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A Stefan model for mass transfer in a rotating disk reaction vessel

Published online by Cambridge University Press:  04 May 2015

C. S. BOHUN
C. S. BOHUN*
Affiliation:
University of Ontario Institute of Technology, Oshawa, ON L1H 7K4, Canada email: sean.bohun@uoit.ca
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Abstract

In this paper, we focus on the process of mass transfer in the rotating disk apparatus formulated as a Stefan problem with consideration given to both the hydrodynamics of the process and the specific chemical reactions occurring in the bulk. The wide range in the reaction rates of the underlying chemistry allows for a natural decoupling of the problem into a simplified set of weakly coupled convective–reaction–diffusion equations for the slowly reacting chemical species and a set of algebraic relations for the species that react rapidly. An analysis of the chemical equilibrium conditions identifies an expansion parameter and a reduced model that remains valid for arbitrarily large times. Numerical solutions of the model are compared to an asymptotic analysis revealing three distinct time scales and chemical diffusion boundary layer that lies completely inside the hydrodynamic layer. Formulated as a Stefan problem, the model generalizes the work of Levich (Levich and Spalding (1962) Physicochemical hydrodynamics, vol. 689, Prentice-Hall Englewood Cliffs, NJ) and will help better understand the natural limitations of the rotating disk reaction vessel when consideration is made for the reacting chemical species.

Keywords

97M1080A2274N2592E2035B40
Type
Papers
Information
European Journal of Applied Mathematics , Volume 26 , Issue 4 , August 2015 , pp. 453 - 475
Copyright
Copyright © Cambridge University Press 2015 

