By Robert Finn
Capillarity phenomena are all approximately us; a person who has obvious a drop of dew on a plant leaf or the spray from a waterfall has saw them. except their often remarked poetic characteristics, phenomena of this type are so regularly occurring as to flee particular detect. during this feel the increase of liquid in a slim tube is a extra dramatic occasion that calls for and at the start defied rationalization; recorded observations of this and related ensue rences should be traced again to instances of antiquity, and for loss of expla country got here to be defined via phrases deriving from the Latin be aware "capillus", which means hair. It used to be no longer till the eighteenth century that an information constructed that those and lots of different phenomena are all manifestations of a few factor that occurs at any time when diversified fabrics are located adjoining to one another and don't combine. If one (at least) of the fabrics is a fluid, which varieties with one other fluid (or gasoline) a unfastened floor interface, then the interface could be known as a capillary surface.
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Additional info for Equilibrium Capillary Surfaces
Example text
If we identify any two such surfaces when one is a continuation of the other, we obtain the correspondence principle [57]: there is a 1-1 correspondence between sessile drops and capillary surfaces. :onclude from the correspondence principle that the set of all symmetric sessile drops can be described by a one parameter family of curves. This property will be basic in what follows. 2. Continuation Properties In view of the preceding remarks, we focus attention on a symmetric capillary surface, with center height U o > O.
2 ([57J). Let i/ > 0 be arbitrary, and 0 < y::S n. There is exactly one symmetric simply connected sessile drop with boundary angle I' and volwne"Y". 2. ~'r is a continuously differentiable function of U o' The lemma does not follow from standard continuous dependence theorems, as the equation is singular at r = O. However, the proof is not basically difficult - it can be obtained for example by exploiting monotonicity properties and simple growth estimates for the solutions - and we do not include details here.
3. For any choice oj' B, 'y, there holds 2 B COSY