Effective viscosity of a concentrated suspension of uncharged porous spheres

A theory of the effective viscosity ηs of a concentrated suspension of porous spheres (soft particles with no particle core) consisting of uncharged polymers in a liquid of viscosity η is presented. We assume that polymer segments are regarded as resistance centers, exerting frictional forces −γu on the liquid flowing in the sphere, where u is the liquid velocity and γ is the frictional coefficient, We derive an expression for the effective viscosity ηs of the suspension, which depends on the radius a and volume fraction ϕ of the spheres and a parameter λ = (γ/η)1/2. This expression covers the viscosity expression derived by Natraj and Chen [V. Natraj, S.B. Chen, J. Colloid Interface Sci. 251 (2002) 200] for the case of dilute suspension of uncharged porous spheres (ϕ → 0) and tends to Simhaʹs result [R.J. Simha, J. Appl. Phys., 23 (1952) 1020] for a concentrated suspension of uncharged rigid spheres (λ → ∞).