Hydrodynamics of a self-propelled camphor boat at the air-water interface

A camphor tablet, when placed at the air-water interface undergoes sublimation and camphor vapour spreads radially outwards across the surface due to Marangoni forces. This steady camphor influx from tablet onto the air-water interface is balanced by the camphor outflux due to evaporation. When spontaneous fluctuations in evaporation break the axial symmetry of Marangoni force acting radially outwards, the camphor tablet is propelled like a boat along the water surface. We report experiments on the hydrodynamics of a self-propelled camphor boat at air-water interfaces. We observe three different modes of motion, namely continuous, harmonic and periodic, due to the volatile nature of camphor. We explain these modes in terms of ratio of two time-scales: the time-scale over which viscous forces are dominant over the Marangoni forces ($\tau_{\eta}$) and the time-scale over which Marangoni forces are dominant over the viscous forces ($\tau_{\sigma}$). The continuous, harmonic and periodic motions are observed when $\tau_{\eta}/\tau_{\sigma} \sim 1$, $\tau_{\eta}/\tau_{\sigma} \geq 1$ and $\tau_{\eta}/\tau_{\sigma} \gg 1$ respectively. Experimentally, the ratio of the time scales is varied by changing the interfacial tension of the air-water interface using Sodium Dodecyl Sulfate.