Mathematical Theory of Liquid Interfaces: Liquid Layers, Capillary Interfaces, Floating Drops and Particles by Erich Miersemann

Author:Erich Miersemann
Language: eng
Format: epub
Publisher: World Scientific Publishing Co. Pte. Ltd.
Published: 2020-07-15T00:00:00+00:00

Then

One obtains these quantities by using a numerical method prescribed in Sec. 7.2.8. Consequently, one can find out for given data d, γw, γl whether or not the plate is repelled or attracted from the wall, and which force is acting on the plate.

Example 5.1. Let σ = 73.8 mN/m, which is approximately the surface tension of water with a temperature of about 20o Celsius. Then one gets approximately κ = 13.3 cm−2. Assume the distance of the plates is 0.1 cm. Suppose that γl = 1° and γw = 179°, then 1 = −50.9 mN, and if γl = 1° and γw = 1°, then 1 = 959.3 mN.

Remark 5.3. Consider the case, see [Finn (2010, 2013); Aspley, He and McCuan (2015)], that the left plate can flow too and let be the net force, i.e., the difference between the forces acting on the right and on the left plate. From formula (5.18) it follows that

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