Stresses in non-equilibrium fluids: Exact formulation and coarse-grained theory

The Journal of Chemical Physics
Matthias KrügerDavid S Dean

Abstract

Starting from the stochastic equation for the density operator, we formulate the exact (instantaneous) stress tensor for interacting Brownian particles and show that its average value agrees with expressions derived previously. We analyze the relation between the stress tensor and forces due to external potentials and observe that, out of equilibrium, particle currents give rise to extra forces. Next, we derive the stress tensor for a Landau-Ginzburg theory in generic, non-equilibrium situations, finding an expression analogous to that of the exact microscopic stress tensor, and discuss the computation of out-of-equilibrium (classical) Casimir forces. Subsequently, we give a general form for the stress tensor which is valid for a large variety of energy functionals and which reproduces the two mentioned cases. We then use these relations to study the spatio-temporal correlations of the stress tensor in a Brownian fluid, which we compute to leading order in the interaction potential strength. We observe that, after integration over time, the spatial correlations generally decay as power laws in space. These are expected to be of importance for driven confined systems. We also show that divergence-free parts of the stress tensor ...Continue Reading

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Citations

May 20, 2018·Physical Review. E·Christian M RohwerMatthias Krüger
Jun 17, 2018·Physical Review. E·Derek Frydel, Rudolf Podgornik
Nov 16, 2020·The European Physical Journal. E, Soft Matter·Florian Vogel, Matthias Fuchs
Mar 20, 2021·Physical Review. E·Dino Osmanović
May 1, 2021·Physical Review Letters·Saeed Mahdisoltani, Ramin Golestanian
Jul 18, 2021·Physical Review. E·Markus GrossS Dietrich

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