Axisymmetric Slow Rotation of Coaxial Soft/Porous Spheres

The steady low-Reynolds-number rotation of a chain of coaxial soft spheres (each with an impermeable hard core covered by a permeable porous layer) about the axis in a viscous fluid is analyzed. The particles may be unequally spaced, and may differ in the permeability and inner and outer radii of the porous surface layer as well as angular velocity. By using a method of boundary collocation, the Stokes and Brinkman equations for the external fluid flow and flow within the surface layers, respectively, are solved semi-analytically. The particle interaction effect increases as the relative gap thickness between adjacent particles or their permeability decreases, which can be significant as the gap thickness approaches zero. A particle's hydrodynamic torque is reduced (its rotation is enhanced) when other particles rotate in the same direction at equivalent or greater angular velocities, but increases (its rotation is hindered) when other particles rotate in the opposite direction at arbitrary angular velocities. For particles with different radii or permeabilities, the particle interaction has a greater effect on smaller or more permeable particles than on larger or less permeable particles. For the rotation of three particles, the presence of the third particle can significantly affect the hydrodynamic torques acting on the other two particles. For the rotation of numerous particles, shielding effects between particles can be substantial. When the permeability of porous layers is low, relative fluid motion is barely felt by the hard cores of the soft particles. The insights gained from this analysis on the effects of interactions among rotating soft particles may be of great importance in many physicochemical applications of colloidal suspensions.