On the role of the Knudsen layer in rapid granular flows

TL;DR

This study investigates the influence of the Knudsen layer on rapid granular flows using simulations, theory, and experiments, establishing criteria for its thickness and identifying when its effects are significant in flow predictions.

Contribution

It introduces a robust criterion for identifying the Knudsen layer thickness and quantifies when its effects must be considered in flow modeling.

Findings

Knudsen layer effects are detectable within 2.5 mean free paths of a boundary.

Navier-Stokes predictions are reliable when the Knudsen layer is less than 20% of the domain.

Deterioration of predictions occurs when the entire domain is within the Knudsen layer.

Abstract

A combination of molecular-dynamics simulations, theoretical predictions, and previous experiments are used in a two-part study to determine the role of the Knudsen layer in rapid granular flows. First, a robust criterion for the identification of the thickness of the Knudsen layer is established: a rapid deterioration in Navier-Stokes-order prediction of the heat flux is found to occur in the Knudsen layer. For (experimental) systems in which heat flux measurements are not easily obtained, a rule-of-thumb for estimating the Knudsen layer thickness follows, namely that such effects are evident within 2.5 (local) mean free paths of a given boundary. Second, comparisons of simulation and experimental data with Navier-Stokes order theory are used to provide a measure as to when Knudsen layer effects become non-negligible. Specifically, predictions that do not account for the presence of a Knudsen layer appear reliable for Knudsen layers collectively composing up to 20% of the domain, whereas deterioration of such predictions becomes apparent when the domain is fully comprised of the Knudsen layer.