Thermocapillary bubble motion

Figure 7-17. Streamlines for thermocapillary motion of a gas bubble for a = 0.8 (a2pg//3), where the bubble velocity is reduced to 20% of its value in the absence of thermocapillary effects. The stream-function values are calculated from Eq. (7-244) with coefficients C and D from Eqs. (7-248). Contour values are plotted in increments of 0.7681.

Some additional effects were considered for the thermocapillary motion of drops and bubbles in an external temperature gradient interaction of a drop with a plane wall [285], and interaction of drops with bubbles or of bubbles with each other [12, 146], In particular, it was shown in [12] that the interaction of drops of radius a decreases with increasing distance l between them as (a/i f for thermocapillary drift, compared with a/l for the motion in the gravitational field. 

Szymczyk, J. and Siekmann, J., Numerical calculation of the thermocapillary motion of a bubble under microgravity, Chem. Eng. Comm., Vol. 69, pp. 129-147, 1988. 

In the remainder of this section an approximate analysis is provided of the thermocapillary problem of motion of a bubble in a gravitational field.28 Thus we suppose that we have... 

Figure 7-16. Schematic diagram of the coordinate systems and undisturbed temperature distribution for thermocapillary-driven motion of a gas bubble.

Consider a spherical bubble of radius a which is moving through a viscous incompressible fluid which contains soluble surfactants. This motion can be due to buoyancy or thermocapillary migration in microgravity applications. It is easier to consider the equivalent problem which has a coordinate system fixed at the center of the bubble, with a uniform stream, of velocity C/qo say, far away. The fluid has density p and kinematic viscosity u and we assume that the surfactant concentration is uniform far from the bubble and has value Coo-... 

Reviews of thermocapillary migration may be found in Refs. 24 and 25. The book by Subramanian and Balasubramaniam [26] provides discussions of both thermocapillary migration and buoyancy-driven bubble motion. 

The thermocapillary migration of liquid drops or bubbles and the influence of Ej on their motion are investigated in a number of works [749-751]. 

Li et al. 48) studied how 1.0 pm particles of polystyrene and poly(methyl methacrylate) interacted when they were melt processed at 180 °C. They observed by confocal microscopy on a hot stage that there was a preferential motion for particles, which they attributed to a buoyancy-driven flow because of the 10% density difference between the polymers. Jang et al. had made a similar observation 49), Li et al. did not consider possible surface-tension induced convection or that droplets could migrate in a temperature gradient, as has been observed by Balasubramaniam et al. for the thermocapillary migration of bubbles 50),... 

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