Semi-analytical solutions of passive scalar transport in generalized Newtonian fluid flow

TL;DR

This paper derives semi-analytical solutions for passive scalar transport in generalized Newtonian fluids flowing in simplified geometries, extending classical Taylor solutions to non-Newtonian fluids with validation against microscale simulations.

Contribution

It introduces a general semi-analytical framework for scalar transport in non-Newtonian fluids without assuming specific rheology, broadening applicability beyond Newtonian models.

Findings

Solutions agree with microscale simulations within numerical error

Applicable to various non-Newtonian fluids like viscoelastic and viscoplastic

Provides analytical tools for enhanced molecular diffusion in low Peclet systems

Abstract

Transport during flow of generalized Newtonian fluids (GNFs) appears often in systems that can be treated in a simplified form as either cylindrical tubes or slit openings between parallel plates. Based on the pioneering work of Taylor, analytical solutions for transport in these simplified systems were derived generally. This includes analytical solutions for advection dominated transport, as well as a computation of the enhanced molecular diffusion coefficient in low Peclet number systems. The newly derived general solutions for species transport were applied to Cross and Carreau model fluids using a semi-analytical solution for velocity of these fluids. The semi-analytical solutions derived herein were compared to microscale simulations and showed agreement to within the numerical error of those simulations. The semi-analytical transport solutions derived here were developed without assuming any specific fluid rheology, thus these solutions can be applied to other non-Newtonian fluids, such as viscoelastic or viscoplastic fluids, as a straightforward extension of this work.