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A new equation for the size distribution of emulsion particles

II. Validity of the equation

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Summary

In the preceding paper a new size distribution equation for emulsion particles was introduced. Though a very good agreement between theory and experiment was found for mechanically prepared emulsions, it was felt desirable to examine critically the limits of its validity. This is done in the present paper with the aid of experimental data from the literature on size distributions of emulsion particles. Two distinct criteria, both of which must be fulfilled, are formulated and applied in judging the validity of the new equation. A comparison with two other well-known distribution equations, viz. the log-probability and the Rosin-Rammler equation, showed that the new equation is to be preferred for representing experimental size distributions of emulsion particles.

Zusammenfassung

In der vorangehenden Arbeit wurde eine neue Teilchengrößen-Verteilungsgleichung fÜr Emulsionen eingefÜhrt. Obwohl fÜr mechanisch präparierte Emulsionen sehr gute Übereinstimmung zwischen Theorie und Experiment vorliegt, schien es wÜnschenswert, die GÜltigkeitsgrenzen kritisch zu prÜfen. Dies geschieht in der vorliegenden Arbeit an Hand von experimentellen Daten aus der Literatur. Zwei wesentliche Kriterien, die beide erfÜllt sein mÜssen, werden formuliert und zur Beurteilung der GÜltigkeit der neuen Gleichung angewendet. Ein Vergleich mit zwei anderen bekannten Teilchengrößen-Gleichungen, der logarithmisch-normalen Gleichung und der Gleichung von Rosin und Rammler, zeigt, daß die neue Gleichung fÜr die Darstellung der experimentellen Teilchengrößenverteilungen bei Emulsionen vorzuziehen ist.

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Abbreviations

a :

size parameter in the distribution equations [1], [4] and [6]

D :

sum of the diameters of all droplets

δ :

distribution parameter in the equations [4] and [6]

n i :

number of droplets in thei-th diameter interval

N :

total number of droplets

R :

cumulative volume percentage over sizex

S :

total surface area of the droplets

v% :

cumulative volume percentage below sizex

dv :

volume of the droplets in the diameter interval fromx tox +dx

V :

total volume of the droplets

x :

variable droplet diameter

x i :

diameter of a droplet in thei-th diameter interval

¯ x pq :

average droplet diameter

X :

parameter of equation [1]; largest droplet diameter.

References

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Bezemer, C., Schwarz, N. A new equation for the size distribution of emulsion particles. Kolloid-Zeitschrift 146, 145–151 (1956). https://doi.org/10.1007/BF01502244

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  • DOI: https://doi.org/10.1007/BF01502244

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