Steady azimuthal flow field induced by a rotating sphere near a rigid disk or inside a gap between two coaxially positioned rigid disks

Geometric confinements play an important role in many physical and biological processes significantly affect the rheology behavior of colloidal suspensions at low Reynolds numbers. On basis linear Stokes equations, we investigate theoretically computationally viscous azimuthal flow induced by slow rotation a small spherical particle located vicinity rigid no-slip disk or inside gap between two coaxially positioned disks same radius. We formulate solution hydrodynamic problem as mixed-boundary-value whole fluid domain, which subsequently transform into system dual integral equations. Near stationary disk, show that resulting equation can be reduced elementary Abel admits unique analytical solution. Between disks, demonstrate transformed Fredholm equations first kind. The latter are solved means numerical approaches. Using our solution, further effect on rotational motion provide expressions mobility function geometry. compare results with corresponding finite-element simulations observe very good agreement.