle hysteresis and surface roughness can be expressed as
θadvθrec=fla1rcosθadvcosθrec2rcosθ+1
(1.10)

where θadv and θrec are the advancing and receding contact angle, respectively.

For a homogeneous surface, an increase in surface roughness leads to an increase in contact angle hysteresis, whereas in the case of a heterogeneous surface, an approach to make fla unity can create a surface with high contact angle and low contact angle hysteresis. Such a surface can exhibit superhydrophobicity with water rolling off since it reduces the contact area of the solid and liquid. This superhydrophobicity may cause damage due to the penetration of liquid into the structures, followed by the escape of trapped air. The critical pressure for the occurrence of this transition can be calculated. Since a higher pressure leads to dropping of liquid into the structure simultaneously, the local contact angle increases due to the pinning at the edge of the surface features. When this contact angle exceeds the advancing contact angle, θadv, the three-phase contact line is depinned and the liquid completely wets the surface features.41 The critical pressure ∆Pbreak is
ΔPbreak=2γsin(θadv+ψ)x
(1.11)
where ψ is the edge angle and x is the lateral distance between the meniscus and the symmetry line (Figure 1.4a and b,
Figure 1.4

Pressure-induced plastron collapse. (a) Increasing Pin results in depinning of the three-phase contact line when the local contact angle reaches θadv; (b) increasing Pin results in a breakthrough when the curvature radius R = x before depinning occurs.

Figure 1.4

Pressure-induced plastron collapse. (a) Increasing Pin results in depinning of the three-phase contact line when the local contact angle reaches θadv; (b) increasing Pin results in a breakthrough when the curvature radius R = x before depinning occurs.

Close modal
). For intrinsic contact angle θadv > π/2 − ψ (Figure 1.4b), eqn (1.11) can be simplified to
ΔPbreak=2γx
(1.12)

Hence the critical pressure difference depends on the surface tension of the liquid and the separation between the surface features. Also, it is less sensitive to surface chemistry.

The validity of the proposed Wenzel and Cassie–Baxter wetting models in a real scenario has always been a question of debate. In 1945, Pease proposed that the wetting of a solid surface is a one-dimensional problem and created an equation based on the line fractions.42 Later, Gao and McCarthy considered the validity of the Wenzel and Cassie–Baxter equations. The models are valid when the contact area reflects the ground-state energies of contact lines and the transition states between them.43 McHale emphasized that the surface fraction in the Cassie–Baxter model and the roughness parameter in the Wenzel model should be considered as global properties of the surface rather than properties of the area under the droplet.44 In addition, according to McHale’s theory, both the Wenzel and Cassie–Baxter states forgot to consider the isolated defects on the surface. Nosonovsky claimed that the Wenzel and Cassie–Baxter models are valid for uniform rough surfaces but not for non-uniform rough surfaces.45 Marmur and Bittoun supported the Wenzel and Cassie–Baxter wetting models and claimed that the models can give a stable contact angle of the surface when the droplet size is adequately large compared with the chemical heterogeneity and roughness wavelength.46 Patankar and co-workers examined the validity of the Cassie–Baxter model for rough surfaces and found that except for pillar-type roughness, the WCA of the surfaces follows the trend of the Cassie–Baxter equation.47 Even though several conflicts exist related to the validity of the Wenzel and Cassie–Baxter models, the use of these models to explain the wettability of surfaces is still popular. Researchers still use these models extensively to explain the wettability of surfaces.48–52 

The working of different kinds of micro- and nanoscale structures that exist in Nature and their biomimicking using advanced lithographic fabrication tools have necessitated the development of improved models. The Wenzel and the Cassie–Baxter models assume single-scale roughness, whereas a hierarchical surface exhibits dual-scale roughness. Patankar developed a model explaining the dual-scale roughness of the surface, where nanoscale roughness is considered over micron-scale structures, exhibiting a better correlation between the experimental data and naturally occurring superhydrophobic surfaces such as the lotus leaf.53 In the model, the solid fraction in the Cassie–Baxter model depends on the side dimension of the micron-scale square pillars a1 and the pillar spacing b1 through the equation
fsl=A1=1[(b1a1)+1]2
(1.13)
Hence the Cassie–Baxter model then becomes
cosθCB=1+A1(1+cosθ)
(1.14)
Similarly, the Wenzel equation becomes
cosθw=[1+4A1(a1h1)]cosθ
(1.15)
where h1 is the height of the micropillars. The hierarchical model consists of micropillars decorated with secondary structures of nanoscale pillars of size a2, spacing b2 and height h2, as shown in Figure 1.5a 
Figure 1.5

(a) Hierarchical model for theoretical analysis; (b) Koch curve.

