Viscosity measurement of non-Newtonian fluids in pressure-driven flows of general geometries based on energy dissipation rate

Abstract

A novel viscosity measurement method is presented, which can be applied to the pressure-driven flow of an inelastic non-Newtonian fluid in an arbitrary geometry. The method is established on the balance of the energy dissipation rate such that the external power is dissipated within the system as viscous dissipation in a laminar regime in the absence of a body force. The effective viscosity can be expressed algebraically in terms of the pressure drop and flow rate and the corresponding effective shear rate is readily determined by flow rate; the relationship between effective viscosity and effective shear rate is found identical to the true material viscosity behavior. The two flow numbers, which depend on flow geometry only and are almost independent of fluid rheology, are involved: the coefficient of energy dissipation rate that associates the total energy dissipation rate to the Reynolds number; and the coefficient of effective shear rate, which relates flow rate to effective shear rate. After analytically validating the method for pressure-driven flow of a power-law fluid in a circular pipe, three different flows with complicated geometries were tested: numerical validations for axisymmetric expansion-contraction flows and flows in a Kenics mixer, and experimental validation for flows in a complex microfluidic array with Xanthan gum solutions. Errors in viscosity were less than 2.9% and 16% in simulations and in experiments, respectively. The method is well-suited for on-line monitoring of in-situ viscosity for non-Newtonian fluid flow in industrial processes.