First-Order Mass Transfer in a Vortex-Dispersion Zone of an Axisymmetric Groove: Laboratory and Numerical Experiments

  • Received : 2010.10.30
  • Accepted : 2010.11.29
  • Published : 2010.12.31


Solute transport through a groove is affected by its vortices. Our laboratory and numerical experiments of dye transport through a single axisymmetric groove reveal evidence of enhanced spreading and mixing by the vortex, i.e., a new kind of dispersion called here the vortex dispersion. The uptake and release of contaminants by vortices in porous media is affected by the flow Reynolds number. The larger the flow Reynolds number, the larger is the vortex dispersion, and the larger is the mass-transfer rate between the mobile zone and the vortex. The long known dependence of the mass-transfer rate between the mobile and "immobile" zones in porous media on flow velocity can be explained by the presence of vortices in the "immobile" zone and their uptake and release of contaminants.


  1. Bajracharya, K., Barry, D.A. (1997) Nonequilibrium Solute Transport Parameters and Their Physical Significance: Numerical and experimental results, J. Contam. Hydrol., 24(3-4), pp.185-204.
  2. Brusseau, M.L., Jessup, R.E., Rao, P.S.C. (1989) Modeling the Transport of Solutes Influenced by Multiprocess Nonequilibrium, Water Resour. Res., 25(9), pp.1971-1988.
  3. Brusseau, M.L. (1992) Nonequilibrium Transport of Organic Chemicals-The Impact of Pore-Water Velocity, J. Contam. Hydrol., 9(4), pp.353-368.
  4. Cao, J., Kitanidis, P.K. (1998) Adaptive Finite Element Simulation of Stokes flow in Porous Media, Adv. Water Res., 22(1), pp.17-31.
  5. Cieslicki, K., Lasowska, A. (1999) Experimental Investigations of Steady flow in a Tube with Circumferential Wall Cavity, Journal of Fluids Engineering, 121, pp.405-409.
  6. Coats, K.H., Smith, B.D. (1964) Dead-End Pore Volume and Dispersion in Porous Media, Soc. Petrol. Eng. J., 4, pp.73-84.
  7. Cunningham, J.A., Werth, C.J., Reinhard, M., Roberts, P.V. (1997) Effects of Grain-Scale Mass Transfer on the Transport of Volatile Organics Through Sediments.1. Model development, Water Resour. Res., 33(12) pp.2713-2726.
  8. de Beer, D., Stoodley, P., Lewandowski, Z. (1997) Measurement of Local Diffusion Coefficients in Biofilms by Microinjection and Confocal Microscopy, Biotechnol. Bioeng., 53(2), pp.151-158.<151::AID-BIT4>3.0.CO;2-N
  9. Haggerty, R., Gorelick, S.M. (1995) Multiple-Rate Mass-Transfer for Modeling Diffusion and Surface-Reactions in Media with Pore-Scale Heterogeneity, Water Resour. Res., 31(10), pp. 2383-2400.
  10. Haggerty, R., Gorelick, S.M. (1998) Modeling Mass Transfer Processes in Soil Columns with Pore-Scale Heterogeneity, Soil Sci. Soc. Am. J., 62(1), pp.62-74.
  11. Haggerty, R., McKenna, S.A., Meigs, L.C. (2000) On the Late-Time Behavior of Tracer Test Breakthrough Curves, Water Resour. Res., 36(12), pp.3467-3479.
  12. Haggerty, R., Fleming, S.W., Meigs, L.C., McKenna, M.C. (2001) Tracer Tests in a Fractured Dolomite. 2. Analysis of Mass Transfer in Single-well Injection-Withdrawal Tests, Water Resour. Res., 37(5), pp.1129-1142,
  13. Haggerty, R., Harvey, C.F., von Schwerin, C.F., Meigs, L.C. (2004) What Controls the Apparent Timescale of Solute Mass Transfer in Aquifers and Soils, A Comparison of Experimental Results, Water Resour. Res., 40(1): Art. No. W01510.
