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Paper IPM / P / 14638  


Abstract:  
We investigate fluid mediated effective interactions in a confined film geometry, between two rigid, noslip plates, where one of the plates is mobile and subjected to a random external forcing with zero average. The fluid is assumed to be compressible and viscous, and the external surface forcing to be of small amplitude, thus enabling a linear hydrodynamic analysis. While the transverse and longitudinal hydrodynamic stresses (forces per unit area) acting on either of the plates vanish on average, they exhibit significant fluctuations that can be quantified through their equaltime, twopoint correlators. For transverse (shear) stresses, the sameplate correlators on both the fixed and the mobile plates, and also the crossplate correlator, exhibit decaying powerlaw behaviors as functions of the interplate separation with universal exponents: At small separations, the exponents are given by â1 in all cases, while at large separations the exponents are found to be larger, differing in magnitude, viz., â2 (for the sameplate correlator on the fixed plate), â4 (for the excess sameplate correlator on the mobile plate) and â3 (for the crossplate correlator). For longitudinal (compressional) stresses, we find much weaker powerlaw decays with exponents â3/2 (for the excess sameplate correlator on the mobile plate) and â1 (for the crossplate correlator) in the large interplate separation regime. The sameplate stress correlator on the fixed plate increases and saturates on increase of the interplate separation, reflecting the nondecaying nature of the longitudinal forces acting on the fixed plate. The qualitative differences between the transverse and longitudinal stress correlators stem from the distinct nature of the shear and compression modes as, for instance, the latter exhibit acoustic propagation and, hence, relatively large fluctuations across the fluid film.
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