Boundary Layer Flow due to the Vibration of a Sphere

Abstract

Boundary layer flow of the Newtonian fluid that is caused by the vibration of inner sphere while the outer sphere is at rest is calculated. Vishik-Lyusternik (Nayfeh refers to this method as the method of composite expansions) method is employed to construct an asymptotic expansion of the solution of the Navier-Stokes equations in the limit of high-frequency vibrations for Reynolds number of $O(\mathrm{1})$. The effect of the Stokes drift of fluid particles is also considered.