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Related Experiment Video

Updated: Jun 21, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

Saffman-Taylor instability for generalized Newtonian fluids.

S Mora¹, M Manna

¹Laboratoire des Colloïdes, Verres et Nanomatériaux, Université Montpellier 2, 34095 Montpellier, France. smora@univ-montp2.fr

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|August 8, 2009

Summary

This study analyzes Saffman-Taylor instability in non-Newtonian fluids within Hele-Shaw cells. It reveals that some shear-thickening fluids exhibit stable normal modes, unlike shear-thinning fluids which can develop faster instabilities.

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Area of Science:

Fluid dynamics
Rheology
Instability phenomena

Background:

The Saffman-Taylor instability is a classic phenomenon in fluid dynamics, typically studied for Newtonian fluids.
Non-Newtonian fluid behavior introduces complexities not fully captured by classical models.
Hele-Shaw cells provide a controlled environment for studying viscous fingering and related instabilities.

Purpose of the Study:

To theoretically investigate the linear Saffman-Taylor instability for a broad range of non-Newtonian fluids.
To derive and analyze Darcy's law for generalized Newtonian fluids in this context.
To identify conditions under which non-Newtonian fluids exhibit different instability behaviors compared to Newtonian fluids.

Main Methods:

Theoretical analysis of fluid flow in a Hele-Shaw cell.
Introduction and application of generalized Newtonian fluid concepts.
Derivation of the growth rate relation for normal modes in non-Newtonian flows.
Calculation of Darcy's law for non-Newtonian fluids.

Main Results:

A generalized Darcy's law is derived for non-Newtonian fluids.
For shear-thinning fluids at high shear rates, the derived Darcy's law avoids classical nonphysical divergences.
Specific non-Newtonian fluids are identified that exhibit faster instability growth than Newtonian fluids under identical conditions.
It is shown that for certain shear-thickening fluids, all normal modes remain stable.

Conclusions:

The study provides a robust theoretical framework for Saffman-Taylor instability in non-Newtonian fluids.
The findings offer new insights into the stability criteria for different classes of non-Newtonian fluids.
This work resolves long-standing issues with classical models for shear-thinning fluids and highlights unique stability characteristics of shear-thickening fluids.