By Robert Finn

Capillarity phenomena are all approximately us; somebody who has noticeable a drop of dew on a plant leaf or the spray from a waterfall has saw them. except their usually remarked poetic traits, phenomena of this kind are so regular as to flee designated realize. during this experience the increase of liquid in a slender tube is a extra dramatic occasion that calls for and before everything defied rationalization; recorded observations of this and related take place rences may be traced again to instances of antiquity, and for loss of expla kingdom got here to be defined by way of phrases deriving from the Latin be aware "capillus", which means hair. It used to be now not till the eighteenth century that an information constructed that those and plenty of different phenomena are all manifestations of a few factor that occurs at any time when diversified fabrics are positioned adjoining to one another and don't combine. If one (at least) of the fabrics is a fluid, which kinds with one other fluid (or fuel) a unfastened floor interface, then the interface can be often called a capillary surface.

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**Additional resources for Equilibrium Capillary Surfaces**

**Example text**

We now ask the question: suppose a small amount of liquid is removed symmetrically Ji'om a sessile drop. Does the resulting drop lie strictly interior to the original one? We consider here only the case 0 < }' :s; n12. We parametrize the solutions once more by uo, and consider solutions u =u(r; u o) and uJ=u(r; u o +6), with 6>0. Let vO(r; uo)=uo-b; then VO(O; uo)=u(O; 11 0) and (r sin Iji)r= Kru b (r sin I/l)r= Kru. Thus r(sinl/l"-sinlp)=K J>. (u b -lI)dp, from which we conclude (UO - u) is increasing in r.

And it follows that the volume of the spherical cap exceeds "Y. 23 a). 23b). 3. '1 = n. The statement was proved for the range 0 < l/J S; nl2 in Chapter 2. 7)). Since duldl/J>O on O

S,n, for any choice of u a > o. U niq ueness is thus proved. 4. 3. The envelope. 5. 3), F(lj;)=ti cos lj; -,:sin lj;=0. Since, as shown above, Ii> 0, /; < 0 on 0 < lj; ~ n, there can be no envelope points on 0