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.