Thermocapillary Migration Research Articles

Thermocapillary migration of a droplet with insoluble surfactant: I. Surfactant cap

The steady thermocapillary migration of a drop, in the presence of a stagnant cap of an insoluble nondiffusing surfactant, is treated theoretically. Gravitational effects are included for completeness, and analytical solutions are obtained under conditions of negligible convective transport of momentum and energy in the bulk phases. The migration velocity of the drop is calculated, and is found to reduce to the proper asymptotes in limiting cases. Typical streamline plots as well as interfacial velocity distributions are displayed. The distribution of surfactant concentration in the cap region is obtained using an ideal film model, and the conditions for the existence of the cap are discussed.

Thermocapillary migration of a large gas slug in a tube

The steady-state motion exhibited by a large gas slug that is contained in a liquid-filled tube and subjected to a linear temperature variation is analyzed, taking the thermally-induced gradient of the gas-liquid surface tension into account. An expression which characterizes the terminal velocity of the gas slug has been derived.

Effect of direct current on the thermocapillary migration of droplets in microgravity

The migration of droplets under the effect of electromagnetic and thermocapillary forces is studied in the case where the electrical conductivity of droplets differs from that of host fluid. The bulk electromagnetic forces in a diluted suspension filling the non-electrical-conducting tube arise due to the interaction between the axial electric current and its magnetic self-field. The temperature gradient in a fluid is caused by Joule heating. The migration of a bubble and a solid particle is also considered. The modified Lamb solution for the Stokes equations is a theoretical basis for the analysis performed.

Thermocapillary migration of droplets: An exact solution for small marangoni numbers

The thermocapillary motion of immiscible spherical droplets placed in an unbounded fluid with a linear temperature distribution is analyzed. For small Marangoni numbers, an exact solution to the Navier-Stokes equations has been found. The velocity field and the terminal velocity of the droplet are the same as those calculated by previous workers in the small Reynolds number limit. Hence the range of applicability of their results has been extended to arbitrary Reynolds numbers, so long as Ma = PrRe remains small (i.e., the convection of energy can be neglected). The shape of the droplet has also been calculated, when the deformations from the spherical shape are small. The results are qualitatively in agreement with the previous results, in the limit Pr → 0, that droplets of the same density as the host fluid do not deform at all, that bubbles tend to deform oblately, and that droplets with the denser fluid inside tend to elongate in the flow direction.

Thermocapillary migration of a gas bubble in an arbitrary direction with respect to a plane surface

The problem of the thermocapillary migration of a gas bubble in an unbounded fluid in the presence of a neighboring rigid plane surface is analyzed in the quasistatic limit of negligible Reynolds and Marangoni numbers. The temperature gradient in the fluid is uniform in the undisturbed state and is oriented at an arbitrary angle relative to the plane surface. The solution is constructed by superposing solutions of the corresponding problems of motion normal to the surface and motion parallel to it. Results are reported in the form of a scalar interaction parameter defined as the ratio of the speed of the bubble in the presence of the plane surface to the speed in its absence. The direction of motion of the bubble is, in general, different from that of the temperature gradient, and is given. The corresponding problem of gravity-driven migration of a gas bubble normal to a plane surface is already solved in the literature. The solution of the parallel migration problem, not reported in the past, is given here. Comparisons of the results in this case show that the plane surface exerts a weaker influence in the thermocapillary migration case. This is due to the more rapid decay, away from the bubble, of the disturbance velocity and temperature gradient fields in this case. Results presented herein show that the surface exerts the greatest influence in the case of motion normal to it, and the weakest in the case of parallel motion.

A note on the thermocapillary migration of a bubble normal to a plane surface

Etude theorique de la migration d'une bulle, dans un milieu liquide, sous l'effet d'un gradient thermique

The slow axisymmetric thermocapillary migration of an eccentrically placed bubble inside a drop in zero gravity

The quasi-static problem of the motion of a bubble contained inside a drop in free fall due to a prescribed axisymmetric temperature field on the drop surface is treated theoretically. The linearity of the problem permits the convenience of calculating and discussing the influence of each pure Legendre mode of the surface temperature field individually. Typical streamlines and isotherms are displayed, and the behavior of the bubble migration velocity is discussed. An approximation for the bubble velocity useful for small values of the ratio of bubble radius to drop radius is presented and compared with the exact results.

Thermocapillary migration of bubbles and droplets

The migration of a droplet in a large liquid body possessing a uniform temperature gradient is analyzed in the creeping flow limit for small values of the Marangoni number (ε). The method of matched asymptotic expansions is used for the solution of the field equations. The migration velocity is calculated to 0(ε 2) and the result reduces to that of Young, Goldstein and Block [10] in the limit of zero Marangoni number.

Use of thermocapillary migration in a controllable heat valve

In accordance with the Marangoni effect, immiscible droplets in a host fluid in which a temperature gradient exists move in the direction of increasing temperature. It is proposed that this thermocapillary migration could be used to construct a ‘‘liquid wick’’ that would return the condensed vapor at the condenser end of a heat pipe back to the evaporator, thus completing the fluid circuit. The droplets would be formed by capillary pressure forcing the condensate through a perforated diaphragm whose temperature would control the droplet flux, and hence the heat flux between the two ends of the heat pipe, thus making it a controllable heat valve.

Thermocapillary migration of a fluid droplet inside a drop in a space laboratory

The thermocapillary migration of a fluid droplet located inside a liquid drop in a space laboratory is analyzed. The quasi-static momentum and energy equations are solved at the instant when the droplet passes the center of the drop. Results are presented for prescribed axisymmetric distributions of temperature on the drop surface.

Thermocapillary migration of a bubble normal to a plane surface

The influence of a plane solid or fluid surface on the thermocapillary migration of a gas bubble moving normal to it in a space laboratory is investigated in the quasi-static limit. Results are presented for a suitably defined “interaction” parameter Ω as a function of the scaled distance of the bubble from the plane surface, and compared with similar predictions for buoyant migration.

Thermocapillary Motion of Bubbles Inside Drops

ABSTRACTThe quasi-static thermocapillary migration of a bubble located inside a drop in free fall is considered for arbitrary axisymmetric temperature fields prescribed on the drop surface. Some results are presented, and an approximation based on the superposition of simpler solutions is discussed.