Surface tension

**Surface tension** is an effect where the surface of a liquid is strong. The surface can hold up a weight, and the surface of a water droplet holds the droplet together, in a ball shape. Some small things can float on a surface because of surface tension, even though they normally could not float. Some insects (e.g. water striders) can run on the surface of water because of this. This property is caused by the molecules in the liquid being attracted to each other (cohesion), and is responsible for many of the behaviors of liquids.

Surface tension has the dimension of force per unit length, or of energy per unit area. The two are equivalent—but when referring to energy per unit of area, people use the term surface energy—which is a more general term in the sense that it applies also to solids and not just liquids.

In materials science, surface tension is used for either surface stress or surface free energy.

## Causes
The cohesive forces among the liquid molecules cause surface tension. In the bulk of the liquid, each molecule is pulled equally in every direction by neighboring liquid molecules, resulting in a net force of zero. The molecules at the surface do not have other molecules on all sides of them and therefore are pulled inwards. This creates some internal pressure and forces liquid surfaces to contract to the minimal area.

Surface tension is responsible for the shape of liquid droplets. Although easily deformed, droplets of water tend to be pulled into a spherical shape by the cohesive forces of the surface layer. In the absence of other forces, including gravity, drops of virtually all liquids would be perfectly spherical. The spherical shape minimizes the necessary "wall tension" of the surface layer according to Laplace's law.

Another way to view it is in terms of energy. A molecule in contact with a neighbor is in a lower state of energy than if it were alone (not in contact with a neighbor). The interior molecules have as many neighbors as they can possibly have, but the boundary molecules are missing neighbors (compared to interior molecules). So, the boundary molecules have a higher energy. For the liquid to minimize its energy state, the number of higher energy boundary molecules must be minimized. The minimized quantity of boundary molecules results in a minimized surface area.

As a result of surface area minimization, a surface will assume the smoothest shape it can. Any curvature in the surface shape results in greater area and a higher energy. So, the surface will push back against any curvature in much the same way as a ball pushed uphill will push back to minimize its gravitational potential energy.

## Effects in everyday life
### Water
Studying water shows several effects of surface tension:

**A**. Rain water forms beads on the surface of a waxy surface, such as a leaf. Water adheres weakly to wax and strongly to itself, so water clusters into drops. Surface tension gives them their near-spherical shape, because a sphere has the smallest possible surface area to volume ratio.

**B**. Formation of drops occurs when a mass of liquid is stretched. The animation shows water adhering to the faucet gaining mass until it is stretched to a point where the surface tension can no longer bind it to the faucet. It then separates and surface tension forms the drop into a sphere. If a stream of water were running from the faucet, the stream would break up into drops during its fall. Gravity stretches the stream, then surface tension pinches it into spheres.

**C**. Objects denser than water still float when the object is nonwettable and its weight is small enough to be borne by the forces arising from surface tension.

**D**. Separation of oil and water (in this case, water and liquid wax) is caused by a tension in the surface between dissimilar liquids. This type of surface tension is called "interface tension", but its physics are the same.

**E**. Tears of wine is the formation of drops and rivulets on the side of a glass containing an alcoholic beverage. Its cause is a complex interaction between the differing surface tensions of water and ethanol. It is induced by a combination of surface tension modification of water by ethanol together with ethanol evaporating faster than water.

Image:Dew 2.jpg|**A.** Water beading on a leaf
Image:Water drop animation enhanced small.gif|**B.** Water dripping from a tap
File:WaterstriderEnWiki.jpg|**C.** Water striders stay atop the liquid because of surface tension
File:1990s Mathmos Astro.jpg|**D.** Lava lamp with interaction between dissimilar liquids; water and liquid wax
Image:Wine legs shadow.jpg|**E.** Photo showing the "tears of wine" phenomenon.

