Effect of surfactants on the deformation of drops and bubbles in Navier–Stokes flow

A numerical method is implemented for investigating the effect of an insoluble surfactant on the deformation of, and structure of the flow around a two-dimensional drop with arbitrary viscosity in simple shear flow. In the computational model, the flow occurs in a two-dimensional channel confined between two parallel plane walls in relative motion. The algorithm combines Peskin’s immersed-interface method with the diffuse-interface 1approximation, wherein the step discontinuity in the fluid properties is replaced by a transition zone defined in terms of a mollifying function. The generalized Navier–Stokes equation incorporating the jump in the interfacial traction is solved by a finite-difference method, while the interface surfactant transport equation is solved by a finite-volume method. Results of numerical simulations document the effect of the surfactant on the drop deformation and structure of the flow over a broad range of conditions, and demonstrate the possibility of interface immobilization due to Marangoni tractions even for mild variations in the surfactant concentration.