Numerical Simulation of Drop Coalescence in the Presence of Inter-Phase Mass Transfer

Abstract

A numerical method for simulation of the deformation and drainage of an axisymmetric film between colliding drops in the presence of inter-phase solute transfer at small capillary and Reynolds numbers and small solute concentration variations is presented. The drops are considered to approach each other under a given interaction force. The hydrodynamic part of the mathematical model is based on the lubrication equations in the gap between the drops and the Stokes equations in the drops, coupled with velocity and stress boundary conditions at the interfaces. Both drop and film solute concentrations, related via mass flux balance across the interfaces, are governed by convection-diffusion equations. These equations for the solute concentration in the drops and the film are solved simultaneously by a semi-implicit finite difference method. Tests and comparisons are performed to show the accuracy and stability of the presented numerical method.