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Paper IPM / P / 15086  


Abstract:  
We study thermal, fluctuationinduced hydrodynamic interaction forces in a classical, compressible, viscous fluid confined between two rigid, planar walls with noslip boundary conditions. We calculate hydrodynamic fluctuations using the linearized, stochastic NavierStokes formalism of Landau and Lifshitz. The mean fluctuationinduced force acting on the fluid boundaries vanishes in this system, so we evaluate the twopoint, timedependent force correlations. The equaltime 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 interplate distances. The equaltime, crossplate force correlation, on the other hand, decays with the inverse interplate 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 counterphase correlations. We show that the timedependent force correlations exhibit damped temporal oscillations for small plate separations and a more irregular oscillatory behavior at large separations. The longrange hydrodynamic correlations reported here represent a ßecondary Casimir effect", because the mean fluctuationinduced force, which represents the primary Casimir effect, is absent.
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