A diffuse-interface method for the containerless freezing of three-phase flows in complex geometries

TL;DR

This paper introduces a diffuse-interface model and a lattice Boltzmann method for simulating three-phase freezing processes in complex geometries, accurately capturing phase changes, wettability, and volume variations.

Contribution

It develops a unified diffuse-interface framework combined with a lattice Boltzmann method to simulate multiphase freezing in complex geometries, including wettability and volume change effects.

Findings

Numerical results agree with experimental data and theoretical solutions.

The method effectively simulates freezing in complex geometries like fractures and porous media.

The approach is efficient for multiphase freezing processes in complex systems.

Abstract

In this work, we first propose a diffuse-interface model for the freezing processes of three-phase flows in complex geometries, and the core of the model to intergratge the Navier-Stokes equations for fluid flows, a modified phase-field equation for gas-liquid interfaces, and an enthalpy approach for solid-liquid phase-change processes in a unified diffuse-interface framework. The volume expansion or shrinkage of the liquid phase caused by the density change during the phase-change process is considered by introducing a mass source term into the continuity equation. The wettability effect in such a gas-liquid-solid multiphase system is also included in the phase-field free energy, thereby avoiding the direct discretization of wetting boundary condition on the complex fluid-solid boundary. Then, we develop a mesoscopic lattice Boltzmann (LB) method to solve the diffuse-interface model for the freezing processes in multiphase systems, and test the accuracy and efficiency of the LB method through some benchmark problems, including the conduction-induced freezing in a semi-infinite space, the three-phase Stefan problem, the droplet solidification on the flat and curved surfaces. It is found that the numerical results are in good agreement with the experimental data and theoretical solutions. Finally, the LB method is further extended to study the freezing dynamics of multiphase flows in a fracture and porous medium, and the numerical results show that the developed method is efficient in the study of freezing processes of multiphase flows in complex geometries.