An inverse methodology for the rheology of a power-law non-Newtonian fluid

Abstract

The current paper presents a novel methodology for calculating the rheological para-meters for dilute aqueous solutions of a power-law non-Newtonian fluid, xanthan gum (XG). Previous studies have verified the fidelity of finite-element modelling of the Navier—Stokes equations for reproducing the velocity fields of XG solutions in a microfluidic T-junction with experimental observations obtained using micron resolution particle image velocimetry (μ-PIV). As the pressure-driven fluid is forced to turn the corner of the T-junction, a range of shear rates, and therefore viscosities, are produced within the flow system. Thus, a setup that potentially establishes the rheological profile of XG from a single experiment is selected. An inverse method based on finding the mapping between the statistical moments of the velocity field and the constitutive parameters of the viscosity profile demonstrated that such a system could potentially be used for the design of an efficient microfluidic rheometer. However, μ-PIV technology is expensive and the equipment is bulky. The current paper investigates whether different flow features could be used to establish the rheological profile.