Thermocapillary migration of a compound drop in an arbitrary viscous flow

被引：0

作者：

Chennuri D. ^{[1
]}

Prakash J. ^{[1
]}

机构：

[1] Department of Mathematics, Ecole Centrale School of Engineering, Mahindra University, Hyderabad

来源：

European Journal of Mechanics, B/Fluids | 2024年 / 106卷

关键词：

Compound drop; Hydrodynamic drag; Migration velocity; Stokes flow; Thermocapillary migration;

D O I：

10.1016/j.euromechflu.2024.05.001

中图分类号：

学科分类号：

摘要：

The thermocapillary migration of a concentric compound drop in an arbitrary viscous flow under the consideration of negligible Reynolds number is investigated. The thermocapillary effect refers to the migration of a drop under the influence of a temperature gradient. The thermal and hydrodynamic problems are examined. The thermal field is governed by the heat conduction equation whereas the hydrodynamic fluid velocities are governed by the linearized Navier–Stokes equations. Presence of temperature gradient results in variation of the interfacial tension which is assumed to depend on temperature linearly. Variation of interfacial gradient leads to the coupling of the hydrodynamic problem with the thermal problem through the boundary condition. A complete general solution of Stokes equations is utilized to obtain closed-form expressions for the velocity vector and pressure. The hydrodynamic forces acting on the compound drop are obtained and expressed in terms of Fax́en's law. Some important asymptotic limiting cases of hydrodynamic drag are also derived. The hydrodynamic drag for cases of uniform flow, shear flow, and heat source with the known ambient flow are derived and it is found that in the case of shear flow, the hydrodynamic drag is contributed only by the thermal component and the shear flow has no effect on it. The obtained results for drag and torque in the limiting cases are in agreement with the existing results in the literature. Furthermore, the migration velocity of the compound drop is obtained by equating the hydrodynamic drag force to zero. The results obtained for migration velocity are explained with the aid of graphs. The migration velocity is found to be a monotonic function of the Marangoni number and the radius of the innermost drop. © 2024 Elsevier Masson SAS

引用

页码：280 / 289

页数：9

共 27 条

[1]

Young N.O., Goldstein J.S., Block M.J., The motion of bubbles in a vertical temperature gradient, J. Fluid Mech., 6, 3, pp. 350-356, (1959)

[2]

Subramanian R.S., Thermocapillary migration of bubbles and droplets, Adv. Space Res., 3, 5, pp. 145-153, (1983)

[3]

Subramanian R.S., Balasubramaniam R., The Motion of Bubbles and Drops in Reduced Gravity, pp. 337-341, (2001)

[4]

Balasubramaniam R., Chai A.T., Thermocapillary migration of droplets: An exact solution for small marangoni numbers, J. Colloid Interface Sci., 119, 2, pp. 531-538, (1987)

[5]

Pratap V., Moumen N., Subramanian R.S., Thermocapillary motion of a liquid drop on a horizontal solid surface, Langmuir, 24, 9, pp. 5185-5193, (2008)

[6]

Darhuber A.A., Troian S.M., Principles of microfluidic actuation by modulation of surface stresses, Annu. Rev. Fluid Mech., 37, 1, pp. 425-455, (2005)

[7]

Bratukhin Y.K., Thermocapillary drift of a droplet of viscous liquid, Fluid Dyn., 10, 5, pp. 833-837, (1975)

[8]

Sandhal S.S., Jhonson R.E., Stokes flow past bubbles and drops partially coated with thin films. part 1. stagnant cap of surfactant film–exact solution, J. Fluid Mech., 126, pp. 237-250, (1983)

[9]

Choudhuri D., Raja Sekhar G.P., Thermocapillary drift on a spherical drop in a viscous fluid, Phys. Fluids, 25, 4, (2013)

[10]

Utada A.S., Lorenceau E., Link D.R., Kaplan P.D., Stone H.A., Weitz D.A., Monodisperse double emulsions generated from a microcapillary device, Science, 308, 5721, pp. 537-541, (2005)

← 1 2 3 →