Strongly confined fluids: Diverging time scales and slowing down of equilibration

TL;DR

This paper investigates the dynamics of strongly confined fluids, revealing diverging relaxation times as confinement increases, with analytical predictions and experimental suggestions for testing these effects.

Contribution

It provides a theoretical analysis of diverging relaxation times in confined fluids and derives explicit formulas for their divergence rates.

Findings

Relaxation times diverge as L^{-3} and L^{-4} for confined and unconfined degrees of freedom.

Analytical expression for the L^{-3} divergence depends on pair potential and distribution function.

Experimental setups are proposed to verify the theoretical predictions.

Abstract

The Newtonian dynamics of strongly confined fluids exhibits a rich behavior. Its confined and unconfined degrees of freedom decouple for confinement length $L \to 0$. In that case and for a slit geometry the intermediate scattering functions $S_{\mu\nu}(q,t)$ simplify, resulting for $(\mu,\nu) \neq (0,0)$ in a Knudsen-gas like behavior of the confined degrees of freedom, and otherwise in $S_{\parallel}(q,t)$, describing the structural relaxation of the unconfined ones. Taking the coupling into account we prove that the energy fluctuations relax exponentially. For smooth potentials the relaxation times diverge as $L^{-3}$ and $L^{-4}$, respectively, for the confined and unconfined degrees of freedom. The strength of the $L^{-3}$ divergence can be calculated analytically. It depends on the pair potential and the two-dimensional pair distribution function. Experimental setups are suggested to test these predictions.