Effective viscosity and Reynolds number of non-Newtonian fluids using Meter model

Abstract

The Meter model (a four-parameter model) captures shear viscosityshear stress relationship (S-shaped type) of polymeric non-Newtonian fluids. We devise an analytical solution for radial velocity profile, average velocity and volumetric flow rate of steady state laminar flow of non-Newtonian Meter model fluids through a circular geometry. The analytical solution converts to the Hagen-Posseuille equation for the Newtonian fluid case. We also develop the formulations to determine effective viscosity, Reynolds number and Darcy's friction factor using measurable parameters as available rheological models do not correctly define these parameters for a given set of flow condition in circular geometry. The analytical solution and formulations are validated against experimental data. The results suggest that the effective Reynolds number and effective friction factor estimated using the proposed formulation helps to characterise non-Newtonian fluid flow through a circular geometry in laminar and turbulent flow.

Hydrodynamic drag reduction of shear-thinning liquids in superhydrophobic textured microchannels

“…5a. This behaviour of the friction factor in smooth channels as a function of shear rate in the entire regime for XG liquids is also similar to what was observed in another investigation (Shende et al 2021).…”

An empirical equation for shear viscosity of shear thickening fluids

“…the rate kinetics of rupture and formation of linkage between the particles of the polymers) [23][24][25] The shear stress-dependent Meter model equation (Eq. 1) [33,36] is a logistic equation which describes S-shape type curve (i.e. Newtonian plateau at high and low shear values and slope at intermediate shear values) of many shear-thinning fluids.…”

A pore network modelling approach to investigate the interplay between local and Darcy viscosities during the flow of shear-thinning fluids in porous media

“…where l T;0 and l T;1 are the low shear rates and high shear rates viscosity plateaus, c T is the consistency and n T is the shearthinning index. This model allows for the development of simple analytical solutions to relate effective viscosity to pressure drop during the flow of a non-Newtonian fluid in a capillary, which is not the case of Carreau fluids despite recent progress [11,15,27,28]. Nonetheless, whereas the truncated power law approximates reasonably well Carreau model under low shear rates, the differences are important at the highest shear rates [3].…”

“…Similar empirical approximations of l eff were also used in the works of López [3], Perrin et al [22] and Shende et al [28]. In order to assess the accuracy of the approximations of l eff provided by Eq.…”