The Einstein viscosity correction in n dimensions

The effective viscosity of a dilute suspension of rigid $\text{n-}\text{dimensional}$ hyperspheres in a viscous fluid at small particle Reynolds numbers is determined; the result being

$\text{μ}{}_{\mathrm{eff}}\text{=μ}\text{1+}\text{n+2}\text{2}\text{φ}$

. Expressions are also given for the $\text{n-}\text{dimensional}$ Stokes velocity and pressure fields for a hypersphere in a pure straining flow.