Front tracking simulation of droplet displacement on solid surfaces by soluble surfactant-driven flows

We provide comprehensive numerical insights into the displacement of droplets subject to soluble surfactant-driven flows. The effects of soluble surfactants on the dynamics of moving contact lines are introduced by the surfactant-dependent generalized Navier boundary condition. We show that surfactant transport significantly influences the displacement patterns of droplets on solid surfaces, affecting both the equilibrium state of the sliding motion and the critical conditions for detachment. In particular, a linear increase in the displacement velocity of a droplet with the dimensionless adsorption depth $K$ is observed. This rate of increase is more pronounced at higher elasticity numbers, as evidenced by a more significant increase in the advancing contact angle. The critical condition for droplet detachment depends on the surfactant's ability to swiftly adsorb from the bulk and replenish at interfaces, which is improved as the Biot number Bi or $K$ increases. Adsorption is enhanced by an increase in Bi, resulting in a decrease in the required time $t_d$ for droplet detachment. However, this enhancement effect becomes nonmonotonic at high Bi values. In contrast, consistently increasing the bulk Peclet number decreases $t_d$, eventually approaching the convection limit where the Marangoni-induced drag force ceases to increase. In addition, surfactant transfer near the moving contact line at a moderate Damköhler number restricts the motion of the advancing contact lines, promoting droplet detachment. For all detachment scenarios, we find that detachment necessitates a critical effective capillary number, and an increase in this number results in an exponential decline in $t_d$.