Cell models for suspension viscosity

Cell models for the viscosity μμ of a suspension of spherical particles in Newtonian fluid of viscosity μ0μ0 are discussed. Various boundary conditions on the outer boundary of the spherical cell lead to different results: the viscosity predicted for a zero velocity perturbation boundary condition is higher than those predicted with zero tangential stress perturbation. However, in all cases Einstein's prediction μ/μ0=1+2.5φ+⋯μ/μ0=1+2.5φ+⋯ holds in the limit of small solid volume fraction φ⪡1φ⪡1.