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Issue 2, 2016
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Hydrodynamic fluctuation-induced forces in confined fluids

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Abstract

We study thermal, fluctuation-induced hydrodynamic interaction forces in a classical, compressible, viscous fluid confined between two rigid, planar walls with no-slip boundary conditions. We calculate hydrodynamic fluctuations using the linearized, stochastic Navier–Stokes formalism of Landau and Lifshitz. The mean fluctuation-induced force acting on the fluid boundaries vanishes in this system, so we evaluate the two-point, time-dependent force correlations. The equal-time correlation function of the forces acting on a single wall gives the force variance, which we show to be finite and independent of the plate separation at large inter-plate distances. The equal-time, cross-plate force correlation, on the other hand, decays with the inverse inter-plate distance and is independent of the fluid viscosity at large distances; it turns out to be negative over the whole range of plate separations, indicating that the two bounding plates are subjected to counter-phase correlations. We show that the time-dependent force correlations exhibit damped temporal oscillations for small plate separations and a more irregular oscillatory behavior at large separations. The long-range hydrodynamic correlations reported here represent a “secondary Casimir effect”, because the mean fluctuation-induced force, which represents the primary Casimir effect, is absent.

Graphical abstract: Hydrodynamic fluctuation-induced forces in confined fluids

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Publication details

The article was received on 16 Sep 2015, accepted on 09 Oct 2015 and first published on 19 Oct 2015


Article type: Paper
DOI: 10.1039/C5SM02346G
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Soft Matter, 2016,12, 441-459

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    Hydrodynamic fluctuation-induced forces in confined fluids

    C. Monahan, A. Naji, R. Horgan, B. Lu and R. Podgornik, Soft Matter, 2016, 12, 441
    DOI: 10.1039/C5SM02346G

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