Figure 1.5

(a) Hierarchical model for theoretical analysis; (b) Koch curve.

Close modal
.It is possible to investigate the wetting on secondary structures by changing the subscripts in eqn (1.13) and (1.14). The hierarchical model could explain the superhydrophobicity of many surfaces more effectively compared with the Wenzel and Cassie–Baxter models.
The introduction of fractal theory by Mandelbrot54 for the evaluation of complex structures encouraged Shibuichi et al. to develop the fractal model of wetting.55 They found that the micro- and nanostructures in Nature can be demonstrated with fractal geometry and thereby can be used to explain the superhydrophobicity of surfaces. One of the popular fractal geometries is the Koch curve, as shown in Figure 1.5b. In fractal geometry, a single geometry is repeated in some fashion that makes the fractal structure more complex to mimic the micro- and nanostructures on the lotus leaf.56 Based on this theory, the Wenzel and Cassie–Baxter equations were modified to
cosθw=(Ll)D2cosθ
(1.16)
cosθCB=f(Ll)D2cosθfla
(1.17)

respectively, where L and l are the upper and lower limit scales of the fractal structures and D is the Hausdorff dimension, i.e. D = log4/log3 = 1.2618.

The contact angle made by a liquid on a solid surface is regarded as a measure of wettability. It is defined as the angle between the tangent to the surface and the tangent to the liquid–air (liquid–fluid) interface at the three-phase contact point, towards the liquid side (Figure 1.6a). Research has been carried out over the last two centuries in the field of wettability and the understanding of the contact angle and its correlation with wettability is not straightforward. Many measurements in the past were carried out with protocols having poor reproducibility. However, recent progress revealed the flaws in the past contact angle measurements and led to interpretations that gave new insights into wettability-related studies. As mentioned earlier, the first scientist to explain the contact angle was Thomas Young and the angle described with Young’s equation is called Young’s contact angle. Thermodynamically, this is considered as the angle that corresponds to the lowest energy state of the system. Young’s contact angle matches the ideal contact angle (which is the contact angle on an ideal surface) when the radii of curvature of the drop become greater than the nanometric size. In the case of real surfaces, which may have roughness and chemical heterogeneities, the surface can have a range of contact angles between the advancing and receding contact angles. This contact angle is often called the apparent contact angle, which is defined as the average contact angle on the entire three-phase contact line (Figure 1.6b). This apparent contact angle is different from the actual contact angle, which is the contact angle that exists locally at any point along the contact line. At equilibrium, the actual contact angle becomes equal to the ideal contact angle.57 However, in a real scenario, the fabrication of an ideal surface and the measurement of the actual contact angle are limited by practical difficulties.

Figure 1.6

(a) Droplet on a solid surface; (b) apparent and actual contact angles on rough and heterogeneous surfaces.

Figure 1.6

(a) Droplet on a solid surface; (b) apparent and actual contact angles on rough and heterogeneous surfaces.

Close modal

The apparent contact angle can represent the metastable contact angle of the system. Thermodynamically, at constant temperature and pressure, the equilibrium of a wetting system is achieved when the Gibbs energy is the minimum. Figure 1.7 shows the imaginary correlation between the Gibbs energy and the apparent contact angle of a system. A heterogeneous system can have multiple minima in the Gibbs energy curve and, corresponding to each minimum, the system exhibits different apparent contact angles. The advancing (highest metastable contact angle) and receding contact angle (lowest metastable contact angle) are also a kind of apparent contact angle. The apparent contact angle associated with the lowest Gibbs energy defines the most stable contact angle. Acquiring the most stable apparent contact angle out of all the possible metastable states is a difficult task. Even though methodologies such as the application of external energy in the form of mechanical vibrations to the surface are adopted for obtaining the most stable apparent contact angle, the use of such methodologies is still a question of debate.58 Another approximation regarding the measurement of the most stable apparent contact angle is that when the size of the droplet is larger (with a ratio of about three orders of magnitude) than the surface roughness or heterogeneity, the contact angle obtained will be near the true value.

