Summary
TheHarkins-Jordan correction factors which make the ring method an accurate and absolute method of measuring surface and interfacial tensions, are calcuated theoretically and made available in a tabulated form. The applicable range of the numerical tabulation far exceeds the range of those available in the literature which have been obtained experimentally. With the tabulation, the ring method may be used to measure the interfacial tensions of liquid systems in which the density difference across the interface is very small and the interfacial tension is large, or in which the density difference is large and the tension is small. The theoretical calculations also provide information on the state of the ring at the liquid interface which may be used to increase accuracy of the ring method.
Zusammenfassung
DieHarkins-Jordan Korrektionsfaktoren, die die Ringmethode als eine genaue und absolute Methode zur Bestimmung von Oberflächen- und Grenzflächenspannungen möglich machen, sind theoretisch berechnet und tabuliert worden. Der anwendbare Bereich dieser numerischen Tafeln überschreitet bei weitem den Bereich jener, die in der Literatur vorvorhanden und experimentell bestimmt worden sind. Mit diesen Tafeln kann man die Ringmethode anwenden für die. Grenzflächenspannungsmessungen flüssiger Systeme, in denen der Dichteunterschied beiderseits der Grenzfläche sehr gering und die Grenzflächenspannung sehr groß ist, oder in denen der Dichteunterschied groß und die Spannung klein ist. Die theoretischen Berechnungen darüber hinaus informieren über die Lage des Ringes an der flüssigen Grenzfläche, woraus eine erhöhte Genauigkeit der Ringmethode abgeleitet werden kann.
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Abbreviations
- a :
-
radius of the ring wire;\(\bar a \equiv a\sqrt {C_{23} } \)
- A i :
-
quantity defined by [13a]
- b :
-
radius of curvature atr = 0 of the inner meniscus
- C 23 :
-
(ϱ2 – ϱ3)g/γ23
- f :
-
Harkins-Jordan factor
- F :
-
maximum equilibrium force of detachment
- g :
-
gravity
- h :
-
height of the ring;\(\bar b \equiv b\sqrt {C_{23} } \)
- r i :
-
r-coordinate of thei meniscus;\(\bar r_i \equiv r_i \sqrt {C_{23} } \)
- R :
-
radius of the ring;\(\bar R \equiv R\sqrt {C_{23} } \)
- v :
-
volume of the liquid raised:\(\bar v \equiv vC_{23}^{3/2} \)
- V :
-
maximumv;\(\bar V \equiv VC_{23}^{3/2} \)
- z o :
-
height of the inner meniscus atr = 0,\(\bar z_0 \equiv z_0 \sqrt {C_{23} } \)
- z i :
-
z-coordinate of thei meniscus,\(\bar z_i \equiv z_i \sqrt {C_{23} } \)
- \ i :
-
shape parameter of thei meniscus
- γ 23 :
-
interfacial tension (23 interface)
- λ i :
-
a quantity defined by [12]
- ϱ i :
-
density of the phasei
- φ i :
-
slope angle of thei meniscus profile
- ψ i :
-
angle between the lines drawn from the center of the ring wire, vertically downwards and to thei contact line
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Huh, C., Mason, S.G. A rigorous theory of ring tensiometry. Colloid & Polymer Sci 253, 566–580 (1975). https://doi.org/10.1007/BF01753960
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DOI: https://doi.org/10.1007/BF01753960