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Dynamics of spreading on ultra-hydrophobic surfaces.

Abstract Despite the extensive variety of applications for ultra-hydrophobic surfaces in industry, technology, and biology, due to their wetting characteristics, there has not been considerable attention in the area of dynamics of wetting on ultra-hydrophobic surfaces. In this research, the experimental investigations have been done by applying forced spreading of several polyethylene-glycol/water mixtures in different weight ratios on Teflon plates and ultra-hydrophobic sprayed glass substrates. Hydrodynamics theory and molecular-kinetic theory have been applied to investigate the dynamics of wetting on these substrates. It has been found that the dynamics of receding motion of liquid contact line on ultra-hydrophobic surfaces could be described perfectly with the molecular-kinetic theory. In the case of advancing motion on an ultra-hydrophobic surface, dynamic contact angle is independent of liquid contact line velocity. The advancing and receding motions of liquid contact line on smooth Teflon plates followed molecular-kinetic theory.

Keywords Wetting dynamics, Ultra-hydrophobic surface, Hydrodynamics, Molecular-kinetic theory, Dynamic contact angle

Introduction

Low-energy surfaces are surfaces on which water does not spread completely and instead it forms a droplet on the surfaces with large contact angles in the range of 40[degrees] and 140[degrees] (e.g., hydrophobic) and equilibrium contact angles larger than 140[degrees] (e.g., ultra-hydrophobic surfaces). Ultrahydrophobic surfaces can be sufficiently described as having extreme water repellency characteristics. Controlling the surface wettability of hydrophobic and super hydrophobic surfaces has extensive industrial applications ranging from coating, painting and printing technology, satellite communications technology, self-cleaning characteristics due to the large water repellency of ultrahydrophobic surfaces, and waterproof clothing to efficiency increase in power and water plants. The high demand for ultra-hydrophobic surfaces in every aspect of daily life requires enhancing the knowledge of their dynamics of wetting and having an adequate understanding of the underlying physics of liquid contact line motion on such surfaces. There has been considerable attention on the spreading phenomena both experimentally (1-31) and theoretically (9,32-49) for hydrophilic (high-energy surfaces) and hydrophobic surfaces (low-energy surfaces) for a long period of time. It has been claimed that spreading dynamics on such surfaces follow either hydrodynamics (4,9,33,38,39) (e.g., due to viscous dissipation in the bulk motion of liquid) or molecular-kinetic theory (40,41) (e.g., dissipation due to friction from molecular attachment/ detachment at the vicinity of liquid contact line on solid surface). Hydrodynamics theory (4,9,33,38,39) focuses on the bulk motion of liquids by applying the assumption of lubrication approximation and describes the dynamics of wetting based on the following dynamic contact angle dependency to capillary number.

Hydrodynamics theory for advancing motion

[[theta].sup.3.sub.A] - [[theta].sup.3.sub.0A] = [alpha]Ca (1)

Hydrodynamics theory for receding motion

[[theta].sup.3.sub.0R] - [[theta].sup.3.sub.R] = [alpha]Ca, (2)

where [[theta].sub.A] is the advancing dynamic contact angle; [[theta].sub.R] is the receding dynamic contact angle; [[theta].sub.0A] is the equilibrium advancing contact angle; [[theta].sub.0R] is the equilibrium receding contact angle; capillary number, Ca = [mu]U/[sigma], which shows the relative importance of viscous force to capillary force; [mu] is the dynamic viscosity of liquid; U is the liquid contact line velocity; and [sigma] is the surface tension of the liquid mixture. Front factor [alpha] is a constant that depends on the physical properties of the liquid mixture (e.g., dynamic viscosity and surface tension) and velocity of liquid contact line.

Molecular-kinetic theory (40,41) focuses on the molecular attachment/detachment at the liquid contact line and considers both solid properties and liquid properties to describe the dependency of dynamic contact angles to the contact line velocity. Blake (40,41) used the activated reaction rate theory by Glasstone, Laidler, and Eyring (50) to describe the molecular adsorption/ desorption of the adsorption sites on the solid surface at the vicinity of liquid contact line based on the following model:

[theta] = [cos.sup.-1] {cos [[theta].sub.0] [+ or -] [2k.sub.B]T /[sigma][[lambda].sup.2] [sinh.sup.-1] (U/2[K.sub.w][lambda])} (3)

The minus sign refers to the advancing motion of the liquid contact line and the plus sign refers to the receding motion of the liquid contact line. [theta] is the dynamic contact angle, [theta].sub.0] is the equilibrium contact angle, [k.sub.B] is the Boltzmann constant, T is the temperature, [K.sub.w] is the equilibrium frequency of molecular adsorption/desorption at the liquid contact line, and [lambda] is the average distance between centers of adjacent adsorption sites on the solid surface where liquid molecules attach/detach. [K.sub.w] and [lambda] are the two fitting parameters in addition to physical properties of liquid mixture that are used to investigate the validity of the molecular-kinetic model on describing the dynamics of wetting of motion of liquid contact line.

