Flow of a colloidal solution in an orthogonal rheometer

TL;DR

This study investigates the complex flow behavior of colloidal solutions in an orthogonal rheometer, revealing boundary layer formation at low Reynolds numbers and exploring novel stress models with non-invertible power-law relationships.

Contribution

It introduces a new class of stress power-law fluid models and analyzes flow behavior under various parameters, including non-invertible models and limiting stress conditions.

Findings

Pronounced boundary layers form at low Reynolds numbers.

New stress power-law models exhibit non-invertibility.

Boundary layer development occurs in limiting stress fluids.

Abstract

The flow of a colloidal solution between two parallel disks rotating with the same angular velocity about two non-coincident axes was studied. The problem has been approached from two perspectives, the first wherein the stress is expressed in terms of a power-law of kinematical quantities, and the second wherein we consider a non-standard model where the symmetric part of the velocity gradient is given by a power-law of the stress. For a range of power-law exponents, the class of models are non-invertible. By varying the material and geometric parameters, changes in the flow behaviour at different Reynolds numbers were analysed. We find that pronounced boundary layers develop even at low Reynolds numbers based on the power-law exponents. The new class of stress power-law fluids and fluids that exhibit limiting stress also show the ability to develop boundary layers.