NDLI: Analytical Results for Sound Wave Propagation in Small-Scale Two-Dimensional Channels

Content Provider	The American Society of Mechanical Engineers (ASME) Digital Collection
Author	Nicolas, G. Hadjiconstantinou
Copyright Year	2003
Abstract	When the characteristic scale of a channel decreases, wave propagation is increasingly dominated by viscous effects. This was first realized by Lamb who predicted that when the channel size is small compared to the diffusion length based on the oscillation frequency, the gas inertia becomes negligible (the fluid motion is effectively quasi-steady) and the flow is isothermal. This parameter regime is referred to as the narrow channel regime. We take advantage of this observation to derive analytical results for wave propagation in small scale channels for arbitrary Knudsen numbers, since due to their small transverse dimensions micro and nanochannels satisfy the narrow channel requirement except at very high frequencies. In the slip-flow regime in particular where the equations of motion can be integrated analytically, we show that thermal effects are always negligible and that the long wavelength approximation is always satisfied for narrow channels. We also discuss how this theory can be extended beyond the narrow channel approximation, that is, to include the effects of inertia and heat conduction to first order. Our results are verified by direct Monte Carlo simulations of the Boltzmann equation.
Sponsorship	Nanotechnology Institute
Starting Page	275
Ending Page	280
Page Count	6
File Format	PDF
ISBN	0791836673
DOI	10.1115/ICMM2003-1030
Volume Number	1st International Conference on Microchannels and Minichannels
Conference Proceedings	ASME 2003 1st International Conference on Microchannels and Minichannels
Language	English
Publisher Date	2003-04-24
Publisher Place	Rochester, New York, USA
Access Restriction	Subscribed
Subject Keyword	Slip flow Sound waves Approximation Inertia (mechanics) Oscillations Dimensions Equations of motion Diffusion (physics) Flow (dynamics) Wavelength Heat conduction Fluids Wave propagation Simulation Temperature effects Engineering simulation
Content Type	Text
Resource Type	Article

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