Steady rotation of an axially symmetric porous particle about its axis of revolution in a viscous fluid using Brinkman model

The steady rotational motion of an axially symmetric porous particle about its axis of symmetry in a viscous fluid is investigated using a semi-analytical approach. The general solution is obtained by utilizing Sampson spherical singularity method based on continuous distribution of a set of spherical singularities along the axis of symmetry within the porous prolate particle or on the fundamental plane within the porous oblate particle. The fluid flow outside the particle is governed by Navier–Stokes equations while the fluid flow inside the porous region is controlled by Brinkman model. The stress jump condition has been applied on the porous/fluid interface. The collocation technique is employed to satisfy the boundary conditions on the surface of the porous particle. Numerical results for the torque acting on the surface of the porous particle are tabulated and represented graphically for different values of the stress jump coefficient and for various values of the axial-to-radial aspect ratio of the spheroidal porous particle. It is found that the dimensionless hydrodynamic torque increases monotonically with the increase of the aspect ratio. Also, the increase of permeability parameter results in a decrease of the torque acting on the particle. The torque decreases monotonically with the increase of stress jump coefficient. The results of the torque acting on a porous spheroid rotating in a viscous flow assuming continuity of tangential stresses on the porous/fluid interface are recovered as a special case when the stress jump coefficient vanishes.