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Paper   IPM / P / 14192
School of Physics
  Title:   Hydrodynamic fluctuation-induced forces in confined fluids
1.  C. Monahan
2.  A. Naji
3.  R.R. Horgan
4.  B. S. Lu
5.  R. Podgornik
  Status:   Published
  Journal: Soft Matter
  Vol.:  12
  Year:  2016
  Pages:   441
  Supported by:  IPM
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 ßecondary Casimir effect", because the mean fluctuation-induced force, which represents the primary Casimir effect, is absent.

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