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Convective nonlinearity in non-newtonian fluids
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.
- 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.
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