Transport in Porous Media

, Volume 127, Issue 2, pp 309–328 | Cite as

An Effect of Sorption on Convective Modes Selection for Solutal Convection in a Rectangular Porous Channel

  • Boris S. MaryshevEmail author
  • Lyudmila S. Klimenko


This paper is devoted to the stability analysis of 3D convective flow in the horizontal channel filled by the porous medium. Solute precipitation (solute sorption) by the porous medium is taken into account within the linear MIM approach. The solute concentration difference across the channel and the external filtration flux are assumed as constant. As a result, conditions of the appearance of two-dimensional convection regimes with respect to possible three-dimensional perturbations were obtained, which made it possible to estimate the range of parameters in which the two-dimensional convection regimes can be observed. The dependencies of the parameters of two-dimensional regimes on the parameters of the problem and on the thickness of the channel are discussed.


Solutal convection Linear sorption Weak nonlinear analysis 



This work was supported by the Russian Science Foundation (Grant 14-21-0090).


  1. Aranson, I., Kramer, L.: The world of the complex Ginzburg-Landau equation. Rev. Mod. Phys. 74, 99 (2002)Google Scholar
  2. Beck, J.L.: Convection in a box of porous material saturated with fluid. Phys. Fluids 15, 13771383 (1972)Google Scholar
  3. Bromly, M., Hinz, C.: Non-Fickian transport in homogeneous unsaturated repacked sand. Water Resour. Res. 40, W07402 (2004)Google Scholar
  4. Das, D., Gaur, V., Verma, N.: Removal of volatile organic compound by activated carbon fiber. Carbon 42(14), 2949–2962 (2004)Google Scholar
  5. Deans, H.A.: A mathematical model for dispersion in the direction of flow in porous media. Soc. Pet. Eng. J. 3, 49–52 (1963)Google Scholar
  6. Ennis-King, J., Preston, I., Paterson, L.: Onset of convection in anisotropic porous media subject to a rapid change in boundary conditions. Phys. Fluids 17, 084107 (2005)Google Scholar
  7. Gershuni, G.Z., Zhukhovitskii, E.M.: Convective stability of incompressible fluids = Konvektivnaya ustoichivost’neszhimaemoi zhidkosti. Israel Program for Scientific Translations (1976)Google Scholar
  8. Gouze, P., Le Borgne, T., Leprovost, R., Lods, G., Poidras, T.; Pezard, P.: Non-Fickian dispersion in porous media: 1. Multiscale measurements using singlewell injection withdrawal tracer tests. Water Resour. Res. 44(6), W06426 (2008)Google Scholar
  9. Govender, S.: Weak non-linear analysis of convection in a gravity modulated porous layer. Transp. Porous Media 60, 33–42 (2005)Google Scholar
  10. Govender, S., Vadasz, P.: Weak nonlinear analysis of moderate Stefan number oscillatory convection in rotating mushy layers. Transp. Porous Media 48, 353–372 (2002)Google Scholar
  11. Harter, R.D., Baker, D.E.: Applications and misapplications of the Langmuir equation to soil adsorption phenomena. Soil Sci. Soc. Am. J. 41, 1077–1080 (1977)Google Scholar
  12. Horton, C.W., Rogers, F.T.: Convection currents in a porous medium. J. Appl. Phys. 16, 367 (1945)Google Scholar
  13. Joseph, D.D.: Fluid Dynamics of Viscoelastic Liquids, vol. 84. Springer, New York (2013)Google Scholar
  14. Kay, B.D., Elrick, D.E.: Adsorption and movement of lindane in soils. Soil Sci. 104(5), 314–322 (1967)Google Scholar
  15. Lapwood, E.R.: Convection of a fluid in a porous medium. Proc. Camb. Philos. Soc. 44, 508 (1948)Google Scholar
  16. Maryshev, B.S.: The effect of sorption on linear stability for the solutal Horton–Rogers–Lapwood problem. Transp. Porous Media 109, 747–764 (2015)Google Scholar
  17. Maryshev, B.: A Non-linear model for solute transport, accounting for sub-diffusive concentration decline and sorption saturation. Math. Model. Nat. Phenom. 11(3), 179–190 (2016)Google Scholar
  18. Maryshev, B., Cartalade, A., Latrille, C., Neél, M.C.: Identifying space-dependent coefficients and the order of fractionality in fractional advection–diffusion equation. Transp. Porous Media 116(1), 53–71 (2017)Google Scholar
  19. Nayfeh, A.H.: Introduction to Perturbation Techniques, pp. 1–24. Wiley, Weinheim (2004)Google Scholar
  20. Nield, D.A., Bejan, A.: Convection in Porous Media, pp. 241–361. Springer, New York (2017)Google Scholar
  21. Nielsen, D.R., Biggar, J.W.: Miscible displacement in soils: I. Experimental information. Soil Sci. Soc. Am. J. 25(1), 1–5 (1961)Google Scholar
  22. Prats, M.: The effect of horizontal fluid flow on thermally induced convection currents in porous mediums. J. Geophys. Res. 71(20), 4835–4838 (1966)Google Scholar
  23. Shklyaev, S., Nepomnyashchy, A.A.: Longwave Instabilities and Patterns in Fluids. Birkhauser, Basel (2017)Google Scholar
  24. Sparks, D.L.: Environmental Soil Chemistry. Elsevier, Amsterdam (2003)Google Scholar
  25. Van Genuchten, M.T., Wierenga, P.J.: Mass transfer studies in sorbing porous media I. Analytical solutions. Soil Sci. Soc. Am. J. 40, 473 (1976)Google Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Institute of Continuous Media Mechanics Ural Branch of Russian Academy of SciencePermRussia

Personalised recommendations