Effect of surfactants on the motion of drops through circular tubes

The effect of surfactants on the motion and deformation of liquid drops in Poiseuille flow through circular tubes at low Reynolds numbers is examined. Assuming no bulk transport of surfactant, the boundary integral method is used in conjunction with a convective-diffusion equation to determine the distribution of surfactant on the deformed surface of the drop. The velocity and shape of the drop as well as the extra pressure loss due to the presence of the drop are calculated. Increasing the surface Péclet number is found to produce large variations in surfactant concentration across the surface of the drop. The resulting interfacial tension gradients lead to tangential (Marangoni) stresses that oppose surface convection and retard the motion of the drop as a whole. For large Péclet numbers, Marangoni stresses immobilize the surface of the drop, leading to a significant increase in the extra pressure loss required to move the drop through the tube. The accumulation of surfactant near the trailing end of the drop partially lowers the interfacial tension on that side, thereby requiring larger deformations to satisfy the normal stress balance. At the same time, the increase in interfacial area associated with drop deformation causes an overall dilution of the surfactant, which, in turn, counteracts the effect of convective transport of surfactant at large Péclet numbers. The effects of these coupled responses are studied over a wide range of the dimensionless parameters.