Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Isothermal squeeze films

Author: W. E. Langlois
Journal: Quart. Appl. Math. 20 (1962), 131-150
DOI: https://doi.org/10.1090/qam/99963
MathSciNet review: QAM99963
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Abstract: A derivation is presented of the equation governing the pressure in a thin, flat film of ideal gas under isothermal conditions, when the surfaces bounding the film are in relative normal and tangential motion. When tangential motion is absent, the pressure equation reduces to a nonlinear heat equation, which admits of very few closed-form solutions. Various approximation methods are discussed, and two problems involving small periodic variation of the gap between parallel plates are solved by a perturbation method for a film in which fluid inertia is negligible.

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DOI: https://doi.org/10.1090/qam/99963
Article copyright: © Copyright 1962 American Mathematical Society

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