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Transient gas flow in elastic microchannels

Published online by Cambridge University Press:  08 May 2018

Shai B. Elbaz ,
Hila Jacob  and
Amir D. Gat Open the ORCID record for Amir D. Gat [Opens in a new window]
Shai B. Elbaz
Affiliation:
Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 3200003, Israel
Hila Jacob
Affiliation:
Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 3200003, Israel
Amir D. Gat*
Affiliation:
Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 3200003, Israel
*
†Email address for correspondence: [email protected]
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Abstract

We study pressure-driven propagation of gas into a two-dimensional microchannel bounded by linearly elastic substrates. Relevant fields of application include lab-on-a-chip devices, soft robotics and respiratory flows. Applying the lubrication approximation, the flow field is governed by the interaction between elasticity and viscosity, as well as weak rarefaction and low-Mach-number compressibility effects, characteristic of gaseous microflows. A governing equation describing the evolution of channel height is derived for the problem. Several physical limits allow simplification of the governing equation and solution by self-similarity. These limits, representing different physical regimes and their corresponding time scales, include compressibility–elasticity–viscosity, compressibility–viscosity and elasticity–viscosity dominant balances. Transition of the flow field between these regimes and corresponding exact solutions is illustrated for the case of an impulsive mass insertion in which the order of magnitude of the deflection evolves in time. For an initial channel thickness which is similar to the elastic deformation generated by the background pressure, a symmetry between compressibility and elasticity allows us to obtain a self-similar solution which includes weak rarefaction effects. The presented results are validated by numerical solutions of the evolution equation.

JFM classification

Compressible Flows: Compressible Flows Low-Reynolds-number flows: Low-Reynolds-number flows Micro-/Nano-fluid dynamics: Microfluidics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 846 , 10 July 2018 , pp. 460 - 481
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Copyright
© 2018 Cambridge University Press 

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