Characteristics of stratified flows of Newtonian/non-Newtonian shear-thinning fluids

TL;DR

This paper derives exact solutions for stratified laminar flows of Newtonian and shear-thinning non-Newtonian fluids, investigates flow characteristics in inclined channels, and proposes an algorithm to predict when shear-thinning effects can be approximated as Newtonian behavior.

Contribution

It provides the first exact solutions for stratified flows involving Carreau shear-thinning fluids and introduces an iterative algorithm to predict Newtonian behavior in two-phase flow modeling.

Findings

Two-phase flow can behave like Newtonian flow despite complex rheology.

The proposed algorithm predicts when shear-thinning effects are negligible.

Exact solutions improve understanding of flow boundaries and practical applications.

Abstract

Exact solutions for laminar stratified flows of Newtonian/non-Newtonian shear-thinning fluids in horizontal and inclined channels are presented. An iterative algorithm is proposed to compute the laminar solution for the general case of a Carreau non-Newtonian fluid. The exact solution is used to study the effect of the rheology of the shear-thinning liquid on two-phase flow characteristics considering both gas/liquid and liquid/liquid systems. Concurrent and counter-current inclined systems are investigated, including the mapping of multiple solution boundaries. Aspects relevant to practical applications are discussed, such as the insitu hold-up, or lubrication effects achieved by adding a less viscous phase. A characteristic of this family of systems is that, even if the liquid has a complex rheology (Carreau fluid), the two-phase stratified flow can behave like the liquid is Newtonian for a wide range of operational conditions. The capability of the two-fluid model to yield satisfactory predictions in the presence of shear-thinning liquids is tested, and an algorithm is proposed to a priori predict if the Newtonian (zero shear rate viscosity) behaviour arises for a given operational conditions in order to avoid large errors in the predictions of flow characteristics when the power-law is considered for modelling the shear-thinning behaviour. Two-fluid model closures implied by the exact solution and the effect of a turbulent gas layer are also addressed.