The use of Delaunay curves for the wetting of axisymmetric bodies
Authors:
P. Basa, J. C. Schön and P. Salamon
Journal:
Quart. Appl. Math. 52 (1994), 1-22
MSC:
Primary 53A10; Secondary 76D45
DOI:
https://doi.org/10.1090/qam/1262313
MathSciNet review:
MR1262313
Full-text PDF Free Access
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Abstract: The wetting of a given solid figure is of importance in many fields of science ranging from physics and materials science to geology and medicine. An important special case that is generic to many situations is the wetting of an axisymmetric solid by a liquid of the same material. This problem is equivalent to minimizing the total surface area of the condensed phase (liquid + solid). Its solution is a mosaic of wet and dry regions on the solid. The shape of the wet regions is described by Delaunay curves. The analytic properties of these curves are discussed, and the wetting of several interesting solid configurations is presented.
P. G. DeGennes, Wetting: Statics and dynamics, Rev. Modern Physics 57, 827–863 (1985)
F. Amar, J. Bernholc, R. S. Berry, J. Jellinek, and P. Salamon, The shapes of first-stage sinters, J. Appl. Phys. 65, 3219–3225 (1989)
D. Hillel, Soil and Water—Physical Principles and Processes, Academic Press, London, 1971
P. Salamon, J. Bernholc, R. S. Berry, M. E. Carrera-Patino, and B. Andresen, The wetted solid—a generalization of Plateau’s problem and its implications for sintered materials, J. Math. Phys. 31, 610–615 (1990)
P. Basa, J. C. Schön, R. S. Berry, J. Bernholc, J. Jellinek, and P. Salamon, Shapes of wetted solids and sinters, Phys. Rev. B 43, 10 8113ff (1991)
W. v. Engelhardt, Interstitial Water of Oil Bearing Sands and Sandstones, Fourth World Petroleum Congress, Rome, 1955, pp. 399–416
R. Finn, Equilibrium Capillary Surfaces, Springer, New York, 1986
R. Osserman, A Survey of Minimal Surfaces, Dover Publications, New York, 1986
H.-P. Cheng and R. S. Berry, Surface melting in clusters and implications for bulk matter, Phys. Rev. A, 45, 7969–7980 (1992)
H.-P. Cheng and R. S. Berry, Clusters and Cluster Assembled Materials, R. S. Averback, J. Bernholc, and D. L. Nelson (Eds.), Materials Research Soc., Pittsburgh, PA, 1991, pp. 241–252
R. M. German, Liquid Phase Sintering, Plenum Press, New York, 1985
L. D. Landau and E. M. Lifshitz, Statistical Physics, 3rd ed., Part 1, Pergamon Press, New York, 1985
B. O’Neill, Elementary Differential Geometry, Academic Press, New York, 1966
C. Delaunay, Sur la surface de revolution dont la Courbure Moyenne est Constante, J. Math. Pures Appl. 6, 309–310 (1841)
P. Concus and R. Finn, The shape of a pendant liquid drop, Philos. Trans. Royal Soc. 292, 307–340 (1979)
R. Finn, Moon surfaces, and boundary behaviour of capillary surfaces for perfect wetting and non-wetting, Proc. London Math. Soc. (3) 57, 542–576 (1988)
G. Bakker, Kapillarität und Oberflächenspannung, Leipzig, Akademische Verlagsgesselschaft, 1928
A. R. Forsyth, Calculus of Variations, Dover Publications, New York, 1960
T. I. Vogel, Stability of a liquid drop trapped between two parallel planes, SIAM J. Appl. Math. 47, 516–525 (1987)
L. Rayleigh, On the capillary phenomena of jets, Scientific Papers Vol. I, Cambridge Univ. Press, Cambridge, 1899, pp. 377–401
J. C. Maxwell, Capillary action, Encyclopedia Britannica, 11th ed., Vol. 5, London, 1910, pp. 256ff
W. H. Fleming, Functions of Several Variables, Springer-Verlag, Berlin and New York, 1977
J. C. C. Nitsche, Vorlesungen über Minimalflächen, Springer-Verlag, Berlin and New York, 1975
P. G. DeGennes, Wetting: Statics and dynamics, Rev. Modern Physics 57, 827–863 (1985)
F. Amar, J. Bernholc, R. S. Berry, J. Jellinek, and P. Salamon, The shapes of first-stage sinters, J. Appl. Phys. 65, 3219–3225 (1989)
D. Hillel, Soil and Water—Physical Principles and Processes, Academic Press, London, 1971
P. Salamon, J. Bernholc, R. S. Berry, M. E. Carrera-Patino, and B. Andresen, The wetted solid—a generalization of Plateau’s problem and its implications for sintered materials, J. Math. Phys. 31, 610–615 (1990)
P. Basa, J. C. Schön, R. S. Berry, J. Bernholc, J. Jellinek, and P. Salamon, Shapes of wetted solids and sinters, Phys. Rev. B 43, 10 8113ff (1991)
W. v. Engelhardt, Interstitial Water of Oil Bearing Sands and Sandstones, Fourth World Petroleum Congress, Rome, 1955, pp. 399–416
R. Finn, Equilibrium Capillary Surfaces, Springer, New York, 1986
R. Osserman, A Survey of Minimal Surfaces, Dover Publications, New York, 1986
H.-P. Cheng and R. S. Berry, Surface melting in clusters and implications for bulk matter, Phys. Rev. A, 45, 7969–7980 (1992)
H.-P. Cheng and R. S. Berry, Clusters and Cluster Assembled Materials, R. S. Averback, J. Bernholc, and D. L. Nelson (Eds.), Materials Research Soc., Pittsburgh, PA, 1991, pp. 241–252
R. M. German, Liquid Phase Sintering, Plenum Press, New York, 1985
L. D. Landau and E. M. Lifshitz, Statistical Physics, 3rd ed., Part 1, Pergamon Press, New York, 1985
B. O’Neill, Elementary Differential Geometry, Academic Press, New York, 1966
C. Delaunay, Sur la surface de revolution dont la Courbure Moyenne est Constante, J. Math. Pures Appl. 6, 309–310 (1841)
P. Concus and R. Finn, The shape of a pendant liquid drop, Philos. Trans. Royal Soc. 292, 307–340 (1979)
R. Finn, Moon surfaces, and boundary behaviour of capillary surfaces for perfect wetting and non-wetting, Proc. London Math. Soc. (3) 57, 542–576 (1988)
G. Bakker, Kapillarität und Oberflächenspannung, Leipzig, Akademische Verlagsgesselschaft, 1928
A. R. Forsyth, Calculus of Variations, Dover Publications, New York, 1960
T. I. Vogel, Stability of a liquid drop trapped between two parallel planes, SIAM J. Appl. Math. 47, 516–525 (1987)
L. Rayleigh, On the capillary phenomena of jets, Scientific Papers Vol. I, Cambridge Univ. Press, Cambridge, 1899, pp. 377–401
J. C. Maxwell, Capillary action, Encyclopedia Britannica, 11th ed., Vol. 5, London, 1910, pp. 256ff
W. H. Fleming, Functions of Several Variables, Springer-Verlag, Berlin and New York, 1977
J. C. C. Nitsche, Vorlesungen über Minimalflächen, Springer-Verlag, Berlin and New York, 1975
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Article copyright:
© Copyright 1994
American Mathematical Society
