Thermocapillary drift velocity

Note that for the thermocapillary drift velocity in the absence of gravitation, the result (5.10.9) is valid not only at small but at arbitrary Reynolds numbers. For B = 0, the flow (5.10.6) satisfies the complete equations of motion without dropping the convective terms (that is, the Navier-Stokes equations.) At the same time, we cannot omit the requirement of small Peclet numbers. 

In [58,59,466,469], more precise results are cited taking into account higher-order approximations with respect to small Reynolds and Peclet numbers. For example, the following expression for thermocapillary drift velocity was found in [466] ... 

The results (5.10.8) for the thermocapillary force Ft and (5.10.9) for the thermocapillary drift velocity, which were obtained under the assumption of a constant temperature gradient remote from the drop, prove to hold also for a varying gradient. These expressions can be rewritten in a vector form as follows [468] ... 

Let us estimate the thermocapillary force applied to a drop and the velocity of the drop thermocapillary drift in the absence of gravitation. We assume the ambient fluid to be infinite and the nonuniform temperature field remote from the drop to be linear in X ... 

In [373], bubble thermocapillary drift was considered in the external temperature gradient at high Peclet numbers. The drift velocity was found to be... 

The corresponding problem was considered in [322, 389], The radiation in [389] was assumed to have the form of a plane-parallel beam being absorbed on the drop surface as on a black body, but freely passing through the exterior fluid. The temperature remote from the drop is assumed to be constant. For the thermocapillary force and for the velocity of thermocapillary drift of the drop in the absence of gravitation, the following expressions were obtained (J is the radiation flux power) ... 

---