Figure 1.7

Gibbs free energy of a liquid on a rough or heterogeneous surface.

Figure 1.7

Gibbs free energy of a liquid on a rough or heterogeneous surface.

Close modal

Dynamic contact and static contact angles are the other types of apparent contact angles. The dynamic contact angle is the contact angle measured under dynamic flow conditions, which are affected by the flow velocity. The static contact angle is the contact angle obtained by just putting the droplet on the surface, and it can have any values between the advancing and receding contact angles. Due to the involvement of random elements in this type of measurement, the static contact angle is not widely accepted for analysis.

Contact angle measurement is an indispensable tool for surface characterization, and many different techniques are available for contact angle measurements, such as the sessile drop method, captive bubble method, Wilhelmy plate method, Washburn method and capillary bridge method, to mention just a few.59–62 Each technique has its merits and challenges, and only the application determines the most suitable method. A brief overview of some commonly adopted techniques to measure the contact angle and contact angle hysteresis is given below.

The sessile drop method is a widely employed technique for the measurement of contact angles, based on analysing the droplet shape. It is performed by capturing an image of a droplet dispensed on a test surface and measuring the contact angle by a fitting procedure. The main components of a sessile drop goniometer are an imaging system with suitable illumination, a motorized dispenser system and a sample stage. A droplet is dispensed and gently applied on the test surface, placed horizontally. Once the droplet has contacted the surface and stabilized by reaching the final wetting state, the image is captured. Since the contact angle measurement depends on the captured image, best practice involves adjusting the illumination and contrast to obtain a sharp image. Several models have been used for fitting the sessile drop image to obtain the contact angle, including the tangential method, which measures the tangent angle at the contact point, and the circular and elliptical methods, which consider the droplet profile as part of a circle and ellipse, respectively.63–65 

A more precise measure of contact angle is provided by the Young–Laplace method, also known as axisymmetric drop shape analysis, which works under the two assumptions that the droplet is axisymmetric and that gravity is the only external force.66–70 Selecting a suitable fitting method is crucial when superhydrophobic surfaces are involved, as larger deviations were observed with different fitting methods and shape deformation by gravity.71–73 According to the previously discussed wetting models, the contact angle is not affected by the droplet size, but it is reasonable to expect that as the droplet volume increases, gravity-induced deformation will strengthen. The volume of the sessile drop must be small so that gravity-induced flattening is minimal, as it results in erroneous contact angle measurements, especially in the case of superhydrophobic surfaces.71,72 Conversely, the droplet volume used for the sessile drop method has to be 2–3 orders of magnitude larger than the surface roughness scale, to avoid contact line deformation by the surface texture.74 Since the technique is based on drop shape analysis, it is crucial to obtain a clear and sharp sessile drop image, set up a baseline of the sessile drop profile and perform correct shape analysis to obtain reproducible and accurate contact angle values. This makes the sessile drop method highly susceptible to operator error, and also assigning a baseline is often difficult for highly wetting surfaces (contact angle < 20°), as the droplet profile is nearly flat. The small surface area and liquid volume requirements are advantages of the sessile drop method over the other available methods.

Contact angle hysteresis is defined as the difference between the advancing and receding contact angles, and from an experimental perspective the advancing and receding contact angles are well defined as the maximum and minimum contact angles while increasing and decreasing the droplet volume, respectively. When the volume of the droplet increases, initially the contact line is pinned while the contact angle increases until it reaches the advancing contact angle. A further increase in volume leads to advance of the contact line. Similarly, on reducing the volume of the droplet, the contact line is stable and the contact angle decreases, reaching a minimum termed the receding contact angle, beyond which the contact line recedes. The image captured at the advancing contact line and receding contact line using the sessile drop goniometer provides the advancing and receding contact angles for assessing the contact angle hysteresis (Figure 1.8a). As discussed earlier, the sessile drop method is susceptible to operator error if a strict protocol is not maintained and also the preparation of the test surface requires detailed attention as it is difficult to provide generalized guidelines for the infinite range of available surfaces.75 Also, the injection and withdrawal of the test liquid should be at a rate at which the dynamic effects are minimal, especially for high-viscosity liquids, which show higher contact angle hysteresis at an increased flow rate.76 

Figure 1.8

Illustration of contact angle hysteresis measurement using (a) the droplet expansion and contraction method, (b) the tilting plate method and (c) the captive bubble method.