### Surfactants
Surface tension is visible in other common phenomena, especially when surfactants are used to decrease it:

* Soap bubbles have very large surface areas with very little mass. Bubbles in pure water are unstable. The addition of surfactants, however, can have a stabilizing effect on the bubbles (see Marangoni effect). Notice that surfactants actually reduce the surface tension of water by a factor of three or more.
* Emulsions are a type of solution in which surface tension plays a role. Tiny fragments of oil suspended in pure water will spontaneously assemble themselves into much larger masses. But the presence of a surfactant provides a decrease in surface tension, which permits stability of minute droplets of oil in the bulk of water (or vice versa).

## Basic physics
### Two definitions
, is work done per unit area. As such, in order to increase the surface area of a mass of liquid by an amount, *δA*, a quantity of work, *\scriptstyle\gammaδA*, is needed.

The reason for this is that the pressure difference across a fluid interface is proportional to the mean curvature, as seen in the Young-Laplace equation. For an open soap film, the pressure difference is zero, hence the mean curvature is zero, and minimal surfaces have the property of zero mean curvature.

### Contact angles
The surface of any liquid is an interface between that liquid and some other medium. 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. Where the two surfaces meet, the geometry will balance all forces.

This means that although the difference between the liquid-solid and solid-air surface tension, \scriptstyle \gamma_\mathrm{ls} - \gamma_\mathrm{sa}, is difficult to measure directly, it can be inferred from the liquid-air surface tension, \scriptstyle \gamma_\mathrm{la}, and the equilibrium contact angle, \scriptstyle \theta, 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:

:\gamma_\mathrm{la}\ >\ 0\ >\ \gamma_\mathrm{ls} - \gamma_\mathrm{sa}

#### 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 Teflon approaches this.
* Du Noüy-Padday method: A minimized version of Du Noüy method uses a small diameter metal needle instead of a ring, in combination with a high sensitivity microbalance to record maximum pull. The advantage of this method is that very small sample volumes (down to few tens of microliters) can be measured with very high precision, without the need to correct for buoyancy (for a needle or rather, rod, with proper geometry). Further, the measurement can be performed very quickly, minimally in about 20 seconds. First commercial multichannel tensiometers [CMCeeker] were recently built based on this principle.
* Wilhelmy plate method: A universal method especially suited to check surface tension over long time intervals. A vertical plate of known perimeter is attached to a balance, and the force due to wetting is measured.
* Spinning drop method: This technique is ideal for measuring low interfacial tensions. The diameter of a drop within a heavy phase is measured while both are rotated.
* Pendant drop method: Surface and interfacial tension can be measured by this technique, even at elevated temperatures and pressures. Geometry of a drop is analyzed optically. For details, see Drop.
* Capillary rise method: The end of a capillary is immersed into the solution. The height at which the solution reaches inside the capillary is related to the surface tension by the equation discussed below.
* Stalagmometric method: A method of weighting and reading a drop of liquid.
* Sessile drop method: A method for determining surface tension and density by placing a drop on a substrate and measuring the contact angle (see Sessile drop technique).
* Vibrational frequency of levitated drops: The surface tension of superfluid 4He has been measured by studying the natural frequency of vibrational oscillations of drops held in the air by magnetics. This value is estimated to be 0.375 dyn/cm at T = 0° K.

## Effects
### Liquid in a vertical tube
An old style mercury barometer consists of a vertical glass tube about 1&nbsp;cm in diameter partially filled with mercury, and with a vacuum (called Torricelli's vacuum) in the unfilled volume (see diagram to the right). Notice that the mercury level at the center of the tube is higher than at the edges, making the upper surface of the mercury dome-shaped. The center of mass of the entire column of mercury would be slightly lower if the top surface of the mercury were flat over the entire crossection of the tube. But the dome-shaped top gives slightly less surface area to the entire mass of mercury. Again the two effects combine to minimize the total potential energy. Such a surface shape is known as a convex meniscus.

