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Universality in statistics of Stokes flow over a no-slip wall with random roughness

Published online by Cambridge University Press:  17 January 2019

Vladimir Parfenyev Open the ORCID record for Vladimir Parfenyev [Opens in a new window] ,
Sergey Belan Open the ORCID record for Sergey Belan [Opens in a new window]  and
Vladimir Lebedev
Vladimir Parfenyev*
Affiliation:
Landau Institute for Theoretical Physics, Ak. Semenova 1-A, 142432, Chernogolovka, Russia National Research University Higher School of Economics, Faculty of Physics, Myasnitskaya 20, 101000, Moscow, Russia
Sergey Belan
Affiliation:
Massachusetts Institute of Technology, Department of Physics, Cambridge, MA 02139, USA
Vladimir Lebedev
Affiliation:
Landau Institute for Theoretical Physics, Ak. Semenova 1-A, 142432, Chernogolovka, Russia National Research University Higher School of Economics, Faculty of Physics, Myasnitskaya 20, 101000, Moscow, Russia
*
†Email address for correspondence: [email protected]
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Abstract

Stochastic roughness is a widespread feature of natural surfaces and is an inherent byproduct of most fabrication techniques. In view of the rapid development of microfluidics, the important question is how this inevitable problem affects the low-Reynolds-number flows that are common for micro-devices. Moreover, one could potentially turn the flaw into a virtue and control the flow properties by means of specially ‘tuned’ random roughness. In this paper we investigate theoretically the statistics of fluctuations in fluid velocity produced by the waviness irregularities at the surface of a no-slip wall. Particular emphasis is laid on the issue of the universality of our findings.

JFM classification

Micro-/Nano-fluid dynamics: Microfluidics Waves/Free-surface Flows: Channel flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 862 , 10 March 2019 , pp. 1084 - 1104
Copyright
© 2019 Cambridge University Press 

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