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2013 | 15 | 3 | 74-77
Tytuł artykułu

Lifetime of a soluble solid particle in a stagnant medium: approximate analytical modelling involving fractional (half-time) derivatives

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Approximate analytical solutions concerning lifetime of soluble solid particles in an unbounded stagnant medium have been developed by simple application of fractional half-time derivative in the Riemann-Liouville sense to express the relationship between the net surface mass flux and the concentration at the interface. The solutions start with the initial formulation of Rice and Do on the time-depletion of the radius of a spherical particle expressed through terms including the solubility parameter as the only key parameter controlling the process of dissolution. The two approximate developed solutions use different scaling and dimensionless variables: The 1st solution is developed by an introduction of a similarity variable [xxx] while the 2nd solution applies the classical scaling using the initial sphere radius as a length scale that leads to dimensionless radius r = R/R0 and time τ = Dt/R02. Both solutions provide approximate relationships close to that of Rice and Do.
Wydawca

Rocznik
Tom
15
Numer
3
Strony
74-77
Opis fizyczny
Daty
wydano
2013-09-01
online
2013-09-20
Twórcy
  • University of Chemical Technology and Metallurgy, Department of Chemical Engineering, Sofia 1756, 8 Kliment Ohridsky, blvd. Bulgaria, jordan.hristov@mail.bg
Bibliografia
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  • 13. Marabi, A., Mayor, G., Burbidge, A., Wallach, R. & Saguy, I.S. (2008). Assessing dissolution kinetics of powders by a single particle approach, Chem. Eng. J. 139 (1), 118-127. DOI: 10.1016/j.cej.2007.07.081.[Crossref][WoS]
  • 14. Rakoczy, R. & Masiuk, S. (2011). Studies of a mixing process induced by a transverse rotating magnetic field , ChemicalEngineering Science, 66 (11), 2298-2308. DOI: 10.1016/j. ces.2011.02.021.[Crossref]
  • 15. Rakoczy, R. (2013). Mixing energy investigations in a liquid vessel that is mixed by using a rotating magnetic field, Chemical Engineering and Processing: Process Intensification, 66, April, 1-11. DOI: 10.1016/j.bbr.2011.03.031.012.[Crossref]
  • 16. Crank, J. (1975). The Mathematics of Diffusion. 2nd ed., Oxford University Press, London.
  • 17. van Keer, R. & Kacur, J. (1998). On a numerical model for diffusion-controlled growth and dissolution of spherical precipitates, Mathematical Problems in Engineering, 4 (2), 115-133. ISSN: 1024123X.
  • 18. Vermolen, F.J., van Mourik, P. & van der Zwaag, S. (1997). Analytical approach to particle dissolution in a finite medium, Mater. Sci. Technol. 13 (4), 308-312. ISSN: 02670836.
  • 19. Vrentas, J.S. & Shin, D. (1980). Perturbation solutions of spherical moving boundary problems. II, Chem. Eng. Sci. 35 (8), 1697-1705. DOI: 10.1016/0009-2509(80)85004-4.[Crossref]
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  • 21. Asthana, R. & Pabi, S.K. (1990). An Approximate Solution for the Finite-extent Moving-boundary Diffusion-controlled Dissolution of Spheres, Materials Science and Engineering, A128 (2), 253-258. DOI: 10.1016/0921-5093(90)90233-S.[Crossref]
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  • 24. Rice, R.G. & Do, D.D. (2006). Dissolution of a solid sphere in an unbounded, stagnant liquid, Chem. Eng. Sci., 61 (2), 775-778. DOI: 10.1016/j.bbr.2011.03.031.[Crossref]
  • 25. Oldham, K.B. & Spanier, J. (1974). The Fractional calculus, New York, USA, Academic Press.
  • 26. dos Santos, M.C., Lenzi, E., Gomes, E.M., Lenzi, M.K. & Lenzi, E.K. (2011). Development of Heavy Metal sorption Isotherm Using Fractional Calculus, Int. Rev. Chem. Eng., 3 (6), 814-817.
  • 27. Pfaffenzeller, R.A., Lenzi, M.K. & Lenzi, E.K. (2011). Modeling of Granular Material Mixing Using Fractional Calculus, Int. Rev. Chem. Eng., 3 (6), 818-821.
  • 28. Hristov, J. (2012). Impedance at the Interface of Contacting Bodies: 1-D example solved by semi-derivatives, ThermalScience, 16, 623-627. DOI: 10.2298/TSCI111125017H.[Crossref]
  • 29. Carslaw, H.S. & Jaeger, J.C. (1959). Conduction of Heatin Solids, London, UK, Oxford University Press.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_pjct-2013-0048
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