Extension of Einstein's viscosity equation to that for concentrated dispersions of solutes and particles

A viscosity equation for concentrated solutions or suspensions is derived as an extension of Einstein's hydrodynamic viscosity theory for dilute dispersions of spherical particles. The derivation of the equation is based on the calculation of dissipation of mechanical energy into heat in the dispersion, subtracting the energy dissipation in the portion of solutes or particles. The viscosity equation derived thus was well fitted to the viscosity-concentration relationship of the concentrated aqueous solutions of glucose and sucrose. For the suspensions of bakers’ yeast, the concentration dependency of viscosity was expressed well with some modification for the flow pattern around suspended particles. It is suggested that these viscosity equations can be widely applied to both diluted and concentrated dispersions of various solutes and particles.