Surprisingly, there has not been any research on modeling the dynamics of wetting on ultra-hydrophobic surfaces despite their extensive variety of applications in several areas of daily life, technology and science, etc. In this research, we have done experimental investigations on the forced spreading dynamics on ultra-hydrophobic surfaces by applying hydrodynamics theory and molecular-kinetic theory. The analytical results obtained from the investigation on dynamics of wetting on ultra-hydrophobic surfaces have been compared with the analytical results obtained from the investigation of the dynamics of wetting on hydrophobic surfaces.

Experimental methods and materials

Sample preparation

We performed the experiments on three different mixtures of polyethylene glycol (PEG) mixed with pure water in different weight ratios, with almost the same surface tension but with different dynamic viscosities of liquid mixtures, to see the effect of the dynamic viscosity of the liquid mixtures on the dynamics of wetting of ultra-hydrophobic surfaces. The dynamic viscosities of all three PEG/water mixtures were measured using a stress-controlled rheometer. All three PEG/water mixtures exhibited Newtonian behavior, as shown in Fig. 1.

The densities of all PEG/water mixtures were also measured using the tensiometer. The surface tension of all PEG/water mixtures was measured using both the tensiometer, applying the ring-tear off method, and the Wilhelmy plate method. Table 1 shows the physical properties of PEG/water mixtures used in the experiments.

The solid substrates that were used to do the experimental investigation of wetting dynamics were smooth Teflon plates and ultra-hydrophobic sprayed glass (e.g., glass was sprayed uniformly on both sides using WX2100 paint). WX2100 paint is manufactured by Cytonix Corporation. WX2100 is an aerosol paint spray which is composed of mineral spirits and fluoropolymers that are driven by a mixture of propane and butane. A glass substrate with dimensions of 50 x 24 x 0.15 [mm.sup.3] (VWR microcover glass) was coated with WX2100 paint. Before coating the glass substrate, the can of WX2100 was shaken for 30 s. Then the can was held vertically, approximately 30 cm away from the glass substrate during spraying the WX2100 paint spray on the surface of the glass. The spraying was done evenly on the glass surface to cover all parts of the glass surface. After coating one side of the glass substrate with WX2100 paint, the coated surface was allowed to dry for at least 2 h. Then the same procedure was done on the other side of the glass. The glass substrate coated with WX2100 became ultra-hydrophobic.

Experimental technique

Force balance method (e.g., Wilhemy plate method) using the tensiometer was applied to perform the experiments for forced spreading mechanism. A tensiometer, which was manufactured by KRUSS GMBH, was used to conduct the measurement of the advancing dynamic contact angle and receding dynamic contact angle by moving the sample platform, which held the pool of liquid, upward and downward, as shown in Fig. 2. A force sensor measured the Measured Force applied on the plate of solid substrate from the solid plate holder, which was connected to the force sensor from the top and it held the solid plate from the bottom, and then the tensiometer software calculated the advancing dynamic contact angle and receding dynamic contact angle using the theoretical formula relating the Measured Force applied on the plate to the advancing and receding dynamic contact angles. The tensiometer applied the analytical method through the force balance method (i.e., Wilhelmy plate method) on the forces applied on the solid plate during the experiment to conduct the dynamic contact angle measurements (i.e., both advancing dynamic contact angle and receding dynamic contact angle). There were four forces which were considered to be applied on the solid plate during its immersion into the pool of the liquid and its immersion from the pool of the liquid. These forces were Capillary Force, [f.sub.capillary], (i.e., due to surface tension of the liquid), the Buoyancy, [f.sub.Buoyancy] due to difference in density of solid plate and density of liquid, Measured Force, [f.sub.measured], (he., tension force from the solid holder which is being measured by tensiometer force sensor) and the Gravity, [f.sub.gravity], (i.e., due to the weight of the solid plate). The Gravity was calibrated at the onset of touch of the edge of the solid plate with the liquid-air interface; hence, the Gravity was not considered during the force measurement and dynamic contact angle measurement. As a result, equation (4) has been applied in the tensiometer software to measure the advancing and receding dynamic contact angle during the experiment.

