LBM Simulation of a Droplet Dripping Down a Hole

Abstract

A droplet dripping through a hole, which is located on a horizontal plate, was simulated in the current work. To overcome the numerical instabilities and accommodate the high density and viscosity ratios, Lee’s LBM model was used to simulate the two-phase flow. Also wettability effect was taken into account by imposing the contact angle between solid-liquid and gas phases using Cahn’s wetting theory. The effects of gravitational acceleration, surface tension, equilibrium contact angle, viscosity ratio, density ratio, and also the geometrical parameters, such as the height and width of the hole, have been investigated separately. In addition to numerical results, high numerical stability and ease of using surface tension and contact angle for controlling fascinated the authors to model this problem. High numerical stability in capturing the remaining fine particles on the surface and slender strip of a droplet passing through a small hole is a significant contribution. The results show that gravitational force and adhesion force caused by surface tension, are opposing forces influencing droplet behaviour. Enhancing the contact angle to more than 90 degrees makes the surface hydrophobic and the droplet will drip under gravitational force. Also increasing the surface tension causes increasing adhesion force, which leads to droplet decay. In this case some parts of the droplet will remain on the surface.