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Hydrodynamic stress correlations in fluid films driven by stochastic surface forcing

Masoud Mohammadi-Arzanagh1,2, Saeed Mahdisoltani1,2, Rudolf Podgornik3,4,5,6, and Ali Naji1,*

  • 1School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran
  • 2Department of Physics, Sharif University of Technology, P.O. Box 11155-9161, Tehran, Iran
  • 3School of Physical Sciences and Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • 4CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
  • 5Department of Theoretical Physics, Jozef Stefan Institute, SI-1000 Ljubljana, Slovenia
  • 6Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia

  • *Corresponding author: a.naji@ipm.ir
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Phys. Rev. Fluids 3, 064201 – Published 29 June, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.064201

Abstract

We study hydrodynamic fluctuations in a compressible and viscous fluid film confined between two rigid, no-slip, parallel plates, where one of the plates is kept fixed while the other one is driven in small-amplitude, translational displacements around its reference position. This jiggling motion is assumed to be driven by a stochastic, external, surface forcing of zero mean and finite variance. Thus, while the transverse (shear) and longitudinal (compressional) hydrodynamic stresses produced in the film vanish on average on either of the plates, these stresses exhibit fluctuations that can be quantified through their equal-time, two-point, correlation functions. For transverse stresses, we show that the correlation functions of the stresses acting on the same plate (self-correlators) as well as the correlation function of the stresses acting on different plates (cross correlators) exhibit universal, decaying, power-law behaviors as functions of the interplate separation. At small separations, the exponents are given by −1, while at large separations, the exponents are found as −2 (self-correlator on the fixed plate), −4 (excess self-correlator on the mobile plate), and −3 (cross correlator). For longitudinal stresses, we find much weaker power-law decays in the large separation regime, with exponents −3/2 (excess self-correlator on the mobile plate) and −1 (cross correlator). The self-correlator on the fixed plate increases and levels off upon increasing the interplate separation, reflecting the nondecaying nature of the longitudinal forces acting on the fixed plate.

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Phys. Rev. Fluids 3, 064201– Published 29 June, 2018
  • Received 13 December 2017
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