We consider the surface area of the entire mass of mercury, including the part of the surface that is in contact with the glass, because mercury does not adhere at all to glass. So the surface tension of the mercury acts over its entire surface area, including where it is in contact with the glass. If instead of glass, the tube were made out of copper, the situation would be very different. Mercury aggressively adheres to copper. So in a copper tube, the level of mercury at the center of the tube will be lower than at the edges (that is, it would be a concave meniscus). In a situation where the liquid adheres to the walls of its container, we consider the part of the fluid's surface area that is in contact with the container to have *negative* surface tension. The fluid then works to maximize the contact surface area. So in this case increasing the area in contact with the container decreases rather than increases the potential energy. That decrease is enough to compensate for the increased potential energy associated with lifting the fluid near the walls of the container.

If a tube is sufficiently narrow and the liquid adhesion to its walls is sufficiently strong, surface tension can draw liquid up the tube in a phenomenon known as capillary action. The height the column is lifted to is given by:

::h\ =\ 2 \sqrt{\frac{\gamma} {g\rho}}

where

:

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:

::h\ =\ \sqrt{\frac{2\gamma_\mathrm{la}\left( 1 - \cos \theta \right)} {g\rho}}.

For mercury on glass, γHg = 487 dyn/cm, ρHg = 13.5 g/cm3 and θ = 140°, which gives hHg = 0.36&nbsp;cm. For water on paraffin at 25&nbsp;°C, γ = 72 dyn/cm, ρ = 1.0 g/cm3, and θ = 107° which gives hH2O = 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.

### The breakup of streams into drops
In day-to-day life we all observe that a stream of water emerging from a faucet will break up into droplets, no matter how smoothly the stream is emitted from the faucet. This is due to a phenomenon called the Plateau–Rayleigh instability, which is entirely a consequence of the effects of surface tension.

The explanation of this instability begins with the existence of tiny perturbations in the stream. These are always present, no matter how smooth the stream is. If the perturbations are resolved into sinusoidal components, we find that some components grow with time while others decay with time. Among those that grow with time, some grow at faster rates than others. Whether a component decays or grows, and how fast it grows is entirely a function of its wave number (a measure of how many peaks and troughs per centimeter) and the radii of the original cylindrical stream.

## Data table
## Gallery of effects

Image:UnstableLiquidSheet.jpg|Breakup of a moving sheet of water bouncing off of a spoon.
Image:SurfaceTension.jpg|Photo of flowing water adhering to a hand. Surface tension creates the sheet of water between the flow and the hand.
Image:Ggb in soap bubble 1.jpg|A soap bubble balances surface tension forces against internal pneumatic pressure.
Image:2006-01-15 coin on water.jpg|Surface tension prevents a coin from sinking: the coin is indisputably denser than water, so it must be displacing a volume greater than its own for buoyancy to balance mass.
Image:Dscn3156-daisy-water 1200x900.jpg|A daisy. The entirety of the flower lies below the level of the (undisturbed) free surface. The water rises smoothly around its edge. Surface tension prevents water filling the air between the petals and possibly submerging the flower.
Image:Surface Tension 01.jpg|A metal paper clip floats on water. Several can usually be carefully added without overflow of water.
Image:3_Moeda_(5).jpg|An aluminium coin floats on the surface of the water at 10&nbsp;°C. Any extra weight would drop the coin to the bottom.

## Notes
## References
## Other websites
* On surface tension and interesting real-world cases
* MIT Lecture Notes on Surface Tension 
* Surface Tensions of Various Liquids
* Calculation of temperature-dependent surface tensions for some common components 
* Surface Tension Calculator For Aqueous Solutions  Containing the Ions H+, NH4+, Na+, K+, Mg2+, Ca2+, SO42–, NO3–, Cl–, CO32–, Br– and OH–.
* The Bubble Wall (Audio slideshow from the National High Magnetic Field Laboratory explaining cohesion, surface tension and hydrogen bonds)