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

• Published in: Langmuir 2007-11, Vol.23 (23), p.11917-11923
• Main Authors: FORNES, José A, DE ZARATE, José M. Ortiz
• Format: Article
• Language: English
• Subjects: Chemistry; Colloidal state and disperse state; Exact sciences and technology; General and physical chemistry; Porous materials; Surface physical chemistry
• ISSN: 0743-7463; 1520-5827
• DOI: 10.1021/la702502q

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 (D eff = 1.43 × 10-10 m2·s-1 for Re = 2), which is in accordance with measurements reported for a similar system (Stepišnik, J.; Callaghan, P. T. Physica B 2000, 292, 296−301; Stepišnik, J.; Callaghan, P. T. Magn. Reson. Imaging 2001, 19, 469-472).