# Gas motion in a microgap between a stationary plate and a plate oscillating in its normal direction

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## Abstract

Unsteady motion of a gas between two parallel plates is investigated in the case where one of the plates starts (harmonic) oscillation in its normal direction. A kinetic–theoretic approach is employed under the condition that the distance between the two plates is comparable to the mean free path of the gas molecules and/or the frequency of oscillation of the plate is comparable to their mean collision frequency. More specifically, the Bhatnagar–Gross–Krook model of the Boltzmann equation is solved numerically for wide ranges of parameters, such as the Knudsen number and the Mach number, with special interest in the fully nonlinear wave motion. As the result, the time evolution of the local flow field and the periodic state attained at later times are obtained accurately. It is shown that, in the periodic state, one-period average of the momentum (or energy) transferred from the oscillating to the stationary plate takes a nonzero value in contrast to the linear theory, and it becomes minimum at an intermediate Knudsen number (for a given oscillation of the plate and for a given distance between the center of the oscillating plate and the stationary plate).

## Keywords

Gas flows in microscales Kinetic theory of gases Moving boundary problems Oscillatory gas flows## Notes

### Acknowledgments

This work was started, while the authors were attending the Semester Program on “Kinetic Theory and Computation” at the Institute for Computational and Experimental Research in Mathematics (ICERM), Brown University in the fall of 2011. They express their gratitude to ICERM for its support and hospitality. This work is supported by the grants-in-aid No. 23360048 and No. 12J02418 from the Japan Society for the Promotion of Science (JSPS).

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