Marangoni Propulsion of Active Particles

Abstract

We study the surfing motion of active 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 to establish a relationship between the propulsion speed and the release of the active chemical. This theoretical relation is utilized to examine the effect of wall confinement and geometry on the Marangoni-driven motion of active particle when the inertial effects are negligible and when the transports of the released agent is dominated by diffusion. Contrary to what might be the usual expectation, we find that the surfers may propel in the lower surface tension direction depending on their geometry and proximity to the bottom of the liquid layer. We then extend our theory beyond the Stokes regime with the aid of the perturbation theory and calculate the leading-order corrections to the propulsion speed due to the advective transport of momentum and mass when (Re, Pe) (denoted by Re and Pe, respectively) are small, but finite. Next, we develop a computational framework that enables us to study the effects of intermediate and large Re and Pe on the propulsion speed. Our numerical approach is validated against theory and available experimental data. Interestingly, our simulations reveal that the normalized propulsion speed initially increases with increasing Re and Pe from zero. It then reaches a maximum and afterward sharply declines when Re or Pe becomes large. That there exist certain intermediate (Re, Pe) at which the Marangoni propulsion reaches a peak is a new discovery that can guide engineering to design Marangoni surfers with superior performance. We also numerically analyze the translational stability of Marangoni surfers of spherical shape. An overset-grid is adopted to carry out the simulations. We demonstrate that a Marangoni surfer can retain its stability at higher Reynolds numbers relative to the same surfer moving at an interface with no Marangoni effect present. Lastly, we computationally investigate the change in the mobility of the surfers as a result of the depth of the liquid layer. We consider the motion of thin cylindrical disks and oblate spheroids for a wide range of release rates and diffusivity of the exuded chemical species, that control the effective (Re, Pe). We show that indeed the surfers can undergo a forward, a backward, or