Skip to main content
SpringerLink
Log in

Chemical Reaction Effect on Convection in Bidispersive Porous Medium

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

The object of this study is to investigate the question of convective movement of a reacting solute in a viscous incompressible occupying a plane layer in a saturated bidisperse porous material. Among the characteristics of a bidisperse porous medium are pores, called macropores, but porosity in the solid skeleton, known as microporosity, arises where there are cracks or fissures in that skeleton. In this paper, a comparison is made between the thresholds for linear instability and those obtained from a global nonlinear energy stability analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Alley, R., Berntsen, T., Bindoff, N.L., Chen, Z., Chidthaisong, A., Friedlingstein, P., Gregory, J., Hegerl, G., Heimann, M., Hewitson, B., et al.: Climate change 2007: The physical science basis, Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Summary for Policymakers. IPCC Secretariat, Geneva, Switzerland. 21p (2007)

  • Andres, J.T.H., Cardoso, S.S.: Onset of convection in a porous medium in the presence of chemical reaction. Phys. Rev. E 83(4), 046312 (2011)

    Google Scholar 

  • Backhaus, S., Turitsyn, K., Ecke, R.: Convective instability and mass transport of diffusion layers in a Hele–Shaw geometry. Phys. Rev. Lett. 106(10), 104501 (2011)

    Google Scholar 

  • Borja, R.I., Liu, X., White, J.A.: Multiphysics hillslope processes triggering landslides. Acta Geotech. 7(4), 261–269 (2012)

    Google Scholar 

  • Borja, R.I., White, J.A.: Continuum deformation and stability analyses of a steep hillside slope under rainfall infiltration. Acta Geotech. 5(1), 1–14 (2010)

    Google Scholar 

  • Burghardt, A., Rogut, J., Gotkowska, J.: Diffusion coefficients in bidisperse porous structures. Chem. Eng. Sci. 43(9), 2463–2476 (1988)

    Google Scholar 

  • Capone, F., De Luca, R., Gentile, M.: Coriolis effect on thermal convection in a rotating bidispersive porous layer. Proc. R. Soc. A 476(2235), 20190875 (2020)

    Google Scholar 

  • Challoob, H.A., Mathkhor, A.J., Harfash, A.J.: Slip boundary condition effect on double-diffusive convection in a porous medium: Brinkman model. Heat Transf. Asian Res. 49(1), 258–268 (2020)

    Google Scholar 

  • Chandrasekhar, S.: Hydrodynamic and hydromagnetic stability (1981)

  • di Santolo, A.S., Evangelista, A.: Calibration of a rheological model for debris flow hazard mitigation in the campania region. In: Landslides and Engineered Slopes. From the Past to the Future, Two Volumes+ CD-ROM. CRC Press, pp. 935–942 (2008)

  • Falsaperla, P., Mulone, G., Straughan, B.: Bidispersive-inclined convection. Proc. R. Soc. A Math. Phys. Eng. Sci. 472(2192), 20160480 (2016)

    Google Scholar 

  • Franchi, F., Nibbi, R., Straughan, B.: Continuous dependence on modelling for temperature-dependent bidispersive flow. Proc. R. Soc. A Math. Phys. Eng. Sci. 473(2208), 20170485 (2017)

    Google Scholar 

  • Gentile, M., Straughan, B.: Bidispersive thermal convection. Int. J. Heat Mass Transf. 114, 837–840 (2017a)

    Google Scholar 

  • Gentile, M., Straughan, B.: Bidispersive vertical convection. Proc. R. Soc. A Math. Phys. Eng. Sci. 473(2207), 20170481 (2017b)

    Google Scholar 

  • Gentile, M., Straughan, B.: Bidispersive thermal convection with relatively large macropores. J. Fluid Mech. 898, A14. https://doi.org/10.1017/jfm.2020.411

    Article  Google Scholar 

  • Hameed, A.A., Harfash, A.J.: Unconditional nonlinear stability for double-diffusive convection in a porous medium with temperature-dependent viscosity and density. Heat Transf. Asian Res. 48(7), 2948–2973 (2019)

    Google Scholar 

  • Harfash, A.J.: Convection in a porous medium with variable gravity field and magnetic field effects. Transp. Porous Media 103(3), 361–379 (2014a)

    Google Scholar 

  • Harfash, A.J.: Three-dimensional simulations for convection in a porous medium with internal heat source and variable gravity effects. Transp. Porous Media 101(2), 281–297 (2014b)