Figure 1.8

Illustration of contact angle hysteresis measurement using (a) the droplet expansion and contraction method, (b) the tilting plate method and (c) the captive bubble method.

Close modal

The tilting plate method is a relatively simple experimental tool used to assess contact angle hysteresis. The technique uses an experimental apparatus similar to the sessile drop goniometer, with a provision to tilt the sample stage. A sessile drop is placed on a horizontal test surface that is gradually tilted, and the sliding angle is defined as the angle of inclination at which the droplet starts to move. As the angle of inclination increases, the droplet deforms, as shown in Figure 1.8b; the contact angle at the leading edge starts to increase to reach a maximum, and conversely the contact angle at the trailing edge decreases to reach a minimum. At the sliding angle, when the drop is about to slide, the contact angles at the leading and trailing edges reach the advancing and receding contact angles.77 The experimental procedure involves recording the image of the droplet at the sliding angle and assessing the droplet profile to determine the advancing and receding contact angles. Even though the tilted plane technique is relatively simple and offers quick contact angle measurements, it has its limitations. The general association of the maximum and minimum contact angles at the sliding angle with the advancing and receding contact angles, respectively, is questionable, especially on surfaces with large hysteresis.78,79 Therefore, use of the tilting plate method is recommended only in situations where other methods are not feasible.

In the captive bubble method, the test surface is immersed and kept on the top of a container filled with the test liquid, and a bubble is injected and captured on the test surface (Figure 1.8c). Similarly to the sessile drop method, imaging and profile analysis give the contact angle. Also, the expansion and contraction of the bubble allow the measurement of the advancing and receding contact angles. However, the captive bubble method is not recommended for surfaces with a contact angle >130°.80 The captive bubble method allows measurements to be carried out in a saturated state and can avoid the influence of drying, making it ideal for surfaces such as contact lenses.81 The method can also be performed with a less dense liquid as a test liquid for studying solid–liquid–liquid systems. Even though this method has advantages such as better monitoring of temperature-dependent contact angle measurements compared with the sessile drop method, the requirement for a large volume of test liquid is an obvious disadvantage.

The Wilhelmy plate method is an indirect method for measuring surface or interfacial tension, contact angles and contact angle hysteresis. The plate refers to a thin, solid test surface fabricated in a uniform shape and homogeneous on all sides, which during the experiment is suspended vertically and gradually immersed in the test liquid (Figure 1.9a). The Wilhelmy plate apparatus consists of a highly precise balance and a height-adjustable stage on which the test liquid is placed in a vessel. The force change detected on the balance will be a combination of the force of wetting and buoyancy and is given by
F=γlvlcosθVΔρg
(1.18)

where γlvl cos θ is the wetting force, γlv is the surface tension of the test liquid, l is the wetted perimeter, θ is the contact angle, V is the volume of displaced liquid, Δρ is the density difference between the test liquid and air and g is the acceleration due to gravity. With the known surface tension of the test liquid and the test solid surface dimensions, the contact angle is measured. The advancing and receding contact angles can be measured by the wetting force of the immersion and withdrawal parts of this technique, respectively (Figure 1.9b). Since the method reduces the measurement to force, the contact angle can be measured with minimum operator error, and the contact angle obtained is already an averaged value. The method relies heavily on the precise geometry of the test surface with the prescribed dimensions that are not feasible in all cases, and studying anisotropic systems is not possible using the Wilhelmy method. The requirement for a large volume of test liquid compared with the drop shape analysis method is also a drawback. However, the Wilhelmy method provides information on the kinetics of both wetting and dewetting modes at different velocities.82 

Figure 1.9

(a) Illustration of the Wilhelmy plate method; (b) measurement steps in the Wilhelmy plate method.

Figure 1.9

(a) Illustration of the Wilhelmy plate method; (b) measurement steps in the Wilhelmy plate method.

Close modal

Different test surfaces, such as a powder, require different measurement approaches. The contact angle of powder samples is normally measured using the Washburn method, which is based on the capillary rise of a test liquid up the powder loaded in a chamber and is used to quantify the wettability. The Washburn method calculates the contact angle indirectly by measuring the uptake of the test liquid by the powder.61 Although the contact angle of a powder can be measured by the sessile drop method after compressing the powder into a tablet, this will lead to errors if the roughness of the tablet is not taken into account. Since the Washburn method relies on the capillary rise of the test liquid through the powder bed, this technique is limited to hydrophilic powders.

