An Interface-Tracking Technique for Multiphase Flow with Soluble Surfactant

TL;DR

This paper extends a surfactant transport model within a hybrid interface-tracking method for multiphase flows, demonstrating high accuracy and efficiency through various benchmark tests and parallel computing capabilities.

Contribution

It introduces a novel adaptation of surfactant transport formulation into the Level Contour Reconstruction Method, enhancing accuracy and parallelization in 3D multiphase flow simulations.

Findings

Accurate surfactant mass conservation verified against exact solutions.

Effective implementation of surface gradients and surface tension forces.

Good agreement with experimental and previous simulation data.

Abstract

We adapt and extend a formulation for soluble surfactant transport in multiphase flows recently presented by Muradoglu & Tryggvason (JCP 274 (2014) 737-757) to the context of the Level Contour Reconstruction Method (Shin et al. IJNMF 60 (2009) 753-778) which is a hybrid method that combines the advantages of the Front-tracking and Level Set methods. Particularly close attention is paid to the formulation and numerical implementation of the surface gradients of surfactant concentration and surface tension. Various benchmark tests are performed to demonstrate the accuracy of different elements of the algorithm. To verify surfactant mass conservation, values for surfactant diffusion along the interface are compared with the exact solution for the problem of uniform expansion of a sphere. The numerical implementation of the discontinuous boundary condition for the source term in the bulk concentration is compared with the approximate solution. Surface tension forces are tested for Marangoni drop translation. Our numerical results for drop deformation in simple shear are compared with experiments and results from previous simulations. All benchmarking tests compare well with existing data thus providing confidence that our adapted LCRM formulation for surfactant advection and diffusion is accurate and effective in three-dimensional multiphase flows. We also demonstrate that this approach applies easily to massively parallel simulations.