Low Reynolds Number Flows around an Impulsively Started Sphere

The unsteady flow field of an incompressible viscous fluid around an impulsively started sphere in slow motion is studied in detail. Integral expressions are derived from the nonlinear vorticity equation and are solved by the method of matched asymptotic expansions. The present analysis shows that five regions are necessary to complete the present singular perturbation problem and the matching with respect to time coordinate is not required in order to obtain unique solutions unlike earlier theories. In the present paper, the transient drag forces for the beginning of motion, intermediate time of motion, and the long-time of motion are obtained in an alternative form and compared with earlier results.