The capillary bridge method is another technique that utilizes capillary action. It is based on capillary bridge formation between the test surface and a liquid bath, and the capillary bridge deformation and the wetted area are investigated to characterize the surface properties.62 The capillary bridge method offers high-precision contact angle measurements and is reported to have the potential to characterize very low contact angle hysteresis. However, the inherent disadvantage of this method is that it involves coating of a transparent sample on a spherical surface, which will not be feasible in all cases.

Wettability is an unavoidable phenomenon in numerous industrial and biological processes. Research on wettability started more than 200 years ago and has progressed rapidly in the last decade, thanks to the advances in surface fabrication and modification technologies. Research in the field of surface engineering unambiguously illustrates that the wettability of a surface can be tuned from superhydrophilicity to superhydrophobicity by controlling its surface chemistry and topography. Among wettability-tailored surfaces, the fabrication of superhydrophobic surfaces is an area where intense research is in progress due to its widespread applications. Most of these fabrication approaches are inspired by the lotus-leaf surface that exhibits not only superhydrophobicity but also self-cleaning behaviour. According to Barthlott and Neinhuis, the micro- and nano-hierarchical structures with a waxy coating on the lotus leaf are the reason for its ultra-water repellency properties.83 In addition to the water repellency and self-cleaning ability of the superhydrophobic surface, properties such as flexibility, air permeability, reversibility, anisotropy and transparency/colour are critical attributes now being considered when fabricating superhydrophobic surfaces for practical applications.

Numerous approaches have been developed to create superhydrophobic surfaces. As pointed out in most of the wetting models proposed so far, enhancement of surface roughness is a critical step in creating superhydrophobicity. In practice, superhydrophobic surface fabrication is achieved via either a top-down or a bottom-up approach. The top-down approach encompasses methods such as chemical/laser/plasma etching, lithography and template-based techniques.84–93 The bottom-up approach mostly involves self-organization and self-assembly techniques such as chemical deposition, layer-by-layer deposition and colloidal assembly.94–101 In addition, there are methods based on a combination of top-down and bottom-up approaches, e.g. electrospinning and casting of polymer solutions and phase separation.102–105 

The importance of superhydrophobic surfaces is evident from their application in many diverse areas. As mentioned earlier, the self-cleaning ability of superhydrophobic surfaces is well known. In addition, a superhydrophobic surface can also be used for applications such as anti-icing, anti-fouling, anti-corrosion, anti-fogging, drag reduction and oil–water separation.27,95,106,107 These properties are desirable for various biological and industrial applications such as anti-biofouling materials for medical uses, anti-icing windows and antennas, self-cleaning windshields for vehicles, stain-resistant textiles, etc.

Despite the plethora of opportunities for superhydrophobic surfaces in diverse areas, the critical issue in this field is the durability of the fabricated surfaces. A superhydrophobic surface can lose its water-repelling nature in certain environmental conditions, hence the success of a superhydrophobic surface is greatly dependent on its ability to retain its structural features or chemical identity over time in order to resist abrasion and erosion. Durability is considered the main problem that limits the industrial/practical applications of most of the reported superhydrophobic surfaces and restricts them only to laboratory uses. The common tests used to prove the durability of a superhydrophobic surface are the following:108 (1) an underwater stability test in which the sample is usually immersed in water for a long period (∼5 h) and the superhydrophobic behaviour is checked following drying of the substrate; (2) stability in an acidic environment wherein the sample is immersed in a solution of pH 6 (the pH of rainwater) for 2 h and the wettability is checked after rinsing with deionized water and drying; (3) stability in an alkaline solution at pH 8.5 (the pH of seawater) for 2 h and the wettability is checked after rinsing with deionized water and drying; (4) stability in an ionic solution where the sample is immersed in 3.5% sodium chloride solution for 2 h and the wettability is checked after rinsing with water and drying; (5) stability in organic solvents where the sample is dipped in a polar organic solvent such as ethanol or a non-polar solvent such as toluene for 30 min and the wettability is checked after drying; (6) mechanical integrity in a test that evaluates resistance to mechanical erosion, caused by a water jet or by other means; (7) heat resistance, where the sample is heated in an oven at 100 °C for 2 h, then cooled to room temperature by natural heat exchange with the environment and the wettability is checked; and (8) UV resistance where the sample is exposed to UV irradiation for 16 h, then the damage to the surface caused by the UV irradiation is evaluated. After all these tests, if the WCA and hysteresis of the surface have remained the same, the surface is considered durable.

