Drop in a Translational Gas Flow

In [340], an approximate solution was obtained for the problem about a translational gas flow (of small viscosity) past a viscous spherical drop. The solution uses expansions with respect to the small parameter 

The fluid motion outside and inside the drop is characterized by different Reynolds numbers (inside the drop, eU-, is used as the characteristic velocity)  

We seek the solution of the problem in the form of asymptotic expansions with respect to the small parameter e. The leading term of the expansion outside the drop is determined by the solution of the problem about the flow past a solid sphere. The leading term inside the drop corresponds to the viscous fluid 

The flow field inside the drop depends only on the two parameters Rei and Re2, and the dependence on Re2 proves unessential. The maximum dimensionless velocity of the fluid inside the drop wmax = wmax(Rei, Re2) is attained at the drop boundary. For Rei 2.5 [338], the following estimates hold  

The difference between the upper and the lower bounds is not very large, which shows that the dependence of the internal flow on the parameter Re2 is weak the above estimates are in a good agreement with known numerical results [262, 498], 

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