Viscous propulsion of a two-dimensional Marangoni boat driven by reaction and diffusion of insoluble surfactant

Abstract

A simple model of viscous propulsion of a two-dimensional Marangoni boat caused by surface diffusion and sublimation (reaction) of insoluble surfactant is formulated and studied analytically. The speed of the boat is determined explicitly as a function of a Damkohler number by fully resolving the Marangoni-induced bulk flow caused by the release of surfactants onto the surface of a semi-infinite viscous fluid. A complementary general integral formula for the boat speed is also derived using the reciprocal theorem.