Drift of a Drop in Complicated Cases

Drift for a nonlinear dependence of the surface tension on temperature. In 

The analysis shows that if the function (5.9.19) has a minimum (i.e., a 0), then the equilibrium plane will be attractive and the equilibrium will be stable (the drift velocity outside the equilibrium plane always is directed to the plane.) For a 0, the equilibrium plane will be repulsive, and the equilibrium will be unstable (the drift velocity is directed from the plane.) Two drops in an equilibrium plane move towards each other if a 0 if a 0, then the drops diverge. 

Radiation-induced thermocapillary motion of a drop. The temperature gradient is the simplest but not the unique method for bringing about the thermocapillary drift of a drop. If the drop is opaque and the fluid is transparent, one can move the drop by a light beam in a uniformly heated fluid. The radiation absorbed by the drop will heat it nonuniformly, thus producing thermocapillary stresses. For dcr/dT 0, the drop will drift towards the warmer part, that is, towards the beam. 

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)  

Here the quantities Ft and Ut are positive if the corresponding vectors are codirected with the radiation beam and negative otherwise. As follows from the second formula in (5.10.10), if o 0, then the drop drifts toward the beam. 

---