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Studies of equations derived for application to dissolution from heterodisperse micronized suspensions

  • Colloid Science
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Summary

A rate constant for the dissolution of drugs in aqueous media is computed taking some account of particle size variation by each of two methods. The first uses the diffusion-based law for the decay of particle size employed byHiguchi and his co-workers. A graphical test suggests that the law is not always applicable. For these cases a second approach, using aWeibull distribution, and making no assumptions about the decay of an individual particle, is devised. TheK-values from the different methods show reasonable agreement with each other. These values also show remarkable agreement with previous work when allowance is made for the assumptions, (explicit or implicit) affecting the particulate surface area exposed to the solvent. The implication of these findings for the pharmaceutical scientist are discussed.

Zusammenfassung

Es wird eine neue Zerfallskonstante für die Auflösung von Arzneien in wässerigen Mitteln errechnet, unter Berücksichtigung der bei jeder der beiden Methoden auftretenden Schwankungen der Teilchengröße. Die erste Methode bedient sich des vonHiguchi und seinen Mitarbeitern angewendeten Diffusionsgesetzes für den Zerfall der Teilchengröße. Ein grafischer Test läßt darauf schließen, daß das Gesetz nicht für alle Fälle anwendbar ist. Für diese Fälle wird ein zweiter Weg ersonnen, bei dem von derWeibull'schen Verteilung Gebrauch gemacht wird, ohne Vermutungen über den Zerfall eines einzelnen Teilchens anzustellen. Die bei den verschiedenen Methoden festgestellten K-Werte stimmen einigermaßen miteinander überein, wenn man die Voraussetzungen — explizite und implizite — berücksichtigt, die die dem Lösungsmittel ausgesetzte und aus Partikeln bestehende Oberfläe beinflussen. Die Implikationen dieser Befunde für den pharmazeutischen Wissenschaftler werden besprochen.

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Abbreviations

t,t i :

Time

K :

Rate constant

S (t):

Total surface area of particles of all sizes at timet

n(t):

Total number of undissolved particles with radii > 0 at timet

n 1 (t):

Total number of undissolved particles with radii > 1μm at timet

n (0):

Total number of particles att = 0

R =R (t):

Undissolved particles radius at timet

R 0 :

Undissolved particle radius at time 0

R s0 :

Initial radius of the smalles undissolved particle(s)

R l0 :

Initial radius of the largest undissolved particle(s)

f(R):

Probability density function for particle size distribution

f(R 0):

Probability density of the particle size distribution att = 0

V (R):

Fraction of the total number of particles with radii > R

B, N :

Weibull distribution parameters

Γ (z):

The Gamma or factorial function

τ :

Variable of integration

D :

Diffusion coefficient of solute diffusing in water

ϱ :

Density of solute

C s ,C 0 :

Saturation and initial concentrations respectively, of solute in water

α:

\(\frac{{2D}}{\varrho }(C_s - C_0 ) = 0.2362 \times 10^{ - 12} m^2 \sec .^{ - 1} \)

γ, λ, θ :

Parameters of fit

W (t):

Undissolved mass of solute at timet

W 0 :

Undissolved mass of solute at zero time

Z s :

Mass of solute required to sature the given volume of solvent

η :

Volume of solution

References

  1. Short, M. P., C. T. Rhodes andW. P. F. Sharkey, J. Pharm. Sci.61, 1732 (1972).

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  2. Niebergall, P. J. andJ. E. Goyan, J. Pharm. Sci.52, 29 (1963).

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  3. Noyes, A. A. andW. R. Whitney, J. Amer. Chem. Soc.19, 930 (1897).

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  4. Higuchi, W. I. andE. N. Hiestand, J. Pharm. Sci.52, 67 (1963).

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  5. Higuchi, W. I., E. L. Rowe andE. N. Hiestand, J. Pharm. Sci.52, 161 (1963).

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Author information

Authors and Affiliations

  1. Cyanamid of Great Britain, Gosport, England

    M. P. Short

  2. Dept. of Mathematics, Portsmouth Polytechnic, Portsmouth, England

    W. P. Sharkey

  3. Dept. of Pharmaceutics, State University of New York at Buffalo, 14207, Buffalo, N. Y., USA

    C. T. Rhodes

Authors
  1. M. P. Short
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  2. W. P. Sharkey
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  3. C. T. Rhodes
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With 7 figures and 7 tables

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Short, M.P., Sharkey, W.P. & Rhodes, C.T. Studies of equations derived for application to dissolution from heterodisperse micronized suspensions. Colloid & Polymer Sci 253, 544–557 (1975). https://doi.org/10.1007/BF01753958

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  • DOI: https://doi.org/10.1007/BF01753958

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