Discrete Dynamics in Nature and Society

Volume 2016, Article ID 8517309, 9 pages

http://dx.doi.org/10.1155/2016/8517309

## Dynamic Behaviors and Energy Transition Mechanism of Droplets Impacting on Hydrophobic Surfaces

School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, China

Received 23 December 2015; Accepted 3 April 2016

Academic Editor: Luisa Di Paola

Copyright © 2016 Qiaogao Huang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The wettability of hydrophobic surfaces and the dynamic behaviors of droplets impacting on hydrophobic surfaces are simulated using a lattice Boltzmann method, and the condition for the rebound phenomenon of droplets impacting on solid surfaces is analyzed. The results show that there is a linear relationship between the intrinsic contact angle and the interaction strength of fluid-wall particles. For hydrophobic surfaces with the same intrinsic contact angle, the micromorphology can increase the surface hydrophobicity, especially the hierarchical micromorphology. The dynamic behaviors of droplets impacting on solid surfaces are affected by the wettability. The surface hydrophobicity is stronger, and the rebound phenomenon occurs easier. If the droplet’s kinetic energy is greater than the sum of the surface energy and the minimum conversion gravitational potential energy when the spreading and shrinking finish, the rebound phenomenon will occur. As the hydrophobic surface’s viscous dissipation is much smaller than the hydrophilic surface’s, the droplet still has high kinetic energy after the spreading and shrinking, which is advantageous to rebound for droplets.

#### 1. Introduction

Recently, more and more researches demonstrate that hydrophobic surface has a good applied prospect in aspects of fluid drag reduction, flow noise reduction, anticontamination, anticorrosion, and so forth [1–3]. For instance, it is used as drag reduction and anticontamination coating of pipe’s inner surface and ship’s hull, as self-cleaning coating of exterior walls and satellite receivers, and as anti-icing and antifrosting coating of components of aeronautics and astronautics, which, with no exception, are related to the movement of droplets on hydrophobic surfaces, especially the dynamic behaviors of droplets impacting on hydrophobic surfaces. Davidson [4] investigated droplets impinging on solid surfaces using a boundary integral method. Pasandideh-Fard et al. [5] simulated the solidification of molten metal droplets on both horizontal and inclined stainless steel surfaces with VOF (Volume of Fluid) and continuous surface tension model. Fujimoto et al. [6] also employed VOF to study the effect of the impact angle on the deformation behavior of droplets. Although several computational models for studying the dynamic behaviors of droplet impacting on solid surface have been developed by researchers, the difficulty of this issue still relies on how to accurately track the position of the free surface. Lattice Boltzmann method, as a new computational fluid method, operates on both mesoscopic and macroscopic levels successfully. In particular, when things come to the numerical simulation of multiphase and multicomponent fluid flows, Shan-Chen model of lattice Boltzmann method can realize thermodynamic phase transition easily with an appropriate potential function [7, 8]. Huang et al. [9] studied the movement of a droplet inside a grooved channel using lattice Boltzmann method. Shi et al. [10] simulated numerically the droplet motion driven by Marangoni effect, which is induced by surface tension gradient on solid-liquid interface with LBM. However, their main concern was the movement of droplets on solid surfaces, and little attention was paid on the hydrodynamic behaviors and energy transition mechanism of droplets impacting on solid surfaces. Hence, this paper investigates the dynamic behaviors of droplets impacting on solid surfaces with different wettability using LBM and discusses the occurring condition of droplets bouncing when the solid surface gets hit from the view of energy.

#### 2. Numerical Method

##### 2.1. Lattice Boltzmann Method

Lattice Boltzmann method, based on mesoscopic kinetic models, has developed into an alternative and promising numerical scheme for simulating fluid flows in recent years. Lattice Boltzmann method, presented in this paper, is based on the streaming and collision of discrete particle density distribution function in the fixed lattice point, and the corresponding evolution function is expressed as [11]where is the particle density distribution function, which depends on position , the particle discrete velocity , and time , is the equilibrium distribution function, and is the dimensionless relaxation time related to the hydrodynamics viscosity.

The left-side of lattice Boltzmann equation represents the streaming of particles, while the right-side represents the collision process, which makes heading for the equilibrium distribution . In D2Q9 model [11], the equilibrium distribution is given by

The discrete velocities are set aswhere is lattice velocity; and are the lattice length and the time step, respectively; is the sound speed in the discrete model, and the weighting factors depend on the link angle ( (); (); ()).

The macroscopic density and velocity are defined as follows:

The macroscopic pressure is given by directly.

##### 2.2. Shan-Chen Model

To introduce intermolecular forces between microscopic particles, Shan and Chen proposed a pseudopotential model [12, 13], which easily coupled microforces, the dominant role of microflow problems. The model reflects the physical nature of fluid dynamics and broadens the application of lattice Boltzmann method in range of simulation of microflow on complex surface with wettability. In Shan-Chen model, fluid particles at site of receive forces from nearest neighbor fluid particles and solid walls, which are written in the following form, respectively:

in (5) is the interaction strength, and in (6) is called adsorption parameter, representing the strength of the force contributed by solid. Varying the parameter allows simulation of different solid surface wettability, where is a “switch” that takes on value one if the site at is a solid and is zero otherwise. is the same direction-dependent weighting factor used before. is the interaction potential function, which must be monotonically increasing and bounded. Therefore, the equation used in this paper is expressed as .

In Shan-Chen model, the effect of interparticle forces is incorporated into the equilibrium distribution function by shifting the equilibrium velocity :

The equation of state is given by

#### 3. Numerical Simulation of the Wettability of Hydrophobic Surfaces

A key parameter for characterizing the wettability of hydrophobic surface is the apparent contact angle, which is mainly determined by material properties and micromorphology. This provides a new research route: first, determine the relationship between the adsorption parameter and the intrinsic contact angle at a specific interaction strength by simulating the contact angle of a smooth solid surface; then construct microtopography on the surface and simulate the apparent contact angle of real solid surface.

##### 3.1. Determining the Intrinsic Contact Angle

The intrinsic contact angle of the smooth solid surface is adjusted by changing the adsorption parameter for a specific interaction strength . The computational domain is a rectangular space of lattice units, and a lattice units is approximately 1.2 *μ*m in physical scale. Dimensionless time , and gravity acceleration . Periodic scheme is used in the left and right boundaries, while no-slip bounce back scheme is used in the top and bottom boundaries. A circular liquid droplet with a diameter of 150 is placed in the middle of the bottom wall.

By the different forces from the solid wall, the fluid drops show different shapes when the system reaches equilibrium. Shapes and contact angles of droplets for different absorption coefficients are shown in Figure 1. The result of fitting and in Figure 2 illustrates that there is a linear relationship between and , and decreases with the increase of . The fitting result is expressed as the linear equation