Wall-bounded multiphase flows of N immiscible incompressible fluids: consistency and contact-angle boundary condition

TL;DR

This paper introduces a thermodynamically consistent phase field model and boundary conditions for simulating wall-bounded multiphase flows with multiple immiscible fluids, ensuring reduction consistency and accurate contact-angle behavior.

Contribution

The work develops a generalized N-phase model with reduction-consistent boundary conditions and an efficient numerical algorithm for simulating complex multiphase flows with wettability effects.

Findings

The model accurately predicts contact angles and wettability effects.

Simulation results agree with de Gennes theory for drop spreading.

The method handles multiple fluid components and solid-wall interactions effectively.

Abstract

We present an effective method for simulating wall-bounded multiphase flows consisting of $N$ ($N\geqslant 2$) immiscible incompressible fluids with different densities, viscosities and pairwise surface tensions. The N-phase physical formulation is based on a modified thermodynamically consistent phase field model that is more general than in a previous work, and it is developed by considering the reduction consistency if some of the fluid components were absent from the system. We propose an N-phase contact-angle boundary condition that is reduction consistent between $N$ phases and $M$ phases ($2\leqslant M\leqslant N-1$). We also present a numerical algorithm for solving the N-phase governing equations together with the contact-angle boundary conditions developed herein. Extensive numerical experiments are presented for several flow problems involving multiple fluid components and solid-wall boundaries to investigate the wettability effects with multiple types of contact angles. In particular, we compare simulation results with the de Gennes theory for the contact-angle effects on the liquid drop spreading on wall surfaces, and demonstrate that our method produces physically accurate results.