ABSTRACT
In the Stokes flow limit, Young et al. [27] developed an exact solution for the velocity of the bubble and the temperature and velocity fields in the liquids. The velocity of the bubble is given by the following expression:
(5)
where kµ is the ratio of the dynamic viscosity of the drop phase to that of the continuous phase and kk is the corresponding ratio of thermal conductivities. The quantity Us is defined by
(6)
where γT is the rate of change of interfacial tension with temperature, and GT is the temperature gradient imposed in the continuous phase fluid. For a bubble, it is generally
reasonable to assume that kµ and kk are both very small compared to unity. Thus the bubble velocity is
(7)
The analysis leading to the formula in Eq. (5) is based on the assumption that the bubble interface is mobile. Merritt and Subramanian [28] performed measurements of the velocity of air bubbles moving under the combined influence of gravity and the thermocapillary driving force in silicone oil. They found agreement with the linear dependence on the bubble radius predicted by Eq. (5).
