Viscous compressible hydrodynamics at planes, spheres and cylinders with finite surface slip.

The European Physical Journal. E, Soft Matter
A ErbaşRoland R Netz

Abstract

We consider the linearized time-dependent Navier-Stokes equation including finite compressibility and viscosity. We first constitute the Green's function, from which we derive the flow profiles and response functions for a plane, a sphere and a cylinder for arbitrary surface slip length. For high driving frequency the flow pattern is dominated by the diffusion of vorticity and compression, for low frequency compression propagates in the form of sound waves which are exponentially damped at a screening length larger than the sound wave length. The crossover between the diffusive and propagative compression regimes occurs at the fluid's intrinsic frequency omega approximately c2rho0/eta, with c the speed of sound, rho0 the fluid density and eta the viscosity. In the propagative regime the hydrodynamic response function of spheres and cylinders exhibits a high-frequency resonance when the particle size is of the order of the sound wave length. A distinct low-frequency resonance occurs at the boundary between the propagative and diffusive regimes. Those resonant features should be detectable experimentally by tracking the diffusion of particles, as well as by measuring the fluctuation spectrum or the response spectrum of trapped pa...Continue Reading

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Citations

Oct 2, 2012·The Review of Scientific Instruments·Yann von HansenRoland R Netz
Oct 20, 2015·Soft Matter·Christopher MonahanRudolf Podgornik
Sep 26, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·B U Felderhof
Jan 15, 2016·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jianyong MoMark G Raizen
Mar 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Humberto Híjar
May 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A Kuhnhold, W Paul
Apr 10, 2017·The Journal of Chemical Physics·Jianyong MoMark G Raizen
Sep 13, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A Kuhnhold, W Paul
Jun 12, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·B U Felderhof
Oct 15, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Simón PobleteRoland G Winkler
Aug 30, 2011·The Journal of Physical Chemistry. B·M BelushkinG Foffi

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