Effects of interfacial transport on the equilibrium fluctuations in fluid layers

Abstract

Complete hydrodynamic theory of the dynamics of equilibrium fluctuations in one-component fluid layers confined by rigid solid boundaries is presented. The dynamic structure factor for such a fluid layer is shown to have both diagonal and off-diagonal elements which depend on the layer height $L$ and on the transport of energy and tangential momentum across the fluid-solid interfaces. The effects of interfacial energy transport have been analyzed in the limits of maximum or vanishing tangential momentum transport (stick or slip boundary conditions on the velocity field). In the presence of interfacial transport, two new propagating modes have been found for each distinct interface. In the limit of maximum energy and/or tangential momentum transport, the new modes differ from the bulk sound modes only by an increased attenuation coefficient. Additional dissipation is in part due to shear created by the boundaries, and in part, since the sound is not isothermal, to heat conduction between the fluid and solid. In the dynamic structure factor, the new modes appear as additional peaks in the vicinity of the Brillouin peaks of the unbounded fluid; for wave vectors typical of light scattering experiments these peaks are found to be significant for $L\ensuremath{\sim}100$ \ensuremath{\mu}m. Since the positions and line shapes of these peaks are very sensitive to interfacial transport, their study may provide a useful experimental probe of transport across the fluid-solid interfaces.