    Google Scholar 

  • Harfash, A.J.: Three dimensions simulation for the problem of a layer of non-boussinesq fluid heated internally with prescribed heat flux on the lower boundary and constant temperature upper surface. Int. J. Eng. Sci. 74, 91–102 (2014c)

    Google Scholar 

  • Harfash, A.J.: Magnetic effect on convection in a porous medium with chemical reaction effect. Transp. Porous Media 106(1), 163–179 (2015)

    Google Scholar 

  • Harfash, A.J.: Resonant penetrative convection in porous media with an internal heat source/sink effect. Appl. Math. Comput. 281, 323–342 (2016a)

    Google Scholar 

  • Harfash, A.J.: Three dimensional simulations for convection induced by the selective absorption of radiation for the brinkman model. Meccanica 51(3), 501–515 (2016b)

    Google Scholar 

  • Harfash, A.J., Challoob, H.A.: Slip boundary conditions and through flow effects on double-diffusive convection in internally heated heterogeneous brinkman porous media. Chin. J. Phys. 56(1), 10–22 (2018)

    Google Scholar 

  • Harfash, A.J., Challoob, H.A.: Nonhomogeneous porosity and thermal diffusivity effects on stability and instability of double-diffusive convection in a porous medium layer: Brinkman model. Nonlinear Eng. 8(1), 293–302 (2019)

    Google Scholar 

  • Harfash, A.J., Meften, G.A.: Couple stresses effect on linear instability and nonlinear stability of convection in a reacting fluid. Chaos Solitons Fractals 107, 18–25 (2018)

    Google Scholar 

  • Harfash, A.J., Meften, G.A.: Couple stresses effect on instability and nonlinear stability in a double diffusive convection. Appl. Math. Comput. 341, 301–320 (2019)

    Google Scholar 

  • Harfash, A.J., Meften, G.A.: Nonlinear stability analysis for double-diffusive convection when the viscosity depends on temperature. Phys. Scripta 95(8), 085203 (2020)

    Google Scholar 

  • Harfash, A.J., Nashmi, F.K.: Triply resonant double diffusive convection in a fluid layer. Math. Model. Anal. 22(6), 809–826 (2017)

    Google Scholar 

  • Hooman, K., Maas, U.: Theoretical analysis of coal stockpile self-heating. Fire Saf. J. 67, 107–112 (2014)

    Google Scholar 

  • Hooman, K., Sauret, E., Dahari, M.: Theoretical modelling of momentum transfer function of bi-disperse porous media. Appl. Therm. Eng. 75, 867–870 (2015)

    Google Scholar 

  • Lin, F.C., Liu, B.H., Huang, C.T., Chen, Y.M.: Evaporative heat transfer model of a loop heat pipe with bidisperse wick structure. Int. J. Heat Mass Transf. 54(21–22), 4621–4629 (2011)

    Google Scholar 

  • Montrasio, L., Valentino, R., Losi, G.L.: Rainfall infiltration in a shallow soil: a numerical simulation of the double-porosity effect. Electron. J. Geotechnol. Eng 16, 1387–1403 (2011)

    Google Scholar 

  • Mottet, L., Prat, M.: Numerical simulation of heat and mass transfer in bidispersed capillary structures: application to the evaporator of a loop heat pipe. Appl. Therm. Eng. 102, 770–784 (2016)

    Google Scholar 

  • Neufeld, J.A., Hesse, M.A., Riaz, A., Hallworth, M.A., Tchelepi, H.A., Huppert, H.E.: Convective dissolution of carbon dioxide in saline aquifers. Geophys. Res. Lett. 37(22), (2010)

  • Nield, D.: A note on the modelling of bidisperse porous media. Transp. Porous Media 111(2), 517–520 (2016)

    Google Scholar 

  • Nield, D., Kuznetsov, A.: Forced convection in a bi-disperse porous medium channel: a conjugate problem. Int. J. Heat Mass Transf. 47(24), 5375–5380 (2004)

    Google Scholar 

  • Nield, D., Kuznetsov, A.: The onset of convection in a bidisperse porous medium. Int. J. Heat Mass Transf. 49(17–18), 3068–3074 (2006)

    Google Scholar 

  • Nield, D., Kuznetsov, A.: The effect of combined vertical and horizontal heterogeneity on the onset of convection in a bidisperse porous medium. Int. J. Heat Mass Transf. 50(17–18), 3329–3339 (2007)

