Generalized theory of capillarity for axisymmetric menisci |
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| Institution: | 1. Key Laboratory of Low-grade Energy Utilization Technologies and Systems, Chongqing University, Chongqing 400044, China;2. Institute of Engineering Thermophysics, Chongqing University, Chongqing 400044, China;3. Institute for Integrated Energy Systems, University of Victoria, P.O. Box 3055 STN CSC, Victoria, BC V8W 3P6, Canada;4. Department of Mechanical Engineering, University of Victoria, P.O. Box 3055 STN CSC, Victoria, BC V8W 3P6, Canada;1. Instituto de Matemática e Estatística, Universidade Federal de Goiâs, 74001-970, Goiânia-GO, Brazil;2. Instituto Federal de Educação Ciência e Tecnologia de Goiâs, Goiânia-GO, 74055-110, Brazil;3. Departamento de Matemática, Universidade de Brasília, 70910-900, Brasília-DF, Brazil;1. NTIS—New Technologies for the Information Society, Faculty of Applied Sciences, University of West Bohemia, Univerzitní 8, 301 00 Plzeň, Czech Republic;2. Department of Mathematics, Faculty of Applied Sciences, University of West Bohemia, Univerzitní 8, 301 00 Plzeň, Czech Republic |
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| Abstract: | A high-curvature generalization of the Laplace equation of capillarity and the Young equation of capillarity (including line tension) is developed for an axisymmetric solid-liquid-fluid system. The most general expressions for the Laplace and Young equations do not assume a particular form for the specific surface free energy. However, when a particular form, i.e., ω(A) = γ(A)∞+ CJJ+ CkK, which is related to Gibbs' expression for a highly curved menisci,1 is assumed to hold for the specific surface free energy then we are able to recover the expected simplified form of the Laplace equation. The corresponding high-curvature Young equation includes a couple which balances the surface moments at the contact line. Unfortunately, the effect of this couple could be confused with the effect of line tension in experiments which attempt to measure the dependence of the contact angle on the contact line radius. |
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