A general approach on the quantification of effective quantities in a pressure-driven flow of inelastic non-Newtonian fluid in arbitrary geometries based on the energy balance

Abstract

In this work, we propose a systematic approach in quantifying the effective viscosity, effective shear rate and pumping characteristics of pressure-driven continuous flows of non-Newtonian fluids in general flow geometries based on the energy balance. Only two flow constants (i.e., the coefficient of effective shear rate and the coefficient of energy dissipation rate), which depend solely on the flow geometry, are employed to quantify flow characteristics of continuous flow systems, independent of viscosity behaviors of a shear-thinning fluid. A similar approach based on the energy dissipation rate, so-called Metzner-Otto correlation [Metzner and Otto, AIChE J., vol. 3, p. 3-10] has been available for more than sixty years in a confined flow of agitator without rigorous derivation. In the present work, we extend the original Metzner-Otto correlation to continuous flows and begin with analytical derivation for this method in a circular pipe flow. Having validated analytically, we apply the present quantification method with the two flow constants to more general types of flows with various viscosity models (Newtonian, power-law, Carreau and Herschel-Bulkley models) such as an axisymmetric expansion/contraction flow with various expansion ratios and a flow in a Kenics mixer in order to show its accuracy and feasibility.