Generalized Fickian approach for phase separating fluid mixtures in smoothed particle hydrodynamics. (English) Zbl 1411.76135
Summary: 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.
MSC:
| 76M28 | Particle methods and lattice-gas methods |
| 65M75 | Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs |
| 76T99 | Multiphase and multicomponent flows |
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