Simulations of soluble surfactants in 3D multiphase flow

• A front-tracking method is developed for treatment of soluble surfactants in 3D.
• The surfactant equations are solved fully coupled with the flow equations.
• Test cases are designed to validate different parts of the numerical method.
• The effects of surfactant on the lateral migration of bubbles are examined.

A finite-difference/front-tracking method is developed for simulations of soluble surfactants in 3D multiphase flows. The interfacial and bulk surfactant concentration evolution equations are solved fully coupled with the incompressible Navier–Stokes equations. A non-linear equation of state is used to relate interfacial surface tension to surfactant concentration at the interface. Simple test cases are designed to validate different parts of the numerical algorithm and the computational results are found to be in a good agreement with the analytical solutions. The numerical algorithm is parallelized using a domain-decomposition method. It is then applied to study the effects of soluble surfactants on the motion of buoyancy-driven bubbles in a straight square channel in nearly undeformable (spherical) and deformable (ellipsoidal) regimes. Finally the method is used to examine the effects of soluble surfactants on the lateral migration of bubbles in a pressure-driven channel flow. It is found that surfactant-induced Marangoni stresses counteract the shear-induced lift force and can reverse the lateral bubble migration completely, i.e., the contaminated bubble drifts away from the channel wall and stabilizes at the center of the channel when the surfactant-induced Marangoni stresses are sufficiently large.