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Updated: Jul 11, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

Convective nonlinearity in non-newtonian fluids

Temmen¹, Pleiner, Liu

¹EMA, Universitat der Bundeswehr Hamburg, Holstenhofweg 85, 22043 Hamburg, Germany.

Physical Review Letters

|October 6, 2000

Summary

Hydrodynamic equations for viscoelastic, non-Newtonian liquids simplify to solid behavior at infinite yield time. This finding uniquely determines the nonlinear convective derivative, resolving a rheology debate.

Area of Science:

Rheology
Polymer Physics
Fluid Dynamics

Background:

Viscoelastic, non-Newtonian liquids exhibit complex flow behaviors.
The formulation of hydrodynamic equations for these materials is an area of active research.
The nonlinear convective derivative is a critical component in rheological models but lacks a universally accepted form.

Purpose of the Study:

To resolve the ongoing contention regarding the nonlinear convective derivative in rheology.
To establish a unique determination of the nonlinear convective derivative for viscoelastic liquids.
To demonstrate the connection between the long-time behavior of viscoelastic liquids and solid mechanics.

Main Methods:

Analysis of hydrodynamic equations in the limit of infinite yield time for stresses.

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Application of principles from solid mechanics to viscoelastic fluid behavior.

Derivation of the nonlinear convective derivative based on the limiting behavior.

Main Results:

The hydrodynamic equations for viscoelastic, non-Newtonian liquids reduce to those for solids at infinite yield time.
This limiting behavior uniquely determines the nonlinear convective derivative.
A specific form of the nonlinear convective derivative is proposed and validated.

Conclusions:

The study provides a definitive solution for the nonlinear convective derivative.
The findings bridge the gap between fluid dynamics and solid mechanics for viscoelastic materials.
This work is expected to advance the understanding and modeling of polymer melts and similar substances.