Time-harmonic waves in Korteweg and nematic-Korteweg fluids
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Updated: May 11, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Patrick E Farrell1, Umberto Zerbinati2
1Charles University, Mathematical Institute, University of Oxford, Oxford, United Kingdom and Mathematical Institute, Faculty of Mathematics and Physics, Czechia.
Abstract:
We derive the Helmholtz-Korteweg equation, which models acoustic waves in Korteweg fluids. We further derive a nematic variant of the Helmholtz-Korteweg equation, which incorporates an additional orientational term in the stress tensor. Its dispersion relation coincides with that arising in Virga's analysis of the Euler-Korteweg equations, which we extend to consider imaginary wave numbers and the effect of boundary conditions. In particular, our extensions allow us to analyze the effect of nematic orientation on the penetration depth of evanescent plane waves, and on the scattering of sound waves by obstacles. Furthermore, we make new, experimentally verifiable predictions for the effect of boundary conditions for a modification of the Mullen-Lüthi-Stephen experiment, and for the scattering of acoustic waves in nematic-Korteweg fluids by a circular obstacle.
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