title: Hydrodynamic fluctuation-induced forces in confined fluids.
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.
authors.affiliation: Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah 84112, USA. chris.monahan@rutgers.edu.
authors.forename: Christopher
authors.initials: C
authors.lastname: Monahan
authors.affiliation: School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran.
authors.forename: Ali
authors.initials: A
authors.lastname: Naji
authors.affiliation: DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge, CB3 0WA, UK.
authors.forename: Ronald
authors.initials: R
authors.lastname: Horgan
authors.affiliation: Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia.
authors.forename: Bing-Sui
authors.initials: BS
authors.lastname: Lu
authors.affiliation: Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia and Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia.
authors.forename: Rudolf
authors.initials: R
authors.lastname: Podgornik