Comparative Analysis of Theories of Thermocapillary Inclusion Motion Under Zero-Gravity Condition

Abstract

The motion of a fine viscous inclusion in a viscous medium under zero-g condition is subjected to theoretical examination. This motion can be qualified as an elementary act of the motion of fine phase particles in composition mixtures: suspensions, emulsions, foamed liquid metals, aerosols. It is interesting to notice, when carrying out a theoretical analysis of thermocapillary inclusion dynamics, that attention is usually centered on a description of the behavior of gaseous and liquid inclusions whereas the behavior of solid inclusions is left beyond any considerations. Such a situation can be understood since the theoretical basis commonly used gives no way to describe the behavior of solid inclusion, although the proper experiments are known now. An approach proposed here allows one to describe thermocapillary dynamics of solid, liquid and gaseous inclusions in the reduced gravity (without influence of any other exertions). It may be used in the interpretation of experiments and technological processes with fine particles.

Thermocapillary phoresis of inclusions with interphase surfactant

“…that coincides with the expression for the thermocapillary phoresis velocity of a rigid inclusion [7] or a drop (or bubble) with a surface rigid crust (for example, an air bubble with an Al 2 O 3 crust inside an Al melt [9]). In the case of a bubble with a rigid crust, it is expedient to suppose β ∼ = 0 in Eq.…”

“…It is easy to see that the thermocapillary phoresis velocity in the cases of a rigid inclusion [7] and a liquid inclusion with the complete surfactant surface film are the same. It does not tend to zero unlike the assertions or the consequences from the known present theory (see, for example [3,[11][12][13][14][15][16][17]).…”

“…The model of the system of liquid medium-foreign inclusion (where r is the radial coordinate of the spherical system, θ is the angular coordinate of the same system, ϕ is the angular measure of a cap formed by surfactant). equation [4][5][6][7]:…”

“…[6][7][8] for the thermocapillary motion velocity of a drop having a clean surface. When ϕ = π and the surfactant film acts as rigid crust, then Eq.…”

“…We believe that the equations, which are the consequences of the theory by Young et al [11], U YGB (ϕ = π, α, β) = U YGB (ϕ, α → ∞, β) = 0 must be replaced with Eq. (7).…”