A FINITE-VOLUME BOUNDARY-ELEMENT METHOD FOR FLOW PAST INTERFACES IN THE PRESENCE OF SURFACTANTS, WITH APPLICATION TO SHEAR-FLOW PAST A VISCOUS DROP/

A finite-volume method is developed for solving the convection-diffusi on equation governing the transport of an insoluble surfactant over a generally evolving fluid interface, using an unstructured triangular g rid. The unstructured grid has significant advantages compared with a structured grid based on global curvilinear coordinates, concerning ad aptability and ability to conserve the total amount of the surfactant. The finite-volume method is combined with a boundary-element method f or Stokes flow to yield an integrated procedure that is capable of des cribing the evolution of an interface from a specified initial state. Several series of simulations of the deformation of a neutrally buoyan t viscous drop suspended in an infinite simple shear flow, or a semi-i nfinite shear flow bounded by a plane wall are performed. The results for the infinite flow extend those presented previously for the partic ular case where the ratio of the drop viscosity to the ambient fluid v iscosity, lambda, is equal to unity. It is shown that the effect of su rfactant transport on the drop deformation and on the effective rheolo gical properties of a dilute suspension becomes increasingly more impo rtant as lambda becomes smaller and the drop reduces to an inviscid bu bble. For semi-infinite flow past a drop above a plane wall, it is fou nd that interfacial stresses due to variations in surface tension faci litate the drop migration away from the wall. (C) 1998 Elsevier Scienc e Ltd. All rights reserved.