Generalized Fickian approach for phase separating fluid mixtures in Smoothed Particle Hydrodynamics

Abstract

In the preparation process of porous polymer membranes, multi-component mass transfer during phase separation leads to the formation of pores. In this paper, we study the Generalized Fickian approach for a phase separating ternary fluid mixture using the Smoothed Particle Hydrodynamics (SPH) method. The thermodynamics are based on the Flory–Huggins equation of state for polymer mixtures with different molar weight and density of the components.We present a validation of the discrete balance equation and study the effect of different molar weight and density on the accuracy of the method separately by considering phase separation in a periodic box in two dimensions. We analyze the mass fraction distribution and the time-evolving reduction of the amount of interface using a mapping scheme based on the rheological Doi–Ohta model. We find good agreement with the diffusion-dominant power law for coarsening. Finally, we apply the proposed SPH model on a realistic Polyvinylidenfluorid/Dimethylformamid/water system. The corresponding, composition-dependent diffusion coefficients are estimated using molecular dynamics simulations.