Flow Past a Sphere Buried in a Porous Media: Concentration Boundary Layer Thickness

Abstract:

In this work, consideration is given to the problem of dissolution of a buried solid sphere in the liquid flowing uniformly through the packed bed around it. The differential equations describing fluid flow and mass transfer by advection and diffusion in the interstices of the bed are presented and the method for obtaining their numerical solution is indicated.From the surface concentration fields, given by the numerical solution, the concentration boundary layer thickness as a function of the relevant parameters were undertaken. Mathematical expressions that relate the dependence with the Peclet number and d/d₁ ratio of an immersed active sphere are proposed to describe the approximate size of the concentration boundary layer thickness.

• Periodical: Diffusion Foundations (Volume 3)
• Pages: 41-59
• DOI: https://doi.org/10.4028/www.scientific.net/DF.3.41
• Online since: February 2015
• Authors: João M.P.Q. Delgado*, M. Vázquez da Silva
• Keywords: Boundary Layer Thickness, Diffusion, Fluid Flow, Mass Transfer, Porous Media, Sphere

References

[1] Alves MA, Delgado JMPQ, Guedes de Carvalho JRF (2006). Mass transfer from cylinders and plane surfaces buried in packed beds in alignment with the flow direction. Chemical Engineering Science 61(4): 1174-1183.

DOI: 10.1016/j.ces.2005.08.017

[2] Avedesian MM, Davidson JF (1973). Combustion of carbon particles in a fluidised bed. Transactions of the Institution of Chemical Engineers 51: 121-131.

[3] Bear J, Verruijt A (1987). Modelling groundwater flow and pollution with computer programs for sample cases, D. Reidel Publishing Company, UK.

[4] Coelho MAN, Guedes de Carvalho JRF (1988a). Transverse dispersion in granular beds: Part I- Mass transfer from a wall and the dispersion coefficient in packed beds. Chemical Engineering Research and Design 66(2): 165-177.

[5] Coelho MAN, Guedes de Carvalho JRF (1988b). Transverse dispersion in granular beds: Part II- Mass transfer from large spheres immersed in fixed or fluidised beds of small inert particles. Chemical Engineering Research and Design 66(2): 178-189.

[6] Currie IG (1993). Fundamental mechanics of fluids, McGraw-Hill, New York, USA, p.150.

[7] Fetter CW (1994). Applied hydrogeology, Third edition, Prentice Hall, Englewood Cliffs.

[8] Ferziger JH, Peric M (1996). Computational Methods for Fluid Dynamics, pp.42-49, Springer-Verlag, Germany.

[9] Fetter, C.W. (1999). Contaminant hydrogeology. 2º Edition, Prentice-Hall International.

[10] Gaskell, P.H. and Lau, A.K.C. (1988). Curvature Compensated Convective Transport: SMART, a New Boundedness Preserving Transport Algorithm. Int. J. Numer. Meth. Fluids 8: 617.

DOI: 10.1002/fld.1650080602

[11] Guedes de Carvalho, J.R. F, Alves, M.A. (1999). Mass transfer and dispersion around active sphere buried in a packed bed. AIChE Journal, 45, 2495-2502.

DOI: 10.1002/aic.690451205

[12] Guedes de Carvalho JRF, Delgado JMPQ, Alves MA (2004). Mass transfer between flowing fluid and sphere buried in packed bed of inerts. AIChE Journal 50(1): 65-74.

DOI: 10.1002/aic.10006

[13] Gunn DJ, England R (1971). Dispersion and diffusion in beds of porous particles. Chemical Engineering Science 26(9) : 1413-1423.

DOI: 10.1016/0009-2509(71)80061-1

[14] Phillips, O.M. (1991). Flow and reactions in permeable rocks. Cambridge University Press.

[15] Pinto, A.M.F.R., Guedes de Carvalho, J.R.F. (1990).

[16] Stoessell, R.K. (1987). Mass transport in sandstones around dissolving plagioclase grains. Geology, 15, 295-298.

DOI: 10.1130/0091-7613(1987)15<295:mtisad>2.0.co;2

[17] Wexler, E.J. (1992). Analytical solutions for one-, two-, and three-dimensional solute transport in ground-water systems with uniform flow. U.S. Geological Survey Techniques of Water-Resources Investigations, Book 3, Chap. B7, 190 p.

DOI: 10.3133/twri03b7

[18] Wilhelm RH (1962). Progress towards the a priori design of chemical reactors. Pure and Applied Chemistry 5(3-4): 403-421.