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Thermocapillary migration of droplets and bubbles in a viscous liquid (review). Multiphase Systems. 15 (2020) 3–4. 144–158 (in Russian).
2020. Vol. 15. Issue 3–4, Pp. 144–158
URL: http://mfs.uimech.org/mfs2020.3.125,en
DOI: 10.21662/mfs2020.3.125
Thermocapillary migration of droplets and bubbles in a viscous liquid (review)
Nasibullaeva E.Sh., Urmancheev S.F.
Mavlyutov Institute of Mechanics UFRC RAS, Ufa, Russia

Abstract

Investigation of the process of accumulation of gas bubbles in the aria of a heat source is, from a physical point of view, quite interesting problem that leads to important conclusions for practical applications. The peculiarity of the process under consideration is that the surface tension of the bubble changes in an alternating temperature field, which, in turn, leads to the appearance of a flow in the boundary layer of the liquid. In the world scientific literature, the discovery and description of the effect of gas bubble migration in the direction of the temperature gradient is usually associated with the experimental work of Yang, Goldstein and Block (1959). Without diminishing its significance, we note that the effect was first predicted in the theoretical work of Fedosov (1956) as a result of solving the problem of the onset of a microflow of a liquid near plane and spherical interphase boundaries in the presence of a temperature gradient. In both works, a significant factor in explaining the described phenomenon was the dependence of surface tension on temperature. After some time, after which it was realized the need to take into account the migration of not only bubbles, but also droplets, in inhomogeneous temperature fields in space technologies, biomedical and other applications, there was a significant number of publications on this subject, and this phenomenon was called thermocapillary migration. This review is devoted to the analysis of the main, in the opinion of the authors of the article, results of experimental, theoretical and applied research to establish the mechanism of migration bubbles and drops in temperature gradient fields. In most works, it is assumed that there is no dependence of the physical properties of a liquid, except for surface tension, on temperature. There are only a few studies where the influence of the temperature dependence of the viscosity coefficient was considered, which gives a new impetus to the continuation of research and the development of the theory of the effect, taking into account the thermorheological properties of working media.

Keywords

Newtonian fluid,
bubble,
drop,
thermocapillary migration,
droplet/bubble migration velocity,
temperature gradient,
surface tension

Article outline

Thermocapillary migration is the ability of droplets which are insoluble in the surrounding fluid, or gas bubbles, which located in uniformly heated liquid, spontaneously move into the hotter region. This motion is caused by tangential thermocapillary forces arising on the surface of a drop or bubble, which force the surrounding liquid to flow around the drop or bubble in the direction of the surface tension gradient (from the warm to the cold pole). The result is a reactive force applied to the drop or bubble that pushes the drop or bubble in the opposite direction. Thus, the thermocapillary migration is a consequence of the convective Marangoni flow arising in liquid media near the interface under the action of tangential capillary forces in the case of inhomogeneity of the surface tension due to the uneven temperature distribution. Interest in this phenomenon is caused, first of all, by important applications in various fields of science and technological processes in space, where Marangoni convection prevails.

Purpose: Аnalysis of the main results of experimental, theoretical and applied research to establish the mechanism of the migration of bubbles and drops in gradient temperature fields.

When solving the problem of thermocapillary migration of a bubble or drop, a gas bubble or a drop of liquid of an initially spherical shape with a dynamically free (interphase) boundary in an unlimited volume of an incompressible Newtonian liquid is considered. Typically, in the formulation of the problem it is assumed that there is an external temperature gradient constant at infinity; the drop is insoluble in liquid; there is no exchange of matter with the environment at the interface; the direction of the temperature gradient is parallel to the gravity acceleration vector (in the presence of gravitational force); the dependence of the physical properties of the liquid, except for surface tension, on temperature is absent; the surface tension coefficient changes linearly with temperature.

Methods: At low Reynolds numbers, the equations of motion are considered in the Stokes approximation. When formulating the boundary conditions, one usually goes over to a coordinate system moving with the center of gravity of the falling sphere. The theoretical methods for determining the velocity of thermocapillary migration of bubbles or drops are based on the expansion of the equations of motion in small powers of either the Reynolds number or the Marangoni number. In numerical calculation methods for tracking the speed of the interface between two media are mainly used either method of the finite volume, or level set methods, or Volume of Fluid method.

As a main finding of the analysis of the works presented in this review, a significant interest of researchers was established in the problem of thermocapillary migration of both bubbles and drops in an inhomogeneous temperature field, as well as the formation of bubble clusters in the region of heat sources. At the same time, it should be noted the growing interest from developers of new technologies in various industries.

Value: In a number of works, along with the inevitable allowance for the dependence of surface tension on temperature, the influence of the temperature dependence of the viscosity coefficient was considered, which gives a new impetus to the continuation of research and the development of the theory of the effect, taking into account the rheological and especially thermorheological properties of working media.

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