PL EN


Preferences help
enabled [disable] Abstract
Number of results
2013 | 15 | 3 | 74-77
Article title

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

Authors
Content
Title variants
Languages of publication
EN
Abstracts
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.
Publisher
Year
Volume
15
Issue
3
Pages
74-77
Physical description
Dates
published
1 - 09 - 2013
online
20 - 09 - 2013
References
  • 1. Noyes, A. & Whitney, W.R. (1987). The Rate of Solution of Solid Substances in their own Solutions, J. Am. Chem. Soc. 19 (12), 930-934.
  • 2. Higuchi,W.I. & Hiestand, E.N. (1963). Dissolution rates of finely divided powders I. Effect of a distribution of particle sizes in a diffusion-controlled process. J. Pharm. Sci., 52 (1), 67-71. DOI: 10.1002/jps.2600520114.[Crossref]
  • 3. Siepmann, J. & Siepmann, F. (2011). Mathematical modeling of drug release from lipid dosage formsInt. J. Pharmaceutics, 418 (1), 42-53. DOI: 10.1016/j.ijpharm.2011.07.015.[Crossref]
  • 4. Haverkamp, R.G. & Welch, B.J. (1998). Modelling the dissolution of alumina powder in cryolite, Chem. Eng. Proc. 37 (2), 177-187. http://dx.doi.org/10.1016/S0255-2701(97)00048-2[Crossref]
  • 5. Dorozhkin, S.V. (1996). Fundamentals of the wet-process phosphoric acid production.1. Kinetics and mechanism of the phosphate rock dissolution, Ind. Eng. Chem. Res. 35 (11), 4328-4335. DOI: 10.1021/ie960092u.[Crossref]
  • 6. Bechtloff, N., Justen, P. & Ulrich, J.(2001). The kinetics of heterogeneous solid-liquid reaction crystallizations-an overview and examples, Chem. Ing. Tech. 73 (5), 453-460. DOI: 10.1002/1522-2640(200105)73:5.[Crossref]
  • 7. Forryan, C.L., Klymenko, O.V., Wilkins, S.J., Brennan, C.M. & Compton, R.G. (2005). Experimental and Theoretical Study of the Surface-Controlled Dissolution of Cylindrical Particles. Application to Solubilization of Potassium Hydrogen Carbonate in Hot Dimethylformamide, J. Phys. Chem. B, 109 (44), 20786-20793. DOI:10.1021/jp058197a.[Crossref]
  • 8. Lu, T.K., Frisella, M.E. & Johnson, K.C. (1993). Dissolution modeling: Factors affecting the dissolution rates of polydisperse powders, Pharm Res 10 (9), 1308-1314. DOI: 10.1023/A:1018917729477.[Crossref]
  • 9. Liu, B.T. & Hsu, J.P. (2006). Theoretical analysis on diffusional release from ellipsoidal drug delivery devices, Chem. Eng. Sci., 61 (6) 1748-1752. http://dx.doi.org/10.1016/j.ces.2005.10.014[Crossref]
  • 10. Sertsou, G. (2004). Analytical Derivation of Time Required for Dissolution of Monodisperse Drug Particles, J. Pharm. Sci., 93 (8), 1941-1943. DOI: 10.1002/jps.20119.[Crossref]
  • 11. Costa, P. & Lobo, J.M.S. (2001). Review: modeling and comparison of dissolution profiles, Europ. J. Pharmac. Sci. 13 (2), 123-133. DOI: 10.1016/S0928-0987(01)00095-1.[Crossref]
  • 12. Allers, T., Luckas, M. & Schmidt, K.G. (2003). Modeling and measurement of the dissolution rate of solid particles in aqueous suspensions. Part I. Modeling, Chem. Eng. Technol. 26 (11), 1131-1136. DOI: 10.1002/ceat.200303007.[Crossref]
  • 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]
  • 20. Vrentas, J.S. & Shin, D. (1980). Perturbation solutions of spherical moving boundary problems. I, Chem. Eng. Sci. 35 (8) 1687-1696. DOI: 10.1016/0009-2509(80)85003-2.[Crossref]
  • 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]
  • 22. Kupiec, K. & Gwadera, M. (2012). On the application of an approximate kinetic equation of heat and mass transfer processes: the effect of body shape, Heat Mass Transfer, 48 (4), 599 -610. DOI: 10.1007/s00231-011-0905-6.[Crossref]
  • 23. Rosner, D.E. (1969). Lifetime of a Highly Soluble Dense Spherical Particle1, The Journal of Physical Chemistry, 73 (2), 382-387. DOI: 10.1021/j100722a019.[Crossref]
  • 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.
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_pjct-2013-0048
Identifiers
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.