Heat Conduction in Momentum-Conserving Fluids: From quasi-2D to 3D systems

TL;DR

This study uses molecular dynamics simulations to explore how heat conduction transitions from anomalous to normal behavior as systems go from quasi-2D to 3D, revealing distinct transport regimes and a dimensional crossover.

Contribution

It identifies three heat transport regimes in momentum-conserving fluids and provides quantitative validation of scaling predictions across dimensions.

Findings

Ballistic regime: conductivity scales linearly with size, autocorrelation remains constant.

Kinetic regime: size-independent conductivity with exponential decay of autocorrelation.

Hydrodynamic regime: quasi-2D systems show logarithmic divergence, 3D systems show finite conductivity.

Abstract

Using nonequilibrium and equilibrium molecular dynamics simulations, we investigate heat conduction in a momentum-conserving mesoscopic fluid modeled by multiparticle collision dynamics. Across quasi-two-dimensional (q-2D) to three-dimensional (3D) systems, we identify three distinct transport regimes: (i) a \emph{ballistic regime}, where thermal conductivity scales linearly with system size ($\kappa \sim L$) and the total heat current autocorrelation function $C(t)$ remains constant; (ii)~a \emph{kinetic regime}, characterized by size-independent $\kappa$ and exponentially decaying $C(t)$, demonstrating that normal heat conduction dominated by kinetic effects is far more ubiquitous than previously observed in 1D systems; and (iii)~a \emph{hydrodynamic regime}, where the q-2D system exhibits logarithmically divergent conductivity ($ \kappa \sim \ln L $ ) with $ C(t) \sim t^{-1} $ , while the 3D system displays finite $ \kappa $ and $ C(t) \sim t^{-3/2} $. Our results, observed in the hydrodynamic regime, quantitatively validate the scaling predictions for heat transport and reveal a clear dimensional crossover -- from 2D-like anomalous transport to 3D Fourier behavior. These results lay a foundation for understanding thermal transport in q-2D to 3D systems and have practical implications for the design of micro- and nanoscale thermal devices.