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References

[1]Abbad, M. & Chang, F. F. Schlumberger, Personal communication. The typical stone sample is 1.5 inches in diameter and held within a 5 inch diameter reaction vessel.Google Scholar
[2]Batchelor, G. K. (1951) Note on a class of solutions of the Navier–Stokes equations representing steady rotationally-symmetric flow. Q. J. Mech. Appl. Math. 4 (1), 29–41.CrossRefGoogle Scholar
[3]Bernardez, L. A. (2008) Dissolution of polycyclic aromatic hydrocarbons from a non-aqueous phase liquid into a surfactant solution using a rotating disk apparatus. Colloids Surf. A: Physicochemical Eng. Asp. 320 (1), 175–182.CrossRefGoogle Scholar
[4]Boomer, D. R., McCune, C. C. & Fogler, H. S. (1972) Rotating disk apparatus for reaction rate studies in corrosive liquid environments. Rev. Sci. Instrum. 43 (2), 225–229.CrossRefGoogle Scholar
[5]Brady, J. F. & Durlofsky, L. (1987) On rotating disk flow. J. Fluid Mech. 175 (1), 363–394.CrossRefGoogle Scholar
[6]Davies, C. W. (1962) Ion Association, Vol. 30, Butterworths, London.Google Scholar
[7]Escudier, M. P. (1984) Observations of the flow produced in a cylindrical container by a rotating endwall. Exp. Fluids 2 (4), 189–196.CrossRefGoogle Scholar
[8]Fredd, C. N. & Fogler, H. S. (1998) The kinetics of calcite dissolution in acetic acid solutions. Chem. Eng. Sci. 53 (22), 3863–3874.CrossRefGoogle Scholar
[9]Harned, H. S. & Hamer, W. J. (1933) The ionization constant of water and the dissociation of water in potassium chloride solutions from electromotive forces of cells without liquid junction. J. Am. Chem. Soc. 55 (6), 2194–2206.CrossRefGoogle Scholar
[10]Hyun, J. M. & Kim, J. W. (1987) Flow driven by a shrouded spinning disk with axial suction and radial inflow. Fluid Dyn. Res. 2 (3), 175–182.Google Scholar
[11]Kaufmann, G. & Dreybrodt, W. (2007) Calcite dissolution kinetics in the system CaCO3-H2O-CO2 at high undersaturation. Geochim. Cosmochim. Acta 71 (6), 1398–1410.CrossRefGoogle Scholar
[12]Kern, D. M. (1960) The hydration of carbon dioxide. J. Chem. Educ. 37 (1), 14.CrossRefGoogle Scholar
[13]Keslin, J. (1978) Viscosity of liquid water in the range −8 °C to 150 °C. J. Phys. Chem. Ref. Data 7 (3), 941–948.Google Scholar
[14]Lasaga, A. (1998) Kinetic Theory in the Earth Sciences, Princeton, New Jersey, Princeton University Press.CrossRefGoogle Scholar
[15]Lehmkuhl, G. D. & Hudson, J. L. (1971) Flow and mass transfer near an enclosed rotating disk: Experiment. Chem. Eng. Sci. 26 (10), 1601–1613.CrossRefGoogle Scholar
[16]Lehto, P., Aaltonen, J., Niemelä, P., Rantanen, J., Hirvonen, J., Tanninen, V. P. & Peltonen, L. (2008) Simultaneous measurement of liquid-phase and solid-phase transformation kinetics in rotating disc and channel flow cell dissolution devices. Int. J. Pharmaceutics 363 (1–2), 66–72.CrossRefGoogle ScholarPubMed
[17]Levich, V. G. & Spalding, D. B. (1962) Physicochemical Hydrodynamics, Vol. 689, Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
[18]Lewis, G. N. & Randall, M. (1961) Thermodynamics, revised by Pitzer, K.S. & Brewer, L., McGraw-Hill, New York.Google Scholar
[19]Lingwood, R. J. (1995) Absolute instability of the boundary layer on a rotating disk. J. Fluid Mech. 299, 17–17.CrossRefGoogle Scholar
[20]Lingwood, R. J. (1996) An experimental study of absolute instability of the rotating-disk boundary-layer flow. J. Fluid Mech. 314 (1), 373–405.CrossRefGoogle Scholar
[21]Lund, K., Fogler, H. S. & McCune, C. C. (1973) Acidization–I. The dissolution of dolomite in hydrochloric acid. Chem. Eng. Sci. 28 (3), 691–700.CrossRefGoogle Scholar
[22]Lund, K., Fogler, H. S., McCune, C. C. & Ault, J. W. (1975) Acidization–II. The dissolution of calcite in hydrochloric acid. Chem. Eng. Sci. 30 (8), 825–835.CrossRefGoogle Scholar
[23]Miklavčič, M. & Wang, C. Y. (2004) The flow due to a rough rotating disk. Z. für Angew. Math. Phys. (ZAMP) 55 (2), 235–246.CrossRefGoogle Scholar
[24]Mitchell, M. J., Jensen, O. E., Cliffe, K. A. & Maroto-Valer, M. M. (2010) A model of carbon dioxide dissolution and mineral carbonation kinetics. Proc. R. Soc. A: Math. Phys. Eng. Sci. 466 (2117), 1265–1290.CrossRefGoogle Scholar
[25]Morse, J. W., Arvidson, R. S. & Lüttge, A. (2007) Calcium carbonate formation & dissolution. Chem. Rev. 107 (2), 342–381.CrossRefGoogle ScholarPubMed
[26]Ockendon, H. (1972) An asymptotic solution for steady flow above an infinite rotating disc with suction. Q. J. Mech. Appl. Math. 25 (3), 291–301.CrossRefGoogle Scholar
[27]Patnaik, P. (2003) Handbook of Inorganic Chemicals, Vol. 28, McGraw-Hill, New York.Google Scholar
[28]Pitzer, K. S. (1981) Characteristics of very concentrated aqueous solutions. Phys. Chem. Earth 13, 249–272.CrossRefGoogle Scholar
[29]Plummer, L. N. & Busenberg, E. (1982) The solubilities of calcite, aragonite and vaterite in CO2-H2O solutions between 0 and 90 °C, and an evaluation of the aqueous model for the system CaCO3-CO2-H2O. Geochim. Cosmochim. Acta 46 (6), 1011–1040.CrossRefGoogle Scholar
[30]Prakongpan, S., Higuchi, W. I., Kwan, K. H. & Molokhia, A. M. (1976) Dissolution rate studies of cholesterol monohydrate in bile acid–lecithin solutions using the rotating-disk method. J. Pharmaceutical Sci. 65 (5), 685–689.CrossRefGoogle Scholar
[31]Stewartson, K. (1953) On the flow between two rotating coaxial disks. Proc. Camb. Philos. Soc. 49 (2), 333–341.CrossRefGoogle Scholar
[32]Taylor, K. & Nasr-El-Din, H. A. (2009) Measurement of acid reaction rates with the rotating disk apparatus. J. Can. Pet. Technol. 48 (6), 66–70.CrossRefGoogle Scholar
[33]Tomlan, P. F. & Hudson, J. L. (1971) Flow near an enclosed rotating disk: Analysis. Chem. Eng. Sci. 26 (10), 1591–1600.CrossRefGoogle Scholar
[34]Usdowski, E. (1982) Reactions and equilibria in the systems CO2-H2O and CaCO3-CO2-H2O (0–50°C). Neues Jahrbuch für Mineralogie. Abhandlungen 144 (2), 148–171.CrossRefGoogle Scholar
[35]Yuan-Hui, L. & Gregory, S. (1974) Diffusion of ions in sea water and in deep-sea sediments. Geochim. Cosmochim. Acta 38 (5), 703–714.CrossRefGoogle Scholar
[36]Zandbergen, P. J. & Dijkstra, D. (1987) Von Káán swirling flows. Annu. Rev. Fluid Mech. 19 (1), 465–491.CrossRefGoogle Scholar
[37]Zeebe, R. E. (2011) On the molecular diffusion coefficients of dissolved CO2, HCO3−, and CO32− and their dependence on isotopic mass. Geochim. Cosmochim. Acta 75, 2483–2498.CrossRefGoogle Scholar