Understanding wetting dynamics and stability of aqueous droplet over superhydrophilic spot surrounded by superhydrophobic surface

Abstract

Patterned superhydrophilic-superhydrophobic (SHL – SHB) surfaces have shown promise in droplet-based biochemical assays. However, fundamental understanding of the behavior of liquid droplets on such patterned surfaces has not received much attention. Here, we report wetting dynamics and stability of an aqueous droplet placed over a superhydrophilic spot $(\theta ~0^{°}$) surrounded by a superhydrophobic surface ($\theta ~{160}^{°}$). We study the shape evolution (contact angle ($\theta$) and contact line diameter ($d_c$)) of an aqueous droplet placed over a horizontal SHL – SHB surface with its volume ${(V}_d)$, using experiments and analytical modeling. The results showed that depending upon the Bond number ($\mathit{Bo}$) and spot diameter ($d_s$), three different regimes: spherical cap with fixed $d_c$ and varying $\theta$ (Regime I), oblate spheroid with fixed $d_c$ and varying $\theta$ (Regime II), and oblate spheroid with varying $d_c$ and fixed $\theta$ (Regime III), are observed. The transition from Regime I to Regime II occurs for $\mathit{Bo}\mathit{~}1$ whereas that from Regime II to Regime III occurs at ${\mathit{Bo}}_{\mathit{cr}}\mathit{~}0.33d_s^{1.30}$. Analysis of the present case wherein the contact line lies at the boundary of SHL – SHB surfaces, revealed anomaly with respect to the statements of Wenzel, Cassie-Baxter and McCarthy. Further, the stability of a droplet placed over the superhydrophilic spot on an SHL – SHB angular surface is studied using experiments and analytical modeling, which showed that the competition between contact line pinning force ${(F}_p)$ and gravitational force ${(F}_g)$ governs its stability. The stable and unstable regimes are identified based on the Bond number ($\mathit{Bo}$) and spot diameter ($d_s$) and the critical Bond number for stable – unstable transition depends on spot diameter as ${\mathit{Bo}}_{\mathit{cr}}\mathit{~}0.5d_s^{-0.93}$.

Introduction

Wetting of solid surfaces is a ubiquitous phenomenon that has great relevance in our day-to-day activities as well as advanced technological applications [1]. Simple naturally occurring processes such as raindrops falling over surfaces have generated curiosity to understand the complex phenomena that decide droplet shape and critical volume before detachment from surfaces. Wetting of some of the fascinating surfaces in nature such as lotus leaves, exterior of desert beetles, eyes of mosquitos provides inspiration to study wetting of complex surfaces. Understanding of these unique surfaces has been utilized to develop special surfaces such as anti-icing surfaces [2], non-wetting cloths and containers [3] for day-to-day use.

The wetting of surfaces is mainly governed by the microstructure and chemical composition of surfaces. According to Young′s law $cos\theta =\frac{{\gamma }_{\mathit{sv}}-{\gamma }_{\mathit{sl}}}{{\gamma }_{\mathit{lv}}}$, on a smooth chemical homogeneous surface, the contact angle of a liquid depends on the surface tension of the liquid ${\gamma }_{\mathit{lv}}$, the interfacial tension between solid-liquid ${\gamma }_{\mathit{sl}}$ and surface energy of solid ${\gamma }_{\mathit{sv}}$. But according to Wenzel if we introduce roughness on a surface having the same energy system as Young, the contact angle will be enhanced [1] i.e. if the smooth surface is hydrophobic, introduction of roughness will provide more hydrophobicity and if the smooth surface is hydrophilic, roughness will offer more hydrophilicity. Later, Cassie-Baxter observed that if we keep increasing the roughness (which affects roughness ratio $r$ and solid fraction $f$), after a critical roughness ${\theta }_c$, if ${\theta }_Y>{\theta }_c$ (where $\mathit{cos}{\theta }_c=\frac{f-1}{r-f}$), droplet will not penetrate into the rough grooves but there will be entrapment of air in the grooves. So the droplet will sit on a solid-air composite surface which gives superhydrophobicity [4]. On the other hand, superhydrophilicity can occur due to capillary impregnation of liquid film through the rough grooves on a high energy surface and consequent spreading of the main liquid over the film. If we consider Cassie impregnation energy state [5] $\mathit{dE}=\left(r-f\right)\left({\gamma }_{\mathit{sl}}-{\gamma }_{\mathit{sv}}\right)dx+(1-f){\gamma }_{\mathit{lv}}dx$, the movement of the contact line is energetically favorable i.e. the precursor film will impregnate the grooves if ${\theta }_Y<{\theta }_c$, where $\mathit{cos}{\theta }_c=\frac{1-f}{r-f}$. Even on a smooth surface, superhydrophilicity is possible, if the spreading parameter $S>0$, where $S={\gamma }_{\mathit{sv}}-{\gamma }_{\mathit{sl}}-{\gamma }_{\mathit{lv}}$.

