Abstract
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.
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