Abstract
This article presents a series solution to the velocity in a two-dimensional long sinusoidal channel. The approach is based on a stream function formulation of the Stokes problem and a series expansion in terms of the width to the length ratio, which is considered small. Results show how immobile zones may appear and even flow separation and nonturbulent eddies, even in the absence of prima facie dead-end pores. It is shown that the flow tends to concentrate in strips connecting pore throats.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bear, J.: 1972, Dynamics of Fluids in Porous Media, American Elsevier, New York.
Brenner, H., and Edwards, D. A.: 1993, Macrotransport Processes, Butterworth-Heinemann, Boston.
Chen, B., Cunningham, A., Ewing, R., Peralta, R. and Visser, E.: 1994, Two-dimensional modeling of microscale transport and biotransformation in porous media, Numer. Methods Partial Differential Equations 10, 65–83.
Hasegawa, E. and Izuchi, H.: 1983, On steady flow through a channel consisting of an uneven wall and a plane wall. Part 1. Case of no relative motion in two walls, Bull. JSME 26(214), 514–520.
Dykaar, B. B.: 1994, Macroflow and macrotransport in heterogeneous porous media, PhD Thesis, Stanford Univ. Civ. Eng.
Dykaar, B. B. and Kitanidis, P. K.: 1996, Macrotransport of a biologically reacting solute through porous media, Water Resour. Res. 32(2), 307–320.
Edwards, D.A., Shapiro, M., Bar-Yoseph, P. and Shapira, M.: 1990, The influence of Reynolds number upon the apparent permeability of spatially periodic arrays of cylinders, Phys. Fluids A 2(1), 45–55.
Edwards, R. A., Shapiro, M., Brenner, H. and Shapira, M.: 1991, Dispersion of inert solute in spatially periodic two-dimensional model porous media, Transport in Porous Media 6, 337–358.
Freeze, R. A. and Cherry, J. A.: 1979, Groundwater, Prentice-Hall, New York.
Gale, J. E., Rouleau, A. and Atkinson, L. C.: 1985, Hydraulic properties of fractures, in Memoires. Hydrogeology of Rocks of Low Permeability, International Association of Hydrogeologists, Tucson, AZ, pp. 1-11.
Happel, J. and Brenner, H.: 1983, Low-Reynolds Number Hydrodynamics, Kluwer, Boston.
Hinch, E. J.: 1991, Perturbation Methods, Cambridge Univ. Press, Cambridge.
Hull, L. C., Miller, J. D. and Clemo, T.M.: 1987, Laboratory and simulation studies of solute transport in fracture networks, Water Resour. Res. 23(8), 1505–1513.
Kundu, P. K.: 1990, Fluid Mechanics, Academic Press, San Diego.
Pozrikidis, C.: 1987, Creeping flow in two-dimensional channels, J. Fluid Mech. 180, 495–514.
Pozrikidis, C.: 1992, Boundary Integral and Singularity Methods for Linearized Viscous Flow, Cambridge Univ. Press.
Raven, K. G., Novakowski, K. S. and Lapcevic, P. A.: 1998, Interpretation of field tracer tests of a single fracture using a transient solute storage model, Water Resour. Res. 24(12), 2019–2032.
Zimmerman, R. W., Kumar, S. and Bodvarsson, G. S.: 1991, Lubrication theory analysis of the permeability of rough-walled fractures, Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 28(4), 325–331.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kitanidis, P.K., Dykaar, B.B. Stokes Flow in a Slowly Varying Two-Dimensional Periodic Pore. Transport in Porous Media 26, 89–98 (1997). https://doi.org/10.1023/A:1006575028391
Issue Date:
DOI: https://doi.org/10.1023/A:1006575028391