The axisymmetric thermocapillary motion of a fluid particle in a tube

Abstract

The thermocapillary migration of a fluid particle in a tube, owing to an imposed axial temperature gradient, is studied theoretically for the case of steady, axisymmetric, creeping, translation in the absence of thermal convection and fluid particle distortion from sphericity, and for an insulated tube. Formulated with these assumptions, the migration is a linear Stokes flow which is separable into two fixed-fluid particle flow idealizations. One is the fluid motion in a quiescent continuous phase, owing only to the thermocapillary surface stress. This stress causes fluid streaming which exerts a lift force on the fluid particle in the direction of the warmer fluid described by a lift coefficient. The second idealization is uniform flow in the absence of thermocapillary forces. The force on the fluid particle owing to this flow represents the hydrodynamic resistance to the forward motion of the fluid particle in the presence of the tube wall, and is described in terms of a drag coefficient. Numerical solutions for the lift and drag coefficients are obtained by a boundary collocation technique.The migration velocity in the tube relative to that under identical conditions in an infinite medium is computed from the ratio of the lift and drag coefficients. The calculations show that for a fixed ratio of the sphere to the tube diameter, as the conductivity of the fluid particle phase decreases relative to that of the continuous phase, a greater proportion of energy is conducted through the gap between the insulated tube wall and the fluid particle. This conduction pattern creates a larger surface temperature gradient, and causes the relative migration velocity to increase. The enhancement in migration for decreasing fluid particle conductivity at a fixed ratio of the sphere to the tube diameter becomes more pronounced as the later ratio increases and the surface gradient intensifies. However, as the gap distance between the sphere and the tube decreases, hydrodynamic retarding forces develop, and these forces are overriding in the sense that the relative migration velocity in the tube decreases monotonically from the value of one as the gap thickness decreases, and therefore the migration velocity in the tube never exceeds the value in an infinite medium.

Non-isothermal bubble rise: non-monotonic dependence of surface tension on temperature

“…Keh et al (2002) investigated the motion of a spherical drop between two parallel plane walls and found that the wall effect could speed up or slow down the droplet depending on the thermal conductivity of the droplet and the imposed boundary conditions at the wall. Chen et al (1991) considered the case of a spherical drop and studied the thermocapillary migration inside an insulated tube with an imposed axial temperature gradient. They found that the migration velocity in the tube never exceeds the value in an infinite medium due to the hydrodynamic retarding forces that are being developed.…”

“…Very recently, Mahesri et al (2014) extended the work of Chen et al (1991) to take into account the effect of interfacial deformation. It was found that as in the case of the spherical drop the migration velocity of the confined drop is always lower than that of an unbounded drop.…”

A Noncontact Picolitor Droplet Handling by Photothermal Control of Interfacial Flow

“…κ represents the wall correction factor as a function of the blockage ratio, d/h (in an infinite fluid, κ is the unity). 23 We regard U as being the migration velocity in a modified YGB relationship 24 in which the gravity and the buoyancy are neglected due to the scale effect:…”

液滴在管中的热变形迁移

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