The diffuse-interface method for two-phase flow with a viscous interface

The diffuse-interface method is an interface capturing technique for multi-phase flow problems based on the Cahn-Hilliard model. In this study, the diffuse-interface method is employed to model a viscous interface, incorporating interfacial viscosity alongside classical interfacial tension. In a previous study utilizing the interface tracking method, interfacial stress was treated as a boundary condition (Jaensson et al., 2021). This study, with the help of the diffuse-interface method, reformulates the interfacial boundary condition into the momentum conservation equation, localizing the interfacial stress at the interface (Grande, 2015; Reusken & Zhang, 2013). Preliminary results from two-dimensional simple problems will be presented.

References¶

Jaensson, N. O., Anderson, P. D., & Vermant, J. (2021). Computational interfacial rheology. Journal of Non-Newtonian Fluid Mechanics, 290, 104507. doi:10.1016/j.jnnfm.2021.104507

Grande, J. (2015). Finite element discretization error analysis of a general interfacial stress functional. SIAM Journal on Numerical Analysis, 53(3), 1236–1255. doi:10.1137/13094815X

Reusken, A., & Zhang, Y. (2013). Numerical simulation of incompressible two-phase flows with a Boussinesq-Scriven interface stress tensor. International Journal for Numerical Methods in Fluids, 73(12), 1042–1058. doi:10.1002/fld.3835