Lateral self-propulsion of Marangoni droplets in stratified fluids

It is well known (Li et al. 2021, Phys. Rev. Lett. 126, 124502) that small (radius R < 1 mm) droplets of silicone oil suspended in a stably stratified ethanol/water mixture become unstable to an oscillatory `bouncing' instability when Ma/Ra^1/2 > 275, where Ra is the Rayleigh number, Ma = R V_M/D is the Marangoni number, D is the diffusivity of ethanol in water, and V_M is the theoretical equatorial velocity of the Marangoni flow driven by gradients of surface tension along the droplet's surface in the limit of infinite D. Here we show that suspended droplets also exhibit lateral self-propulsion, which may or may not be accompanied by bouncing, when R exceeds a critical value. Laboratory experiments together with scaling analysis based on boundary-layer theory show that self-propulsion sets in via spontaneous symmetry breaking when Ma > 1.3 X 10⁵. We also find that far beyond onset the velocity of steady self-propulsion is U ≈ 0.003 V_M. When viewed from above, translating droplets are seen to describe curved or spiral trajectories that we quantify by calculating the mean squared displacement as a function of time.