Droplet impact on nano-textured bumps: Topology effects

Highlights

• The droplet impact on super-hydrophobic nano-textured bumps is investigated.

• The dynamics of droplet impact on smooth and textured bumps are explained.

• The impact conditions satisfied by the bump geometrical parameters and the droplet Weber number for the Cassie state are explored.

Abstract

Using the lattice Boltzmann method (LBM), the dynamics of a single droplet impacting on desert-beetle inspired, super-hydrophobic, nano-textured bumps was numerically investigated. The focus was placed on the effects of post height, inter-post spacing, bump radius of curvature and impact velocity represented by the Weber number. Three droplet states after the impact were captured, i.e., the suspended Cassie state, the sticky Wenzel state and rebound. The interfaces among these states were then determined in parametric maps generated from the current study. Since the droplets in the Cassie state can be easily removed from the surface and thus favorable for water collection. The conditions satisfied for this state by the geometrical parameters and the Weber number were explored. The results showed that, at moderate impact speeds, droplets impacting on nano-textured bumps with sufficiently high posts or sufficiently small inter-post spacing were generally in the Cassie state and hence favorable for water collection. If these conditions are satisfied, the bump surface curvature only plays a marginal role.

Introduction

Water demand is ever increasing with world's growing population. Around one third of total population are facing water shortage problem [1]. In such a situation fog harvesting can be a viable, sustainable and potential source of water. In nature plants and animals have skilled the survival abilities to collect water from fog. For example, the Namib desert beetles can live in area with very little rainfall [2]. Their back is composed of bumpy hydrophilic/super-hydrophobic patterns, i.e., the hydrophilic bumps are surrounded by super-hydrophobic valleys featuring microstructures of flattened hemispheres, which assist in collection of passing by fog droplets [3].

Inspired by this kind of beetles, several surfaces have been mimicked and investigated for condensation process [4], [5], [6], [7]. However, in fog harvesting process, droplet impact is another leading phenomenon for water collection [8]. Therefore, a surface with the best overall water collection efficiency should perform well for both condensation and droplet impact processes.

Droplet impact on smooth as well as textured surfaces has been widely investigated. Normal impacts have been comprehensively reviewed by Yarin [9]. In addition to level surfaces, several works on single and multiple droplets impact on inclined surfaces have also been conducted in the past [10], [11], [12], [13], [14]. Recently, several studies have been conducted to investigate droplet impact on smooth convex surfaces [15], [16], [17]. Liu et al. [16] studied droplet impact on Echevaria leaves, which have convex/concave architecture. Their results showed nearly 40% reductions in contact time owing to asymmetric bounce off. Khojasteh et al. [17] studied droplet impact on hydrophobic and super-hydrophobic hemispherical surfaces and focused on the effects of Weber number, surface curvature and contact angle. They found higher area of liquid in contact with the hemispherical surface compared to flat surfaces.

Apart from smooth surfaces, droplet impact on level textured surfaces has also been investigated [18], [19], [20], [21], [22], [23], [24], [25], [26]. Wang et al. [23] investigated water droplet impacts on super-hydrophobic carbon nanotube arrays with different wetting properties, and found droplet rebound at contact angle 163° and no rebound at contact angle 140° Aria and Gharib [24] studied droplet impact dynamics on super-hydrophobic carbon nanotube arrays by focusing on the critical Weber number, coefficient of restitution, spreading factor and contact time. Their results showed excellent water repellency with no droplet pinning. Kwak et al. [25] looked at the effects of droplet velocity, surface wettability, Weber number and the surface free energy on droplet impact on nano-textured surfaces, and developed a relationship for transitions from rebound to wetting and from rebound to splashing regimes. Tsai et al. [26] experimentally investigated droplet impingement on super-hydrophobic surfaces with similar contact angles but different surface roughness, i.e., one surface with regular polymeric micro-patterns and the other with rough carbon nanofibers. Similar outcomes, including the Cassie state, complete rebound, partial rebound, trapping of an air bubble, jetting, and sticky vibrating water balls, were observed at small Weber numbers for both surfaces. However, at larger Weber numbers, the splashing impacts forming several satellite droplets were observed to be more favorable for rough carbon nanofiber surfaces.

Besides, Shen et al. [27] studied millimeter-scale droplet impingement on a convex super-hydrophobic surface consisting of hierarchical micro-nano structures, and found quicker rebound compared to flat surfaces and a reduction of 28.5% in the contact time. However, in their study effects of post dimensions such as inter-post spacing, post width and height, surface curvature and impact velocity were not investigated.

Different from the above studies, the current work is focused on fog droplet impact dynamics on micro-scale bumps with nanotextures, inspired from desert beetle super-hydrophobic surface's micro-scale hemispherical bumps. The state of droplet subsequent to the impact can be crucial to water collection. A droplet impacting on nano-textured bumps can either rebound or deposit. The rebounding droplet jumps back to atmosphere, and is hence lost, which reduces the water collection rate. On the other hand, the deposited droplet can have two possible states: the Cassie–Baxter state (droplet remains suspended on the nanostructures) or the Wenzel state (droplet penetrates the nanostructures and touches the bottom surface). Droplet in the Cassie state can be easily removed from the surface and thus more favorable for water collection, while the wetting and rebounding droplets may degrade the surface's water collection efficiency. The state of droplet after the impact depends on the bump geometrical parameters and impact velocity. Therefore, in the present study the focus is placed on the effects of Weber number, post height, inter-post spacing and bump surface curvature on the droplet impact dynamics. We aim to find the relationships between bump geometrical parameters and Weber number, so as to determine the parameter ranges where the Cassie state is promoted. These parameter ranges are helpful in the design of bumps for better water collection.