Analytical and computational methods for Two-phase flow with soluble surfactant

A hybrid method is used to determine the influence of surfactant solubility on two-phase flow by solution of a reduced transition layer equation near a fluid interface in the limit of large

bulk Peclet number. The method is applied to finding the evolution of a drop of arbitrary viscosity that is deformed by an imposed linear strain or simple shear flow. A semi-analytical solution of the transition layer equation is given that expresses exchange of surfactant between its bulk and interfacial forms in terms of a convolution integral in time. Results of this semi-analytical solution are compared with the results of a spatially spectrally accurate numerical solution. Although both the hybrid method and its semi-analytical solution are valid in three dimensions, the two-dimensional context of this study allows additional validation of results by comparison with those of conformal mapping techniques applied to inviscid bubbles.