Transient flow caused by a sudden impulse or twist applied to a sphere immersed in a viscous incompressible fluid

An analytic solution of the linearized Navier-Stokes equations is presented for the flow of an incompressible viscous fluid about a sphere suddenly set in motion by an impulse or twist. Mixed slip-stick boundary conditions are assumed to hold at the surface of the sphere. The transient flow pattern depends on the mass and moment of inertia of the sphere. The impulsive translational motion of the sphere generates an expanding vortex ring. Conservation of total momentum is discussed and the momentum of the fluid is expressed as a sum of a potential and a viscous contribution. Conservation of total angular momentum is verified in the case of rotational motion. (c) 2007 American Institute of Physics.