Lattice Boltzmann simulation of a water droplet penetrating a micropillar array in a microchannel

Abstract

Water droplets penetrating a microchannel equipped with an array of micropillars are commonly seen in engineering applications, ranging from micro-electro-mechanical systems to macro-heat-transfer facilities. Understanding the detailed droplet dynamics in this process is therefore beneficial to the advancement of many fields of industry. In this study, we adopt a nonorthogonal multiple-relaxation-time lattice Boltzmann model to simulate a water droplet penetrating a micropillar array in a microchannel. We first validate our model against the experimental results of (a) off-center impact of a water droplet on a ridged superhydrophobic surface and (b) impact of a water droplet on a curved superhydrophobic surface. Then a comprehensive parametric study is carried out by changing the droplet initial velocity, opening fraction of the micropillar array, and wettability of the micropillar surface. It is found that when the droplet penetrates the micropillar array, its fingering dynamics in the longitudinal direction is governed by the competition between the dynamic and capillary pressures, while the permeation process in the lateral and vertical directions is dominated by the capillary effect. The change of the droplet initial velocity and configuration setup can significantly influence the droplet penetration velocity, maximum wetted surface area, and penetration rate. Finally, a theoretical model is proposed to describe the transient evolution of the droplet penetration mass for a variety of Weber numbers, opening fractions, and static contact angles.