Editing Surface tension (section)

===Puddles on a surface===
[[Image:SurfTensionEdgeOfPool.png|thumb|Profile curve of the edge of a puddle where the contact angle is 180°. The curve is given by the formula:<ref name="cwp"/> <math display="block">x - x_0 = \frac 1 2 H \cosh^{-1}\left(\frac {H}{h}\right) - H \sqrt{1 - \frac{h^2} {H^2}}</math> where <math display="inline">H = 2 \sqrt{ {\gamma} / {g \rho}}</math>]]
[[Image:Exploring new continents 1200728.JPG|thumb|Small puddles of water on a smooth clean surface have perceptible thickness.]]

Pouring mercury onto a horizontal flat sheet of glass results in a [[Puddle#Physics|puddle]] that has a perceptible thickness. The puddle will spread out only to the point where it is a little under half a centimetre thick, and no thinner. Again this is due to the action of mercury's strong surface tension. The liquid mass flattens out because that brings as much of the mercury to as low a level as possible, but the surface tension, at the same time, is acting to reduce the total surface area. The result of the compromise is a puddle of a nearly fixed thickness.

The same surface tension demonstration can be done with water, lime water or even saline, but only on a surface made of a substance to which water does not adhere. Wax is such a substance. Water poured onto a smooth, flat, horizontal wax surface, say a waxed sheet of glass, will behave similarly to the mercury poured onto glass.

The thickness of a puddle of liquid on a surface whose contact angle is 180° is given by:<ref name="cwp">{{Cite book|title=Capillarity and Wetting Phenomena—Drops, Bubbles, Pearls, Waves|author1=Pierre-Gilles de Gennes|author-link1=Pierre-Gilles de Gennes|author2=Françoise Brochard-Wyart|author3=David Quéré|publisher=Springer|year=2002|isbn=978-0-387-00592-8|others=Alex Reisinger}}</ref>

<math display="block">h = 2 \sqrt{\frac{\gamma} {g\rho}}</math>

where

* {{mvar|h}} is the depth of the puddle in centimeters or meters.
* {{mvar|γ}} is the surface tension of the liquid in dynes per centimeter or newtons per meter.
* {{mvar|g}} is the acceleration due to gravity and is equal to 980&nbsp;cm/s<sup>2</sup> or 9.8&nbsp;m/s<sup>2</sup>
* {{mvar|ρ}} is the density of the liquid in grams per cubic centimeter or kilograms per cubic meter

[[Image:Surface tension.svg|thumb|Illustration of how lower contact angle leads to reduction of puddle depth]]

In reality, the thicknesses of the puddles will be slightly less than what is predicted by the above formula because very few surfaces have a contact angle of 180° with any liquid. When the contact angle is less than 180°, the thickness is given by:<ref name="cwp"/>

<math display="block">h = \sqrt{\frac{2\gamma_\mathrm{la}\left( 1 - \cos \theta \right)} {g\rho}}.</math>

For mercury on glass, {{math|''γ''<sub>Hg</sub>}} = 487 dyn/cm, {{math|''ρ''<sub>Hg</sub>}} = 13.5 g/cm<sup>3</sup> and {{mvar|θ}} = 140°, which gives {{math|''h''<sub>Hg</sub>}} = 0.36&nbsp;cm. For water on paraffin at 25&nbsp;°C, {{mvar|γ}} = 72 dyn/cm, {{mvar|ρ}} = 1.0 g/cm<sup>3</sup>, and {{mvar|θ}} = 107° which gives {{math|''h''<sub>H<sub>2</sub>O</sub>}} = 0.44&nbsp;cm.

The formula also predicts that when the contact angle is 0°, the liquid will spread out into a micro-thin layer over the surface. Such a surface is said to be fully wettable by the liquid.{{Clear right}}