Thermocapillary motion of a spheroidal drop in an immiscible fluid
Journal
International Journal of Multiphase Flow
Journal Volume
184
Start Page
105072
ISSN
0301-9322
Date Issued
2025-03
Author(s)
Jai Prakash
DOI
10.1016/j.ijmultiphaseflow.2024.105072
Abstract
A theoretical investigation of the problem of thermocapillary motion of a spheroidal drop freely suspended in a viscous incompressible fluid with a prescribed constant temperature gradient along the axis of revolution of the drop is presented under the steady limit of vanishing Péclet and Reynolds numbers. The flow fields in the exterior and interior of the drop are governed by the Stokes equations whereas the temperature fields in both the regions are governed by Laplace's equation. The general solution for prolate and oblate spheroidal drops can be expressed as infinite series in the forms of separation of variables for temperature distribution and of semi-separation of variables for the stream function. The leading order coefficients can be obtained using suitable boundary conditions which can be numerical values obtained from boundary collocation method or explicit formulas derived analytically. The thermocapillary migration velocity of the spheroidal drop is evaluated numerically with adequate convergence behavior for various values of the internal-to-external viscosity ratio, axial-to-radial aspect ratio and the relative thermal conductivity of the drop. It is revealed that the normalized thermocapillary migration velocity increases with the aspect ratio except for the case when the relative thermal conductivity of the drop is small and the internal-to-external viscosity ratio is relatively large. It is further observed that the normalized migration velocity approaches zero for an oblate spheroidal drop with the aspect ratio approaching zero and can be much greater than unity for a prolate spheroidal drop with a large value of the aspect ratio.
Subjects
Creeping flow
Drag force
Spheroidal drop
Thermocapillary migration
Viscous fluids
Publisher
Elsevier BV
Type
journal article