Effect of soluble surfactant on the motion of a confined droplet in a square microchannel

Surfactants are widely used in the manipulation of drop motion in microchannels, which is commonly involved in many applications, e.g., surfactant assisted oil recovery and droplet microfluidics. This study is dedicated to a crucial fundamental problem, i.e., the effects of a soluble surfactant on drop motion and their underlying mechanisms, which is an extension of our previous work of an insoluble-surfactant-covered droplet in a square microchannel [Z. Y. Luo, X. L. Shang, and B. F. Bai, "Marangoni effect on the motion of a droplet covered with insoluble surfactant in a square microchannel," Phys. Fluids 30, 077101 (2018)]. We make essential improvements to our own three-dimensional front-tracking finite-difference model, i.e., by further integrating the equation governing surfactant transport in the bulk fluid and surfactant mass exchange between the drop surface and bulk fluid. We find that the soluble surfactant generally enlarges the droplet-induced extra pressure loss compared to the clean droplet, and enhancing surfactant adsorption tends to intensify such an effect. We focus specifically on the influences of four soluble-surfactant-relevant dimensionless parameters, including the Biot number, the dimensionless adsorption depth, the Damkohler number, and the bulk Peclet number. Most importantly, we discuss the mechanisms underlying the soluble surfactant effect, which consists of two aspects similar to the insoluble case, i.e., the reduced surface tension to decrease droplet-induced extra pressure loss and the enlarged Marangoni stress playing the opposite role. Surprisingly, we find that the enlarged Marangoni stress always makes the predominant contribution over the reduced surface tension in the effects of above-mentioned four soluble-surfactant-relevant dimensionless parameters on drop motion. This finding explains why the droplet-induced extra pressure loss increases with the film thickness, which is opposite to that observed for clean droplets.