A Finite-volume/Boundary-element Method for Flow Past Interfaces in the Presence of Surfactants, with Application to Shear Flow Past a Viscous Drop

Abstract A finite-volume method is developed for solving the convection–diffusion equation governing the transport of an insoluble surfactant over a generally evolving fluid interface, using an unstructured triangular grid. The unstructured grid has significant advantages compared with a structured grid based on global curvilinear coordinates, concerning adaptability and ability to conserve the total amount of the surfactant. The finite-volume method is combined with a boundary-element method for Stokes flow to yield an integrated procedure that is capable of describing the evolution of an interface from a specified initial state. Several series of simulations of the deformation of a neutrally buoyant viscous drop suspended in an infinite simple shear flow, or a semi-infinite shear flow bounded by a plane wall are performed. The results for the infinite flow extend those presented previously for the particular case where the ratio of the drop viscosity to the ambient fluid viscosity, λ , is equal to unity. It is shown that the effect of surfactant transport on the drop deformation and on the effective rheological properties of a dilute suspension becomes increasingly more important as λ becomes smaller and the drop reduces to an inviscid bubble. For semi-infinite flow past a drop above a plane wall, it is found that interfacial stresses due to variations in surface tension facilitate the drop migration away from the wall.