Drag Force and Velocity of Motion

The solution of the hydrodynamic part of the problem, as before, can be written in the form of the stream functions (5.10.6), where the constant B remains undetermined as yet. 

The approximate solution of the thermal and diffusion problem can be found by the method of matched asymptotic expansions (see Section 4.4) with the stream functions (5.10.6) one must retain only the zero and the first terms of the expansions with respect to low Peclet numbers and use the boundary conditions (5.10.5) and (5.11.2) to obtain the following values of the constant B and the force acting on the drop  

The drop velocity in the gravitation field can be found from the condition of the zero sum of the forces (5.11.3), the gravitational force, and the buoyancy force  

Mass and Heat Transfer Under Complicating Factors 

For B 0, the force (5.11.3) is, as usual, a drag force. For B 0, the force (5.11.3) becomes a propulsion force, since it is codirected with the drop motion. 

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