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Updated: Oct 3, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Variational formulation for the dynamics of soft matter including inertia
1Department of Mathematical Sciences and Interdisciplinary Centre for Mathematical Modelling, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom.
Abstract:
The motion of liquids and soft matter is over-damped and "slow" when viscosity dominates. In this (low Reynolds-number) limit and when the system is isothermal, the equations of motion may be generated via Onsager's variational principle, which neglects inertia. This variational approach is immensely powerful, being used to obtain equations of motion for colloidal fluids, droplets on surfaces, and much more. However, inertia can play a role, manifesting as vibrations and under-damped motion. Here, we show how to extend this variational framework so that it remains valid when damping/dissipation and inertia are both equally important.
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