Numerical procedure for simulation of multicomponent and multi-layered phase diffusion

Abstract

A mass balance error-free numerical procedure for simulation of multicomponent and multi-layered phase diffusional reactions has been suggested, based on an explicit fixed grid finite difference method. Basically, a local equilibrium was assumed at each phase interface and one dimensional movement of interfaces was considered. Attention was paid to the treatments of newly formed thin phase layers and different molar volumes among interacting phases, together with the removal of a mass balance error. Specially derived finite difference forms were used to treat phase layers thinner than two inter-grid distances. A new flux balance equation which is independent from the molar volume differences among phases and leaves no mass balance error was developed by a transformation of space variable system and by a systematic analysis of sources of mass balance error, respectively. Through some model simulations, it could be shown that the present numerical procedure cantreat multi-layered phase diffusion including thin layered phases and can reproduce transitions of layer sequences during diffusional reactions successfully, leaving no mass balance error.