A new equation for the size distribution of emulsion particles

Summary A study of experimental data from the literature provided grounds for believing that the particle size distributions of emulsions can be represented by a single general size distribution equation. In the present paper this distribution equation, which contains two parameters, is derived statistically. Verification with published experimental data on several oil-in-water emulsions and with own data on water-in-oil emulsions yielded very good agreement for mechanically prepared emulsions.

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Zusammenfassung Ein Studium der experimentellen Ergebnisse aus dem Schrifttum legt nahe, daß die Teilchengrößenverteilungen von Emulsionen durch eine einzige generelle Verteilungsgleichung dargestellt werden können. Die vorliegende Arbeit gibt eine statistische Ableitung dieser Verteilungsfunktion, die zwei Parameter enthält. Die PrÜfung mit veröffentlichten experimentellen Ergebnissen an verschiedenen öl-in Wasser-Emulsionen und mit eigenen Experimenten an Wasser- in öl-Emulsionen ergab fÜr mechanisch präparierte Emulsionen sehr gute Übereinstimmungen.

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List of symbols A constant - a parameter of the equation; characteristic diameter - constant - constant - D sum of the diameters of all globules - dd sum of the diameters of the globules in the diameter interval fromx tox +dx - m number of categories - N total number of globules - n _i number of globules ini-th category - dn number of globules in the diameter interval fromx tox +dx. - _i number of volume elements in thei-th category - P probability - p number of volume elements in volumeV - S total surface area of the globules - s surface area of a globule - s _i surface area of a globule in thei-th category - ds surface area of the globules in the diameter interval fromx tox +dx - V total volume of the globules - v volume of a globule - v _i volume of a globule in thei-th category - v _x cumulative volume below sizex - dv volume of the globules in the diameter interval fromx tox +dx - w specific surface area of a globule - w _i specific surface area of a globule in thei-th category - X parameter of the equation; largest globule occurring - x variable globule diameter - X _i diameter of a globule in thei-th category.