Editing Surface tension (section)

===Surface curvature and pressure===
[[Image:CurvedSurfaceTension.png|thumb|right|Surface tension forces acting on a tiny (differential) patch of surface. {{mvar|δθ<sub>x</sub>}} and {{mvar|δθ<sub>y</sub>}} indicate the amount of bend over the dimensions of the patch. Balancing the tension forces with pressure leads to the [[Young–Laplace equation]]]]

If no force acts normal to a tensioned surface, the surface must remain flat. But if the pressure on one side of the surface differs from pressure on the other side, the pressure difference times surface area results in a normal force. In order for the surface tension forces to cancel the force due to pressure, the surface must be curved. The diagram shows how surface curvature of a tiny patch of surface leads to a net component of surface tension forces acting normal to the center of the patch. When all the forces are balanced, the resulting equation is known as the [[Young–Laplace equation]]:<ref name="cwp"/>
<math display="block">\Delta p = \gamma \left( \frac{1}{R_x} + \frac{1}{R_y} \right)</math>
where:
*{{math|Δ''p''}} is the pressure difference, known as the [[Laplace pressure]].<ref name="Physics and Chemistry of Interfaces">{{cite book | title = Physics and Chemistry of Interfaces | author1 = Butt, Hans-Jürgen | author2 = Graf, Karlheinz | author3 = Kappl, Michael | year = 2006 | page = 9|isbn=978-3-527-60640-5|publisher=Wiley}}</ref>
*{{mvar|γ}} is surface tension.
*{{mvar|R<sub>x</sub>}} and {{mvar|R<sub>y</sub>}} are [[Radius of curvature (mathematics)|radii of curvature]] in each of the axes that are parallel to the surface.
The quantity in parentheses on the right hand side is in fact (twice) the [[mean curvature]] of the surface (depending on normalisation).
Solutions to this equation determine the shape of water drops, puddles, menisci, soap bubbles, and all other shapes determined by surface tension (such as the shape of the impressions that a [[water strider]]'s feet make on the surface of a pond).
The table below shows how the internal pressure of a water droplet increases with decreasing radius. For not very small drops the effect is subtle, but the pressure difference becomes enormous when the drop sizes approach the molecular size. (In the limit of a single molecule the concept becomes meaningless.)

{| class="wikitable" style="float:center; clear:right;"
|+ {{math|Δ''p''}} for water drops of different radii at [[standard conditions for temperature and pressure|STP]]
|-
! style="width:120px;" | Droplet radius
| style="width:120px;" | 1&nbsp;mm
| style="width:120px;" | 0.1&nbsp;mm
| style="width:120px;" | 1&nbsp;[[micrometre|μm]]
| style="width:120px;" | 10&nbsp;[[nanometer|nm]]
|-
! {{math|Δ''p''}} ([[Atmosphere (unit)|atm]])
| 0.0014
| 0.0144
| 1.436
| 143.6
|}
{{Clear right}}