Abstract
It is difficult to determine the representative apparent viscosity of a pseudoplastic liquid in a stirred vessel because the viscosity of the liquid varies with on the shear rate in the vessel. Until now, the method proposed by Metzner and Otto has exclusively been applied to the determination of this value. In this study, we proposed a new method for determining the representative viscosity, ηa, by averaging the viscosity distribution in the vessel using a weight of dissipation function on the basis of numerical simulation results, without any power correlation with a Newtonian liquid. Further, we calculated the representative shear rate, Γ, from ηa using a rheological equation presenting the pseudoplasticity; then, we found that Metzner's constant, B, can be expressed as the function of the impeller Reynolds number, Red. The reliability of this method was ascertained by comparing the results with those obtained when using the conventional Metzner's method: better conservation of flow similarity was achieved when scaling up the vessel using the proposed method than when employing the conventional method.
