Optimal Marangoni surfing

We study the surfing motion of active spheroidal particles located at a flat liquid-gas interface. The particles create and maintain a surface tension gradient by asymmetrically discharging a surface tension-reducing agent. We employ theory and numerical simulation to investigate the Marangoni propulsion of these active surfers. First, we use the reciprocal theorem in conjunction with singular perturbation expansions to calculate the leading-order corrections to the propulsion speed of the surfers due to the advective transport of momentum and mass when the Reynolds and Peclet numbers (denoted by Re and Pe, respectively) are small but finite. We learn, perhaps surprisingly, that the propulsion speed increases rather significantly with the negative of ln(Re) and ln(Pe), when both parameters are very small. Next, we apply numerical simulations to examine the effects of intermediate and large values of Re and Pe on the propulsion speed. Consistent with the theoretical predictions, our simulations reveal that the normalized propulsion speed initially increases with increasing Re and Pe from zero. Interestingly, however, we find that the speed then reaches a maximum and afterward sharply declines when Re and Pe become large. That there exist certain intermediate Reynolds and Peclet numbers at which the Marangoni propulsion reaches a peak is a new finding that can guide engineers to design Marangoni surfers with superior performance.