Marangoni effect on the motion of a droplet covered with insoluble surfactant in a square microchannel

Despite its significance in various applications, e.g., droplet microfluidics and chemical enhanced oil recovery, the motion of surfactant-laden droplets in non-circular microchannels remains an unsolved fundamental problem. To facilitate studies in this area, we present a systematic investigation on the motion of a droplet covered with an insoluble surfactant in a square microchannel. This work is realized via our three-dimensional front-tracking finite-difference model with integration of the convection-diffusion equation for surfactant transport on a deforming drop surface. Our results indicate significant effects of the surfactant on steady-state characteristics of droplet motion, especially the droplet-induced additional pressure loss in the channel. More particularly, the surfactant-induced reduction in drop surface tension remarkably lowers the additional pressure loss, but this effect can be fully counteracted by the effect of surface tension gradient induced Marangoni stress (i.e., to enlarge the additional pressure loss). The increasing effect of the Marangoni stress is primarily determined by two surfactant-related dimensionless parameters, i.e., the surface Peclet number and the elasticity number. The additional pressure loss significantly increases with either of them increasing. Besides, the Marangoni effect on the droplet-induced additional pressure loss also strongly depends on three other independent parameters, i.e., it is inhibited by decreasing the size ratio of the drop to the channel, increasing the viscosity ratio of the drop to the surrounding fluid, or increasing the capillary number. Finally, we discuss the mechanism of the Marangoni effect on drop motion via analyzing the distributions of the surfactant concentration and drop surface velocity on a three-dimensional drop surface.