An analytical model for micro-droplet steady movement on the hydrophobic wall of a micro-channel

Based on a macroscopic force balance analysis, an analytical solution in terms of dynamic contact angle is obtained for steady velocity of a droplet driven by a shear flow and moving on the hydrophobic wall of a microchannel. The multiphase free-energy 3-D Lattice Boltzmann method (LBM) is applied to simulate the deformation of the droplet in order to obtain the dynamic contact angle of the moving micro-droplet in the analytical solution. The droplet velocities predicted by the analytical solution are found in good agreement with the LBM simulation results.