Thermocapillary motion of a solid cylinder near a liquid-gas interface

Abstract

The motion of a solid, infinitely long cylinder perpendicular to a convective liquid-gas interface due to thermocapillarity is investigated via an analytical model. If the cylinder temperature differs from the bulk temperature, a temperature gradient exist along the liquid-gas interface. This results in surface tension gradients at the liquid-gas interface, causing fluid flow around the particle which induces propulsion. For small particles, and thus small Péclet and Reynolds numbers the steady-state equations for temperature and flow fields are solved exactly using two-dimensional bipolar cylindrical coordinates. The velocity of the cylinder as a function of separation distance from the liquid-gas interface is determined for the case of a constant temperature or a constant heat flux on the surface of the cylinder. A larger temperature gradient at the liquid-gas interface in the latter system leads to a larger cylinder velocity and a higher propulsion efficiency. The thermocapillary effect result in larger force on a cylinder than forces arising from other self-propulsion mechanisms.