Steady-state hydrodynamics of a viscous incompressible fluid with spinning particles

The steady-state hydrodynamics of a viscous incompressible fluid with spinning particles is studied on the basis of extended Stokes equations. The profiles of flow velocity and spin velocity in simple flow situations may be used to determine the vortex viscosity and spin viscosity of the molecular liquid or fluid suspension. As an example, one situation studied is the flow generated by a uniform torque density in a planar layer of infinite fluid. The spinning particles drive a nearly uniform flow on either side of the layer, in opposite directions on the two sides. The Green function of the extended Stokes equations is derived. The translational and rotational friction coefficients of a sphere with no-slip boundary conditions, and the corresponding flow profiles, are calculated.