Thermocapillary migration of a fluid sphere parallel to an insulated plane
Journal
Langmuir
Journal Volume
15
Journal Issue
25
Date Issued
1999
Author(s)
Abstract
An analytical study is presented for thermocapillary migration of a fluid sphere in a constant prescribed temperature gradient parallel to an adiabatic plane. The Peclet and Reynolds numbers are assumed to be small, so that the temperature distributions and flow fields of the fluids inside and outside the droplet are governed by the Laplace and Stokes equations, respectively. A method of reflections is used to obtain the asymptotic formulas for temperature and velocity fields in the quasi-steady situation. The thermally insulated plane may be a solid wall (no-slip) and/or a free surface (perfect-slip). The boundary effect on the asymmetric thermocapillary motion of a droplet parallel to a plane is found to be weaker than that on the axisymmetric thermocapillary migration of a sphere normal to a plane with constant temperature. In comparison with the motion driven by gravitational force, the interaction between the particle and the boundary is less significant under thermocapillary migration. Even so, the interaction between a plane and a fluid sphere can be very strong when their gap thickness approaches zero. For thermocapillary migration of a droplet parallel to a solid plane, the plane surface reduces the translational velocity of the droplet. In the case of a droplet migrating parallel to a free surface due to thermocapillarity, the translating velocity of the particle can be either greater or smaller than that which would exist in the absence of the plane surface, depending on the relative thermal conductivity of the droplet and its relative distance from the plane. Both the droplet velocity and the region affected by the surface are evaluated by considering the droplet mobility. Generally speaking, a free surface exerts less influence on the particle movement than a solid wall.
SDGs
Type
journal article