A thermodynamically consistent and conservative diffuse-interface model for gas-liquid-solid multiphase flows

TL;DR

This paper introduces a thermodynamically consistent diffuse-interface model for gas-liquid-solid multiphase flows, incorporating a novel free energy formulation, a solid phase indicator, and a lattice Boltzmann method for simulation.

Contribution

It proposes a new ternary phase-field based free energy and a solid phase indicator within a conservative diffuse-interface framework for multiphase flows.

Findings

The model accurately captures interface dynamics and wetting properties.

Energy dissipation is validated in stationary geometries.

Simulations demonstrate effectiveness in complex geometries and multiphase interactions.

Abstract

In this work, a thermodynamically consistent and conservative diffuse-interface model for gas-liquid-solid multiphase flows is proposed. In this model, a novel free energy for the gas-liquid-solid multiphase flows is established according to a ternary phase-field model, and it not only contains the standard bulk and interface free energies for two-phase flows, but also includes some additional terms to reflect the penalty in the solid phase and the wettability on the solid surface. Furthermore, a smooth indicator function of the solid phase is also introduced in the consistent Navier-Stokes equations to achieve a high viscosity in the solid phase and preserve the velocity boundary conditions on the solid surface. Based on the proposed diffuse-interface model, the fluid interface dynamics, the fluid-structure interaction, and the wetting property of the solid surface can be described simply and efficiently. Additionally, the total energy is also proved to be dissipative for the two-phase flows in the stationary geometries. To test the present diffuse-interface model, we develop a consistent and conservative lattice Boltzmann method and conduct some simulations. The numerical results also confirm the energy dissipation and good capability of the proposed diffuse-interface model in the study of two-phase flows in complex geometries and gas-liquid-particle multiphase flows.