Abstract
Based on the phase-field method, the problem of two-phase flow in a micro-fluidic device and the interaction of the fluid components with a wall are discussed, and the transport equations for the two-phase flow given. Then, a numerical technique to solve equations for micro-fluidic quadrate devices is proposed by the finite difference method, and the numerical simulation of the flow and deformation of a droplet and multiple droplets in a cubic pipe demonstrated. It is found that the dimensionless constants Pe, Ca are important parameters, and affect the deformation of the droplet. The deformation of the droplet increases with high Pe. If the parameter Ca is between 0.35 and 0.50, the curvature at the end of the droplet decreases gradually from a positive value to negative, and become concave at the end.