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 exists 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 results in larger force on a cylinder than forces arising from other self-propulsion mechanisms.