Low-Frequency Velocity Correlation Spectrum of Fluid in a Rectangular Microcapillary

TLDR: Here, the motion of a viscous fluid, at constant temperature, in a rectangular semipermeable channel, is considered and the velocity correlation function in a fluid enclosed within the pore boundaries features a slow long time-tail decay.

Abstract: In addition to the fast correlation for local stochastic motion, the velocity correlation function in a fluid enclosed within the pore boundaries features a slow long time-tail decay. At late times, the flow approaches that of an incompressible fluid. Here, we consider the motion of a viscous fluid, at constant temperature, in a rectangular semipermeable channel. The fluid is driven through the rectangular capillary by a uniform main pressure gradient. Tiny pressure gradients are allowed perpendicular to the main flux. We solve numerically the three-dimensional Navier-Stokes equations for the velocity field to obtain the steady solution. We then set and solve the Langevin equation for the fluid velocity. We report hydrodynamic fluctuations for the center-line velocity together with the corresponding relaxation times as a function of the size of the observing region and the Reynolds number. The effective diffusion coefficient for the fluid in the microchannel is also estimated (Deff = 1.43 x 10(-10) m2.s-1 for Re = 2), which is in accordance with measurements reported for a similar system (Stepisnik, J.; Callaghan, P. T. Physica B 2000, 292, 296-301; Stepisnik, J.; Callaghan, P. T. Magn. Reson. Imaging 2001, 19, 469-472).