Phase-field-based lattice Boltzmann method for the transport of insoluble surfactant in two-phase flows

TL;DR

This paper introduces a second-order phase-field model and a lattice Boltzmann method for accurately simulating insoluble surfactant transport in two-phase flows, capturing interface dynamics and Marangoni effects.

Contribution

It develops a novel LB method tailored for surfactant transport within a phase-field framework, ensuring accurate interface capturing and flow simulation.

Findings

The LB method correctly recovers the surfactant transport equation.

Numerical tests demonstrate high accuracy and good performance.

The model effectively simulates insoluble surfactant behavior in two-phase flows.

Abstract

In this work, we present a general second-order phase-field model for the transport of insoluble surfactant in incompressible two-phase flows. In this model, the second-order local Allen-Cahn equation is applied for interface capturing, a general form of the simple scalar transport equation [S. S. Jain, J. Comput. Phys. 515, 113277 (2024)] is adopted for interface-confined surfactant, and the consistent and conservative Navier-Stokes equations with the Marangoni force is used for fluid flows. To solve this model, we further developed a mesoscopic lattice Boltzmann (LB) method, in which the LB model for surfactant transport equation is proposed under the general LB framework for the convection-diffusion type equation, and it can correctly recover the governing equation for surfactant transport. The accuracy of the present LB method is tested by several benchmark problems, and the numerical results show it has a good performance for the transport of the insoluble surfactant in two-phase flows.