    Google Scholar 

  • Nield, D., Kuznetsov, A.: Natural convection about a vertical plate embedded in a bidisperse porous medium. Int. J. Heat Mass Transf. 51(7–8), 1658–1664 (2008)

    Google Scholar 

  • Nield, D., Kuznetsov, A.: A note on modeling high speed flow in a bidisperse porous medium. Transp. Porous Media 96(3), 495–499 (2013)

    Google Scholar 

  • Pooley, E.J.: Centrifuge Modelling of Ground Improvement for Double Porosity Clay, vol. 246, vdf Hochschulverlag AG (2015)

  • Rubin, E., De Coninck, H.: Ipcc special report on carbon dioxide capture and storage. Cambridge University Press, UK. TNO (2004): Cost Curves for CO2 Storage, Part, 2, 14 (2005)

  • Straughan, B.: The energy method, stability, and nonlinear convection, 2nd edn. Springer, New York (2004)

    Google Scholar 

  • Straughan, B.: Convection with Local Thermal Non-equilibrium and Microfluidic Effects, vol. 32. Springer (2015)

  • Straughan, B.: Mathematical Aspects of Multi-porosity Continua. Springer (2017)

  • Straughan, B.: Horizontally isotropic bidispersive thermal convection. Proc. R. Soc. A Math. Phys. Eng. Sci. 474(2213), 20180018 (2018)

    Google Scholar 

  • Straughan, B.: Anisotropic bidispersive convection. Proc. R. Soc. A 475(2227), 20190206 (2019a)

    Google Scholar 

  • Straughan, B.: Horizontally isotropic double porosity convection. Proc. R. Soc. A 475(2221), 20180672 (2019b)

    Google Scholar 

  • Szczygieł, J.: Diffusion in a bidispersive grain of a reforming catalyst. Comput. Chem. 23(2), 121–134 (1999)

    Google Scholar 

  • Szczygieł, J.: Enhancement of reforming efficiency by optimising the porous structure of reforming catalyst: Theoretical considerations. Fuel 85(10–11), 1579–1590 (2006)

    Google Scholar 

  • Szczygieł, J.: Control of transport phenomena in the interior of the reforming catalyst grain: a new approach to the optimisation of the reforming process. Fuel Process. Technol. 92(8), 1434–1448 (2011)

    Google Scholar 

  • Taqvi, S.M., Vishnoi, A., Levan, M.D.: Effect of macropore convection on mass transfer in a bidisperse adsorbent particle. Adsorption 3(2), 127–136 (1997)

    Google Scholar 

  • Valus, J., Schneider, P.: Transport characteristics of bidisperse porous \(\alpha\)-aluminas. Appl. Catal. 16(3), 329–341 (1985)

    Google Scholar 

  • Ward, T., Cliffe, K., Jensen, O., Power, H.: Dissolution-driven porous-medium convection in the presence of chemical reaction. J. Fluid Mech. 747, 316 (2014)

    Google Scholar 

  • Yeh, C.C., Chen, C.N., Chen, Y.M.: Heat transfer analysis of a loop heat pipe with biporous wicks. Int. J. Heat Mass Transf. 52(19–20), 4426–4434 (2009)

    Google Scholar 

Download references

Acknowledgements

We are indebted to two anonymous referees for their pointed remarks that have led to improvements in the manuscript.

Funding

No funding has been received for this article.

Author information

Authors and Affiliations

  1. Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah, Iraq

    Alaa Jabbar Badday

  2. Department of Mathematics, College of Sciences, University of Basrah, Basrah, Iraq

    Akil J. Harfash

Authors
  1. Alaa Jabbar Badday
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Akil J. Harfash
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

AJH proposed the model, carried out the computations and drafted the introduction and the stability analysis results sections; AJB contributed to the sections namely Governing equations, linear instability and nonlinear stability. Both authors gave final approval for publication.

Corresponding author

Correspondence to Akil J. Harfash.

Ethics declarations

Conflict of interest

We have no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Badday, A.J., Harfash, A.J. Chemical Reaction Effect on Convection in Bidispersive Porous Medium. Transp Porous Med 137, 381–397 (2021). https://doi.org/10.1007/s11242-021-01566-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11242-021-01566-6

Keywords

Search

Navigation