Spherical cell approach for the effective viscosity of suspensions

In the present paper, the spherical cell approach is employed for addressing the effective viscosity of suspensions of spherical particles. The proposed derivation is based on the only assumption which constitutes the essence of the spherical cell approach: a representative part of the suspension is a spherical cell which contains a particle surrounded by the continuous phase. In contrast with the previous studies on this topic, no additional assumptions are used in the present analysis. The general method of derivation and the final result, which represents the effective viscosity as a function of the solid-phase volume fraction, are compared with earlier studies where the spherical cell approach was applied for describing the effective viscosity.