Editing Surface tension (section)

===Contact angles===
{{Main|Contact angle}}
The surface of any liquid is an interface between that liquid and some other medium.<ref group=note>In a [[mercury barometer]], the upper liquid surface is an interface between the liquid and a vacuum containing some molecules of evaporated liquid.</ref> The top surface of a pond, for example, is an interface between the pond water and the air. Surface tension, then, is not a property of the liquid alone, but a property of the liquid's interface with another medium. If a liquid is in a container, then besides the liquid/air interface at its top surface, there is also an interface between the liquid and the walls of the container. The surface tension between the liquid and air is usually different (greater) than its surface tension with the walls of a container. And where the two surfaces meet, their geometry must be such that all forces balance.<ref name="s_z"/><ref name="cwp"/>

{| style="float:right;"
|-
|[[Image:SurfTensionContactAngle.png|thumb|255px|right|Forces at contact point shown for contact angle greater than 90° (left) and less than 90° (right)]]
|}

Where the two surfaces meet, they form a [[contact angle]], {{mvar|θ}}, which is the angle the tangent to the surface makes with the solid surface. Note that the angle is measured ''through the liquid'', as shown in the diagrams above. The diagram to the right shows two examples. Tension forces are shown for the liquid–air interface, the liquid–solid interface, and the solid–air interface. The example on the left is where the difference between the liquid–solid and solid–air surface tension, {{math|''γ''<sub>ls</sub> − ''γ''<sub>sa</sub>}}, is less than the liquid–air surface tension, {{math|''γ''<sub>la</sub>}}, but is nevertheless positive, that is

<math display="block">\gamma_\mathrm{la} > \gamma_\mathrm{ls} - \gamma_\mathrm{sa} > 0</math>

In the diagram, both the vertical and horizontal forces must cancel exactly at the contact point, known as [[Mechanical equilibrium|equilibrium]]. The horizontal component of {{math|''f''<sub>la</sub>}} is canceled by the adhesive force, {{math|''f''<sub>A</sub>}}.<ref name="s_z"/>

<math display="block">f_\mathrm{A} = f_\mathrm{la} \sin \theta</math>

The more telling balance of forces, though, is in the vertical direction. The vertical component of {{math|''f''<sub>la</sub>}} must exactly cancel the difference of the forces along the solid surface, {{math|''f''<sub>ls</sub> − ''f''<sub>sa</sub>}}.<ref name="s_z"/>

<math display="block">f_\mathrm{ls} - f_\mathrm{sa} = -f_\mathrm{la} \cos \theta</math>

{| class="toccolours" border="1" style="float: right; clear: right; margin: 0 0 1em 1em; border-collapse: collapse;"
|+'''Some liquid–solid contact angles'''<ref name="s_z"/>
|- style="text-align:center; background:#c0c0f0;"
! Liquid
! Solid
! Contact<br>angle
|-
| [[water]]
| rowspan="6" |
{| cellpadding="0" cellspacing="0" border="0"
|- style="background:#f8f8f8;"
|soda-lime glass
|- style="background:#f8f8f8;"
| lead glass
|- style="background:#f8f8f8;"
| [[fused quartz]]
|}
| rowspan="6" style="text-align:center;"|0°
|-
| [[ethanol]]
|-
| [[diethyl ether]]
|-
| [[carbon tetrachloride]]
|-
| [[glycerol]]
|-
| [[acetic acid]]
|-
| rowspan="2"|[[water]]
| paraffin wax
| style="text-align:center;"|107°
|-
| silver
| style="text-align:center;"|90°
|-
| rowspan="3"| [[iodomethane|methyl iodide]]
| soda-lime glass
| style="text-align:center;"|29°
|-
| lead glass
| style="text-align:center;"|30°
|-
| fused quartz
| style="text-align:center;"|33°
|-
| [[mercury (element)|mercury]]
| soda-lime glass
| style="text-align:center;"|140°
|}

Since the forces are in direct proportion to their respective surface tensions, we also have:<ref name="cwp"/>

<math display="block">\gamma_\mathrm{ls} - \gamma_\mathrm{sa} = -\gamma_\mathrm{la} \cos \theta</math>

where
* {{math|''γ''<sub>ls</sub>}} is the liquid–solid surface tension,
* {{math|''γ''<sub>la</sub>}} is the liquid–air surface tension,
* {{math|''γ''<sub>sa</sub>}} is the solid–air surface tension,
* {{mvar|θ}} is the contact angle, where a concave [[Meniscus (liquid)|meniscus]] has contact angle less than 90° and a convex meniscus has contact angle of greater than 90°.<ref name="s_z">Sears, Francis Weston; Zemanski, Mark W. (1955) ''University Physics 2nd ed''. Addison Wesley</ref>

This means that although the difference between the liquid–solid and solid–air surface tension, {{math|''γ''<sub>ls</sub> − ''γ''<sub>sa</sub>}}, is difficult to measure directly, it can be inferred from the liquid–air surface tension, {{math|''γ''<sub>la</sub>}}, and the equilibrium contact angle, {{mvar|θ}}, which is a function of the easily measurable advancing and receding contact angles (see main article [[contact angle]]).

This same relationship exists in the diagram on the right. But in this case we see that because the contact angle is less than 90°, the liquid–solid/solid–air surface tension difference must be negative:

<math display="block">\gamma_\mathrm{la} > 0 > \gamma_\mathrm{ls} - \gamma_\mathrm{sa}</math>

====Special contact angles====
Observe that in the special case of a water–silver interface where the contact angle is equal to 90°, the liquid–solid/solid–air surface tension difference is exactly zero.

Another special case is where the contact angle is exactly 180°. Water with specially prepared [[polytetrafluoroethylene|Teflon]] approaches this.<ref name="cwp"/> Contact angle of 180° occurs when the liquid–solid surface tension is exactly equal to the liquid–air surface tension.

<math display="block">\gamma_\mathrm{la} = \gamma_\mathrm{ls} - \gamma_\mathrm{sa} > 0\qquad \theta = 180^\circ</math>
{{Clear right}}