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On the role of the Knudsen layer in rapid granular flows. (English) Zbl 1119.76069

Summary: A combination of molecular dynamics simulations, theoretical predictions and previous experiments are used in a two-part study to determine the role of Knudsen layer in rapid granular flows. First, a robust criterion for the identification of thickness of Knudsen layer is established: a rapid deterioration in Navier-Stokes order prediction of the heat flux is found to occur in 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. Secondly, 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 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 Knudsen layer.

MSC:

76T25 Granular flows
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