Spreading dynamics of reactive surfactants driven by Marangoni convection

We consider the spreading dynamics of some insoluble surface-active species along an aqueous interface. The model includes both diffusion, Marangoni convection and first-order reaction kinetics. An exact solution of the nonlinear transport equations is derived in the regime of large Schmidt number, where viscous effects are dominant. We demonstrate that the variance of the surfactant distribution increases linearly with time, providing an unambiguous definition for the enhanced diffusion coefficient observed in the experiments. The model thus presents new insight regarding the actuation of camphor grains at the water-air interface.