New insights into the classical molecular transport theory

TL;DR

This paper challenges classical molecular transport theory by demonstrating that transport coefficients are proportional to the mean square free path, not just the mean free path, affecting the accuracy of transport predictions.

Contribution

It reveals that the molecular transport coefficient depends on the mean square free path, providing a more accurate theoretical framework supported by simulations.

Findings

Transport coefficients are proportional to the mean square free path.

Classical theory may misestimate transport coefficients for different free path distributions.

Simulation results confirm the importance of the second moment of free path distribution.

Abstract

In the classical transport theory, the coefficients such as the diffusion, thermal conductivity and viscosity of fluid are usually expressed in a form proportional to the mean free path of molecules. We point out that this may cause a great misunderstanding in the molecular transport theory and prove from multiple perspectives of theory and simulation that the molecular transport coefficient is actually proportional to the mean square free path, i.e., the second moment of the free path distribution function. For two systems with the same mean free path but different molecular free path distributions, the classical expression gives the same transport coefficient, whereas the expression with the mean square free path predicts different transport coefficients, in which their difference may vary from zero to several times as the distribution function becomes more dispersed.