Hydrodynamic interaction of two droplets covered with insoluble surfactant in shear flow

Despite its significance in various applications, e.g., droplet microfluidics and enhancing oil recovery, the effects of surfactants on the hydrodynamic interactions of droplets in shear flow still need to be clarified. This paper presents a systematic investigation on the hydrodynamic interaction of two droplets covered with the insoluble surfactant in a simple shear flow, which is realized by using our own three-dimensional front-tracking code. Our results indicate that surfactants significantly affect the hydrodynamic interactions of droplets, characterized by the maximum deviation in the z-direction and the shear-induced self-diffusion. Then, we examine the effects of surfactant-relevant parameters, i.e., the surface Peclet number and the elasticity number. Both the maximum deviation in the z-direction and the shear-induced self-diffusion increase with the elasticity number and the surface Peclet number. Specifically, we find two mechanisms underlying the effects of surfactant on the hydrodynamic interaction of two droplets. First, Marangoni stress induced by surfactant sharply increases the maximum deviation in the z-direction when the surface Peclet number is large. It is because that Marangoni stress hinders liquid drainage from the near-contact region and thickens the liquid film between the droplets. Second, hydrodynamic interactions during crossing lead to considerable alterations of the shape and local surfactant concentration, resulting in an irreversible trajectory shift of the droplets. So, the shear-induced self-diffusion sharply rises at the high surface Peclet number.