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Time-harmonic waves in Korteweg and nematic-Korteweg fluids.
Patrick E Farrell1, Umberto Zerbinati2
1Charles University, Mathematical Institute, University of Oxford, Oxford, United Kingdom and Mathematical Institute, Faculty of Mathematics and Physics, Czechia.
Physical Review. E
|April 18, 2025
Summary
We derived a nematic Helmholtz-Korteweg equation for acoustic waves in Korteweg fluids. This new model analyzes nematic orientation effects on wave penetration and scattering, offering experimental predictions.
Area of Science:
- Fluid dynamics
- Acoustics
- Materials science
Background:
- The Helmholtz-Korteweg equation models acoustic waves in Korteweg fluids.
- Nematic fluids exhibit unique orientational properties influencing wave behavior.
Purpose of the Study:
- To derive a nematic variant of the Helmholtz-Korteweg equation.
- To extend existing analyses to include imaginary wave numbers and boundary conditions.
- To investigate the impact of nematic orientation on acoustic wave phenomena.
Main Methods:
- Derivation of the nematic Helmholtz-Korteweg equation.
- Analysis of dispersion relations, incorporating imaginary wave numbers.
- Investigation of boundary condition effects on wave phenomena.
Main Results:
- A nematic Helmholtz-Korteweg equation was successfully derived.
- The dispersion relation aligns with extensions of Euler-Korteweg equations.
- Analysis revealed nematic orientation effects on evanescent wave penetration and scattering by obstacles.
Conclusions:
- The derived nematic equation provides a framework for studying acoustic waves in nematic fluids.
- New, experimentally verifiable predictions are made for modified experiments and scattering scenarios.
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