Exponential Formula for Computing Effective Viscosity

An exponential model is proposed in this paper for evaluating the effective viscosity of a particle-fluid mixture. First, the theoretical consideration is restricted to the dilute condition without the effects of dynamic particle interactions and fluid turbulence. This leads to a power series expressed in terms of particle concentration, which can be viewed as an extension of the Einstein’s formula. The derived expression is then modified by including indirectly effects of inter-particle collisions, fluid turbulence and random motion of the particles, which can cause the effective viscosity to be increased significantly with increasing particle fraction in the mixture. Finally comparisons are made between the present study and various theoretical and empirical results available in the literature and satisfactory agreement is observed.