[f.sub.Measured] + [f.sub.Capillary] + [f.sub.Buoyancy] = 0 (4)

The Capillary Force and Buoyancy Force were evaluated using equations (5a) and (5b) which are shown as follows:

[f.sub.Capillary] = 2[sigma](w + t) COS [theta] (5a)

[f.sub.Buoyancy] = [rho]gwtx (5b)

In equations (5a) and (5b), w is the width of the solid plate, t is the thickness of the solid plate, [sigma] is the surface tension of the liquid, [rho] is the density of the liquid, g is the gravitational acceleration, [theta] is the dynamic contact angle (i.e., advancing or receding dynamic contact angle), and x is the immersion depth at each instant of the experiment. The speed of the motion of the sample platform was set to a constant specific speed for each experiment to have a steady motion of the sample platform during measurement and to control the speed of the three-phase contact line. All experiments were performed at room temperature.

Results and discussion

The spreading dynamics on hydrophobic surfaces follow the molecular-kinetic theory for both advancing and receding motion, as shown in Fig. 3. Figure 3 shows the dependency of the dynamic contact angle to the contact line velocity for the forced spreading experiments done for two different weight ratios of mixtures of PEG/water on smooth Teflon plates using tensiometer equipment applying the Wilhelmy plate method. The general form of hydrodynamics theory was also applied to investigate the dynamics of wetting on a hydrophobic surface (e.g., smooth Teflon plate) and we found that the hydrodynamics theory is not an appropriate model to describe the dynamics of wetting on smooth Teflon plates on complete range of contact line velocity.

For the case of ultra-hydrophobic surfaces, the dynamics of wetting showed a completely different behavior. The dynamics of wetting (e.g., dynamic contact angle variation vs contact line velocity) for receding motion is not the same as the dynamics of wetting for advancing motion for the same system of solid/liquid/vapor in the same experiment as obtained from tensiometer measurements. The advancing dynamic contact angle is almost independent of the capillary number and it is almost a constant value for the whole range of contact line velocity especially for a large contact line velocity range. As it is shown in Fig. 4, only for a very low contact line velocity range, the dynamic contact angle decreases as the contact line velocity increases with a very small slope due to the effect of stick-slip behavior which most likely occurred for the ultra-hydrophobic surfaces and beyond that low contact line velocity; the advancing dynamic contact angle is independent of the liquid contact line velocity for the rest of velocity range.

For the case of the receding motion of the liquid contact line on ultra-hydrophobic surfaces, hydrodynamic theory could not be applied to describe the dynamics of wetting. The molecular-kinetic theory, which focuses on the molecular attachment/detachment at the vicinity of the liquid contact line, has been found to be the best model to describe the dynamics of wetting on ultra-hydrophobic surfaces. Figure 5 shows the details of the fitting of molecular-kinetic theory on the experimental results obtained for receding motion of ultra-hydrophobic surface in the pool of PEG/water liquid mixture. This is due to the fact that the molecular-kinetic theory focuses on both solid and liquid properties to describe the dependency of dynamic contact angles to the liquid contact line velocity.

Conclusions

The molecular-kinetic theory was the appropriate model to describe the dynamics of wetting on hydrophobic surfaces for both advancing and receding motion, as was shown for the forced spreading experiments on smooth Teflon plate into/out of the pool of PEG/water mixtures. The equilibrium advancing contact angles of the PEG/water liquid mixtures on ultra-hydrophobic surfaces are above 140[degrees] and there is a small window of variation for the advancing dynamic contact angle to change by increasing the liquid contact line velocity on ultra-hydrophobic surfaces. Due to this fact, the advancing dynamic contact angle of the PEG/water mixtures on ultra-hydrophobic surfaces is independent of the contact line velocity. The molecularkinetic theory was the best model to describe the dynamics of wetting on ultra-hydrophobic surfaces for receding motion since the molecular-kinetic theory focuses on the liquid molecular displacement at the vicinity of the liquid contact line by considering both properties, solid substrate and liquid properties. Hydrodynamics theory is not an appropriate model to describe the dynamics of wetting on ultra-hydrophobic surfaces since the liquid contact line on the ultrahydrophobic surface is most likely moving on the liquid/air interface where shear stress is negligible and the lubrication approximation is not valid to be used to describe the dynamics of wetting.

DOT 10.1007/s11998-015-9686-z

A. Mohammad Karim ([mail]), H. P. Kavehpour

Department of Mechanical and Aerospace Engineering,

University of California, Los Angeles, CA 90095-1597, USA

e-mail: alireza.m.k.2010@gmail.com

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Table 1: The measured physical properties of the PEG/water
mixtures used in forced spreading experiments with a
tensiometer

                                      Dynamic    Surface
                      Density (kg/   viscosity   tension
Liquid sample          [m.sup.3])     (Pa.s)      (N/m)

10 wt% PEG/water          1012        0.0607      0.054
12.5 wt% PEG/water        1018         0,081      0.048
20 wt% PEG/water          1031        0.1295      0.052


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Author:Karim, A. Mohammad; Kavehpour, H.P.
Publication:Journal of Coatings Technology and Research
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Date:Sep 1, 2015
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