Exponential formula for computing effective viscosity

An exponential model is proposed for evaluating the effective viscosity of a particle–fluid mixture. First, theoretical consideration is restricted to the dilute condition without 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 Einsteinʹs formula. The derivation is then extended using an exponential model for the condition of high particle concentrations. The exponential formula obtained, which is not subjected to the maximum particle concentration, is found comparable to various empirical formulas available in the literature.