Lattice Boltzmann Method for Interface-Restricted Transport of a Scalar Field and Its Application to Surfactant-Laden Multiphase Flows

The transport of a scalar field (e.g., surfactants) restricted on interfaces arises in certain multiphase flows. Its sharp-interface model was proposed by Stone (Phys. Fluids, 1990), which was then recast into a diffuse-interface formulation via a delta-function regularization by Teigen et al. (J. Comp. Phys., 2009). However, the latter involves singularities compromising its numerical implementation. Recently, Jain and Mani (Annu. Res. Briefs., CTR, Stanford Univ., 2022) circumvented this issue by applying a variable transformation, which effectively leads to an interface-bound scalar transport equation with an additional interfacial sharpening flux term that prevents a lateral diffusion into the bulk phases. We will discuss a novel central moment lattice Boltzmann method (LBM) to simulate the interface-bound transport model proposed by Jain and Mani. It is coupled with another LBM for interface capturing based on the conservative Allen-Cahn equation, and further extended by incorporating with an LBM solver for the two-fluid motion modulated by Marangoni stresses. The resulting approach is validated against certain benchmark problems and then applied to study surfactant-laden drop deformation and break up in a shear flow as well as bubble dynamics.