Research in the field of wettability is progressing rapidly. Even though several controversies exist regarding the current theoretical models of wettability and a complete understanding of this phenomenon is yet to be achieved, the fabrication of superhydrophobic surfaces is attracting increased attention owing to their potential applications. Theoretical models predict that the modification of surface chemistry and roughness can yield superhydrophobic surfaces and researchers are employing various strategies to fabricate such surfaces. In this chapter, we have discussed wetting models such as Young’s, Wenzel, Cassie–Baxter, hierarchical and fractal models, etc., and the major conflicts that exist in this field. The various approaches to measuring the water contact angle that is used to quantify the wettability and their merits and demerits have been discussed in detail and it was elucidated that the choice of method is largely context based. Finally, a brief account of superhydrophobicity and the various approaches to fabricating such surfaces and their applications has been presented and the importance of further research in this emerging research area has been unambiguously illustrated. However, it should be noted that the fabrication of stable and durable superhydrophobic surfaces is still challenging. Also, most of the fabrication approaches in most of the studies reported so far are expensive and are mostly applicable to rigid and flat surfaces. Hence large-scale production requires further progress in fabrication that is cost-effective and scalable. In addition, obtaining transparent superhydrophobic surfaces is still challenging because when the mean size of rough particles or the surface roughness is >100 nm it affects the reflectivity and causes significant scattering. Moreover, the large-scale fabrication of defect-free superhydrophobic surfaces with the existing techniques is a formidable task. Many of the reported studies lack information related to the resistance of superhydrophobicity against abrasion-induced wear. Long-term durability of transparent superhydrophobic surfaces and their poor abrasion resistance are major shortcomings. Another challenging task in this area is the condensation of water vapour on superhydrophobic surfaces, which makes them sticky rather than water repelling, especially when the roughness size scale favours condensation. In addition, when the impact of the kinetic energy of a droplet is sufficient to overcome the barrier of the air pockets in the superhydrophobic surfaces, the air may be easily removed and the surfaces could lose their superhydrophobic behaviour.

However, the advances in micro- and nanoscale fabrication technologies could circumvent many of the challenges that exist today. Future work on superhydrophobic surfaces can be multifunctional. It can combine self-cleaning properties with additional functions, such as superoleophobicity, anti-biofouling, optical transparency, oleophobicity, etc. Moreover, by exploiting the concentration enrichment capability of superhydrophobic surfaces, these substrates can find utility as analytical platforms. By integrating with plasmonic nanoparticles, the plasmonic superhydrophobic surfaces can find increasing applications in chemical and biological sensing. In addition, the drag reduction capability of superhydrophobic surfaces can be exploited in areas from microfluidics to the surfaces of airplanes.

By exploring the potential of superhydrophobic surfaces to separate active electrode materials from liquid electrolytes effectively and the consequent creation of high interfacial capacitances, these surfaces can be used as ultrahigh-energy storage centres. The intrinsic water-repelling behaviour makes superhydrophobic surfaces favourable candidates for electronics in humid environments. As most superhydrophobic surfaces are superoleophilic in nature, these surfaces could be utilized for oil–water separation. Many areas, such as solar cells, vehicle windshields, mirrors, etc., demand a coating that is transparent and anti-reflective, and superhydrophobic surfaces can find increasing applications here. Further, with the use of external electric or magnetic fields, the movement on these surfaces of droplets of fluids with electric or magnetic responsive behaviour is much easier. Recently, these surfaces have begun to find emerging applications in the areas of structural colour surfaces, anti-biofouling and corrosion resistance.

Alina Peethan and Aravind M. acknowledge the receipt of Dr T. M. A. Pai PhD fellowships from the Manipal Academy of Higher Education. S. D. G. gratefully acknowledges financial support from the Manipal Academy of Higher Education, the FIST programme of the Government of India (SR/FST/PSI-174/2012), the Department of Science and Technology, Government of India (IDP/BDTD/20/2019), and the Science and Engineering Research Board (CRG/2020/002096).

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