Paper number 1137
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MATHEMATICAL STUDY OF LAPLACE AND YOUNG EQUATIONS IN THE CASE OF THE CONTACT BETWEEN A DROP AND FIBRE |
T. Hamieh1 and A. Brillard2
1Institut de Chimie des Surfaces et Interfaces (I.C.S.I.-C.N.R.S).-UPR 9069
15, Rue Jean Starcky - B.P.2488-68057- Mulhouse Cedex - France
2Université de Haute-Alsace, 2, Rue des Frères Lumières
68093 - Mulhouse Cedex - France
| Summary | This paper constitutes a mathematical contribution on the theory of capillarity in a particular case of the contact of a drop on a cylindrical fibres, by gaving a new formulation of the Laplace and Young equations in that case and proving the effect of the gravity force on the calculation of the contact angle of a drop on a fibre and the surface tension of the solid. The mechanical equilibrium conditions which describe the state of balance across the separation surface or along the contact line were derived as force balance relations between pressure, surface tension and the geometric shape of the surface or the contact line; by using the classical method of the Lagrange multipliers and the variation theory. Our results are limited to capillary systems which are either in axisymmetric geometry or whose surfaces may be described by non-parametric surface function of the form u = u(x,z). In many practical cases, the geometry of the solid is typically axisymmetric. A typical case of a axisymmetric solid, which was not mathematically very studied in literature, is that of a liquid drop in axisymmetric position in contact with a horizontal or vertical rigid cylindrical surface. |
Keywords | fibre, contact angle, thermodynamics, Laplace and Young equations, drop, surface energy, Lagrange multipliers. |