Abstract

We develop an analytical framework and numerical methods for the determination of the coefficient of self-diffusivity for the transport of a rarefied gas in channels, in the limit of large Knudsen number. We provide an effective method for determining the influence of channel surface micro-structure on the value of diffusivity. We also show how characteristic numbers of the system, namely geometric parameters of the micro-structure, the spectral gap of a Markov transition operator defined for a given micro-structure, and the tangential momentum accommodation coefficient of a commonly used model of surface scattering, are related. Examples of micro-structures are investigated regarding the relation of these quantities numerically and analytically.

Committee Chair

Renato Feres

Committee Members

Likai Chen, Todd Kuffner, Ari Stern, Gregory Yablonsky,

Degree

Doctor of Philosophy (PhD)

Author's Department

Mathematics

Author's School

Graduate School of Arts and Sciences

Document Type

Dissertation

Date of Award

Spring 5-15-2020

Language

English (en)

Author's ORCID

http://orcid.org/0000-0002-8169-562X

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Mathematics Commons

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