Comments on “calculation of advancing and receding contact angles. I. Drops on inclined planes”

Letters to the Editors on "Calculation of Advancing and Receding Contact Angles I. Drops on Inclined Planes"

Comments

Dr. Princen is quite correct in his statement (1) t h a t the equations given in Lamb's book (2) were only intended for cylindrical drops and that the writer in his paper (3) did not use the classical t r e a t m e n t for the system of axisymmetric drops. I t has been found, however, that treatment of drops as a large number of very thin cylinders

in Fig. 1. The calculated contact angles for drops I, II, and I I I were 140.4, 139.3, and 140.1, ° respectively. The surface tension of mercury varies from 400 to 500 dynes/cm according to the purity (5). The profile of a drop of triple distilled mercury on clean glass was measured and is plotted in Fig. 2. The smooth curve is the calculated curve,

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FIG. 1. Experimental data of Bashforth and Adams for drops I, II, and I I I (ref. (4)) given by ope~ points and corresponding curves calculated by equations given in Ref. (3).

gives very close agreement with experimental data. For example, the experimental data for mercury drops of Bashforth and Adams (4) gave, by use of their table, values of surface tension irom 340.6 to 367.5 dynes/cm and contact angles from 139.4 to 148.3 °. The data for drops I, II, and I I I shown in Fig. 2 of Ref. (4) were, therefore, used in the writer's computer program based on the equations in question. The surface tension was calculated from the data of drop I I I and this value (431.6 dynes/cm) used in plotting the three curves

with values of 485 dynes/cm for the surface tension and 138.4 ° for the contact angle. The equations can be used to describe very large drops by making k = 1, but the Bashforth and Adams table cannot be used for such drops since the value of b, which is used as a unit of measurement, approaches infinity. Admittedly, the above calculated values for the surface tension could be high, but this would still not explain why an equation involving elliptic

Journal of Colloid and Interface Science,

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Vo]. 37, No. 1, September 197i

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LETTERS TO THE EDITORS

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FIG. 2. Experimental data for a drop of triple distilled mercury oa clean glass given by open points and corresponding curve calculated by equations given in Ref. (3). integrals gives a very close fit to experimental data at every point of the curve. REFERENCES 1. PRINCEN, H. M., J. Colloid Interface Sci. 36~ $ 157 (1971). 2. LAMB, It., "Statics," pp. 275-280. Cambridge Univ. Press, Cambridge (1928). 3. LOMAS, It., J. Colloid Interface Sci. 33~ 548 (1970). 4. BASHFORTH, F . , AND ADAMS, $. C., "An Attempt

to Test the Theories of Capillary Action," University Press, Cambridge (1883). 5. KAYE, G. W. C., AND LABY, T. H., "Tables of Physical and Chemical Constants," Longmans, London (1966). H. LOMAS,

Department of Organic Chemistry, Ontario Research Foundation, Sheridan Park, Ontario, Canada Received February 17,1971; accepted May 14, 1971

Journal of Colloid and Interface Science, Vol. 37, No. 1, September 1971