Cell models for suspension viscosity

Mobilities of a Spherical Particle Straddling the Interface of a Semi-Infinite Brinkman Flow

The motion of a spherical particle straddling the flat interface of a semi-infinite Brinkman flow is considered under the conditions of low Reynolds number and zero capillary number regime. The analysis is applied in the case of 90 deg contact angle and when the viscosity of the constituent fluid in the Brinkman region is much more than that of the adjacent fluid. Analytical expressions for the hydrodynamic scalar resistance coefficients are obtained and represented graphically as a function of the slip parameter at the surface of the particle and the permeability parameter of the porous region. The hydrodynamic mobilities are also obtained and represented in tables. The limiting cases of Stokes clear fluid and Darcy's flow are recovered.

Cell Models for the Primary Electroviscous Effect

The primary electroviscous effect in a nondilute suspension of charged spherical particles is studied by means of cell models. The governing equations are derived, and then analytic results are obtained by restricting attention to the limit of thin double layers, small Hartmann and Peclet numbers, and small potentials. Previous work has assumed that the velocity at the outer boundary of the cell is identical to the imposed flow, as proposed by Simha (J. Appl. Phys. 1952, 23, 1020). Results with this boundary condition are compared against those predicted when the tangential shear stress on the outer boundary is assumed to be unperturbed, as proposed by Happel (J. Appl. Phys. 1957, 28, 1288). Both the hydrodynamic and electroviscous contributions to the effective viscosity are smaller with the Happel boundary condition, showing that such cell models offer a range of predictions and should be used with caution.