A review of the literature shows that superhydrophobic and superhydrophilic surfaces have been extensively studied. Recently, composite surfaces comprising both superhydrophobic and superhydrophilic areas patterned on a single surface have gained attention. Such composite surfaces have recently been used for various applications such as droplet-based cell culturing [6], cell trapping [7], [8], cell encapsulation [9], cell-protein interaction [9], gene expression [10], proteomics [11], selective cooling or heating [12], self-cleaning and antifogging [13], water harvesting[14] and fog collector[15]. A review of the literature clearly indicates that although composite (superhydrophobic-superhydrophilic (SHL – SHB) surfaces have been used for various applications, fundamental understanding of the behavior of liquid droplets on such surfaces is missing in the literature. By studying the wetting behavior of composite surfaces in horizontal and inclined configurations, the full potential of such surfaces can be realized.

According to Wenzel and Cassie-Baxter, wetting is a 2D phenomenon, which means contact angle of a droplet depends on the wetting condition of the contact area underneath the droplet. But according to McCarthy [16], on a composite surface, wetting is a 1D phenomenon, which means contact angle only depends on the three-phase contact line and does not depend on the liquid-solid contact area on which droplet is resting. Here we have observed that when the contact line lies at the boundary of superhydrophobic-superhydrophilic surfaces, Wenzel, Cassie-Baxter and McCarthy statements do not get satisfied. Our study showed that static contact angle is independent of surface energy, surface roughness or solid fraction when the contact line is at the boundary of SHL-SHB surfaces. When a droplet rests on a homogeneous surface, total Gibb’s free energy is the combination of three interfacial energies only, hence gravity and drop volume have no effect on equilibrium contact angle [17]. Here total Gibb’s free energy of a droplet is the sum of three interfacial energies and the potential energy thus the equilibrium contact angle is obtained by minimizing total Gibb’s free energy for a fixed drop volume. We observed that volume of droplet can affect the equilibrium contact angle below a critical Bond number (where the contact line is at the boundary of SHL-SHB surface) whereas beyond the critical Bond number (where the contact line is on SHB surface), contact angle is independent of volume.

Several experimental, numerical and analytical studies on the dynamics of liquid droplets, including drop stability, contact angle and contact line diameter with droplet volume and properties, on homogenous horizontal and inclined surfaces have been reported [18], [19], [20], [21], [22]. Thermodynamic approach has been taken to analyse such droplets on homogenous surfaces that show a significant deviation from Young, Wenzel and Cassie-Baxter relations [17]. Analysis of droplet shape on homogeneous surface has been studied using ellipsoidal model [23]. The dynamics of liquid drops on surfaces in angular configurations have relevance in paint spraying [24], liquid condensation [25] or pesticides on leaves [26]. Several studies have been carried out for studying advancing and receding contact angles on hydrophobic or hydrophilic surfaces [19], [20], [21], [22], [23], [24], [25], [26]. Although there are a few numerical studies reporting contact angle hysteresis [27], [28], there are no experimental studies on superhydrophobic ($>{150}^{°}$) or superhydrophilic ($<5^{°}$) surfaces. A review of the literature shows that although dynamics of droplets on homogenous surfaces in horizontal and inclined configurations have been well studied, studies on composite surfaces is not attempted yet.

Here, we investigate the wetting behaviour of an aqueous droplet placed over a superhydrophilic spot $(\theta ~0^{°}$) surrounded by a superhydrophobic area ($\theta ~{160}^{°}$). The variation of contact angle ($\theta$) and contact line diameter ($d_c$) of aqueous droplets of different volumes (1–500 µl) over the superhydrophilic spot of different sizes (1–5 mm) is studied using experiments and analytical model. We found that depending upon the Bond number ($\mathit{Bo}$) and spot diameter ($d_s$), three different regimes: spherical cap with fixed $d_c$ and varying $\theta$, oblate spheroid with fixed $d_c$ and varying $\theta$, and oblate spheroid with varying $d_c$ and fixed $\theta$, are observed. Depending on the application, spot diameter and drop volume can be independently varied to operate in the desired regime. For example, the spherical cap regime can be used for fabrication of microlenses [29] of different base diameters and curvatures simply by changing the spot (superhydrophilic) diameter and drop volume. Similarly, droplets of large volumes can be placed in a stable configuration (either in spherical cap or oblate spheroid regime) over an array of superhydrophilic spots of a fixed diameter, surrounded by superhydrophobic area, without spreading – to create large array liquid elements similar to the 96-well plate – for various biochemical applications. For the contact line at the boundary of SHL – SHB surfaces, a departure from Wenzel, Cassie-Baxter and McCarthy statements was observed. Further, we have studied the stability of a droplet placed over a superhydrophilic spot on an angular SHL-SHB surface using experiments and analytical model, which showed that the competition between contact line pinning force ${(F}_p)$ and gravitational force ${(F}_g)$ govern its stability.