  14. He, C.H., Ahmadi, G. (1998) Particle Deposition with Thermophoresis in Laminar and Turbulent Duct Flows, Aerosol Sci. Tech., 29(6), pp.525-546.
  15. Hemmat, M., Borhan, A. (1995) Creeping Flow Through Sinusoidally Constricted Capillaries, Phys. Fluids, 7(9), pp.2111-2121
  16. Kim Y.W, Seo, B.M., Hwang, S.M., Park, C.S. (2010) Derivation of the First-Order Mass-Transfer Equation for a Diffusion-Dominated Zone of a 2-D Pore, KSME-B, 34(2), pp.99-103
  17. Kitanidis, P.K., Dykaar, B. (1997) Stokes Flow in a Slowly Varying Two-Dimensional Periodic Pore, Trans. Porous Media, 26, pp.89-98.
  18. Leneweit, G., Auerbach, D. (1999) Detachment Phenomena in Low Reynolds Number Flows Through Sinusoidally Constricted Tubes, J. Fluid Mech., 387, pp.129-150.
  19. Meigs, L.C., Beauheim, R.L. (2001) Tracer Tests in a Fractured Dolomite. 1. Experimental Design and Observed Tracer Recoveries, Water Resour. Res., 37(5), pp.1113-1128.
  20. Ranade, V.V., Dommeti, S.M.S. (1996) Computational Snapshot of Flow Generated by Axial Impeller in Baffled Stirred Vessels, Chem. Eng. Res. Design, 74(A4), pp.476-484.
  21. Rao, P.S.C., Rolston, D.E., Jessup, R.E., Davidson, J.M. (1980) Solute Transport in Aggregated Porous Media-Theoretical and Experimental Evaluation, Soil Sci. Soc. Am. J., 44(6), pp.1139-1146.
  22. Rao, P.S.C., Jessup, R.E., Rolston, D.E., Davidson, J.M., Kilcrease, D.P. (1980) Experimental and Mathematical Description of Non-Adsorbed Solute Transfer by Diffusion in Spherical Aggregates, Soil Sci. Soc. Am. J., 44(4), pp.684-688.
  23. Sanyal, J., Vasquez, S., Roy, S., Dudukovic, M.P. (1999) Numerical Simulation of Gas-Liquid Dynamics in Cylindrical Bubble Column Reactors, Chem. Eng. Sci., 54(21), pp.5071-5083.
  24. Sardin, M., Schweich, D., Leij, F.J., van Genuchten, M.T. (1991) Modeling the Nonequilibrium Transport of Linearly Interacting Solutes in Porous Media-A Review, Water Resour. Res., 27(9), pp.2287-2307.
  25. Schumer, R., Benson, D.A., Meerschaert, M.M., Baeumer, B. (2003) Fractal Mobile/Immobile Solute Transport, Water Resour. Res., 39(10), Art. No. 1296.
  26. Stehfest, H. (1970) Numerical Inversion of Laplace Transforms, Commun.ACM. 13, pp.47-49.
  27. van Genuchten, M.T., Wierenga, P.J. (1976) Mass Transfer Studies in Sorbing Porous Media. 1. Analytical Solutions, Soil Sci. Soc Am. J., 40, pp.473-480.
  28. Villeramaux, J. (1981) Theory of Linear Chromatography, in Percolation Processes, Theory and Applications, edited by A.E. Rodrigues and D. Tondeur, NATO ASI Ser., Ser. E, 33, pp.83-140.
  29. Villeramaux, J. (1987) Chemical Engineering Approach to Dynamic Modeling of Linear Chroma- Tography: A Flexible Method for Representing Complex Phenomena from Simple Concepts, J. Chromatogr. 406, pp.11-26,
  30. Villeramaux, J. (1990) Dynamics of Linear Interactions in Heterogeneous Media: A Systems Approach, J. Pet. Sci. Eng., 4(1), pp.21-30.
  31. Werth, C.J., Cunningham, J.A., Roberts, P.V., Reinhard, M. (1997) Effects of Grain-Scale Mass Transfer on the Transport of Volatile Organics Through Sediments. 2. Column Results, Water Resour. Res., 33(12), pp.2727-2740
  32. Glueckauf, E. (1955) Theory of Chromatography, part 10, Formulae for Diffusion into Spheres and their Application to Chromatography, Trans. Faraday Soc., 51, pp.1540-1551,
  33. Valocchi, A.J. (1990) Use of Temporal Moment Analysis to Study Reactive Solute Transport in Aggregated Porous Media, Geoderma, 46(1-3), pp.233-247.