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A Solute Flux Near a Solid Wall as a Reason for the Observation of Anomalous Transport

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Abstract

The paper is devoted to the study of the reasons of anomalous transport observation in the experiments with microchannels. Usually, retardation of such transport is associated with the interaction of solute particles with channel walls. In the present paper, we have shown that the viscous interaction of the flow and solid wall can be the reason for the anomalous transport observation. It was illustrated on a specific example of a passive solute transport through the channel. The effect of diffusion on such transport was investigated numerically. The power law decline of concentration with respect to time was obtained in a wide range of parameters.

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References

  • Ajdari, A., Bontoux, N., Stone, H.A.: Hydrodynamic dispersion in shallow microchannels: the effect of cross-sectional shape. Anal. Chem. 78(2), 387–392 (2006)

    Article  Google Scholar 

  • Aris, R.: On the dispersion of a solute in a fluid flowing through a tube. Proc. R. Soc. London A 235, 67–77 (1956)

    Article  Google Scholar 

  • Bhaumik, S.K., Kannan, A., DasGupta, S.: Taylor–aris dispersion induced by axial variation in velocity profile in patterned microchannels. Chem. Eng. Sci. 134, 251–259 (2015)

    Article  Google Scholar 

  • Birkhoff, G., Varga, R.S., Young, D.: Alternating direction implicit methods. Adv. Comput. 3, 189–273 (1962)

    Article  MathSciNet  Google Scholar 

  • Bromly, M., Hinz, C.: Non-fickian transport in homogeneous unsaturated repacked sand. Water Resour. Res. 40, W07402 (2004)

    Article  Google Scholar 

  • Deans, H.A.: A mathematical model for dispersion in the direction of ow in porous media. Soc. Pet. Eng. J. 3(01), 49 (1963)

    Article  Google Scholar 

  • Einstein, A.: On the theory of the brownian movement. Ann. Phys. 19(4), 371 (1906)

    Article  Google Scholar 

  • Gaponenko, Y., Gousselnikov, V., Santos, C.I.A.V., Shevtsova, V.: Near-Critical Behavior of fick diffusion coefficient in taylor dispersion experiments. Microgravity Sci. Technol. 31, 475–486 (2019)

    Article  Google Scholar 

  • Gouze, P., Le Borgne, T., Leprovost, R., Lods, G., Poidras, T., Pezard, P.: Non-fickian dispersion in porous media: 1. Multiscale measurements using single-well injection with- drawal tracer tests. Water Resour. Res. 44(6), W06426 (2008)

    Article  Google Scholar 

  • Latini, M., Bernoff, A.J.: Transient anomalous diffusion in Poiseuille flow. J. Fluid Mech. 441, 399–411 (2001)

    Article  Google Scholar 

  • Lighthill, M.J.: Initial development of diffusion in poiseuille flow. J. Inst. Maths Appl. 2, 97–108 (1966)

    Article  Google Scholar 

  • 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 (2017)

    Article  MathSciNet  Google Scholar 

  • Pachepsky, Y., Benson, D., Rawls, W.: Simulating scale-dependent solute transport in soils with the fractional advective–dispersive equation. Soil Sci. Soc. Am. J. 64, 1234–1243 (2000)

    Article  Google Scholar 

  • Schumer, R., Benson, D.A., Meerschaert, M.M., Baeumer, B.: Fractal mobile/immobile solute transport. Water Resour. Res. 39(10) (2003)

  • Taylor, G.I.: Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. London A 219, 186–203 (1953)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Van Genuchten, M.T., Wierenga, P.J.: Mass transfer studies in sorbing porous media: II. Experimental evaluation with tritium (3H2O). Soil Sci. Soc. Am. J. 41(2), 272 (1977)

    Article  Google Scholar 

  • Vedel, S., Bruus, H.: Transient Taylor–Aris dispersion for time-dependent flows in straight channels. J. Fluid Mech. 691, 95–122 (2012)

    Article  Google Scholar 

  • Velarde, M.G., Starov, V.M.: Spreading dynamics: a succinct account of some basic questions. Micrograv. Sci. Technol. 18, 21–24 (2006)

    Article  Google Scholar 

  • Vikhansky, A.: Thermal convection of a viscoplastic liquid with high Rayleigh and Bingham numbers. Phys. Fluids 21(10), 103103 (2009)

    Article  Google Scholar 

  • Vikhansky, A., Wang, W.: Taylor dispersion in finite-length capillaries. Chem. Eng. Sci. 66 (4), 642–649 (2011)

    Article  Google Scholar 

  • Zaks, M.A., Nepomnyashchy, A.: Subdiffusive and superdiffusive transport in plane steady viscous flows. PNAS 18, 18245–18250 (2019)

    Article  MathSciNet  Google Scholar 

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Correspondence to Lyudmila S. Klimenko.

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Maryshev, B.S., Klimenko, L.S. A Solute Flux Near a Solid Wall as a Reason for the Observation of Anomalous Transport. Microgravity Sci. Technol. 33, 3 (2021). https://doi.org/10.1007/s12217-020-09862-4

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