Surface tension is the energy per unit area due to having a surface in a liquid. It has the dimension of force per unit length, or energy per unit area. The two are equivalent, but when referring to energy per unit of area, it is common to use the term surface energy, which is a more general term in the sense that it applies also to solids. Surface tension is used for liquids, while surface stress and surface energy are more commonly used for solids.

An example of its relevance is the tendency of liquid surfaces at rest to shrink to the minimum surface area possible. Because of the relatively high attraction of water molecules to each other through a web of hydrogen bonds, water has a higher surface tension (72.8 millinewtons (mN) per meter at 20 °C) than most other liquids. This allows objects with a higher density than water such as razor blades and insects (e.g. water striders) to float on a water surface without becoming even partly submerged.

The magnitude of the surface tension is connected to the forces between the molecules at the surface. Therefore surfactants are often used to reduce it so there is more contact between the liquid and another material, for instance detergents. It can also lead to pressure inside water bubbles, as well as many other phenomena; it is a classic, well-studied property common to all liquids. Causes

Due to the cohesive forces, a molecule located away from the surface 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 an equal number of molecules on all sides of them and therefore are pulled inward. This creates some internal pressure and forces liquid surfaces to contract to the minimum area.

There is also a tension parallel to the surface at the liquid-air interface which will resist an external force, due to the cohesive forces between the molecules.

The forces of attraction acting between molecules of the same type are called cohesive forces, while those acting between molecules of different types are called adhesive forces. The balance between the cohesion of the liquid and its adhesion to the material of the container determines the degree of wetting, the contact angle, and the shape of the meniscus. When cohesion dominates (specifically, adhesion energy is less than half of cohesion energy) the wetting is low and the meniscus is convex at a vertical wall (as for mercury in a glass container). On the other hand, when adhesion dominates (when adhesion energy is more than half of cohesion energy) the wetting is high and the similar meniscus is concave (as in water in a glass).

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 imbalance in cohesive forces of the surface layer. In the absence of other forces, drops of virtually all liquids would be approximately spherical. The spherical shape minimizes the necessary "wall tension" of the surface layer according to Laplace's law.

Another way to view surface tension is in terms of energy. A molecule in contact with a neighbor is in a lower state of energy than if it were alone. The interior molecules have as many neighbors as they can possibly have, but the boundary molecules are missing neighbors (compared to interior molecules) and therefore have higher energy. For the liquid to minimize its energy state, the number of higher energy boundary molecules must be minimized. The minimized number of boundary molecules results in a minimal surface area. As a result of surface area minimization, a surface will assume a smooth shape.

Physics

Physical units Surface tension, represented by the symbol γ (alternatively σ or T), is measured in force per unit length. Its SI unit is newton per metre but the cgs unit of dyne per centimetre is also used, particularly in the older literature. For example,

Definition

Surface tension can be defined in terms of force or energy.

In terms of force Surface tension of a liquid is the force per unit length. In the illustration on the right, the rectangular frame, composed of three unmovable sides (black) that form a "U" shape, and a fourth movable side (blue) that can slide to the right. Surface tension will pull the blue bar to the left; the force required to hold the movable side is proportional to the length of the mobile side. Thus the ratio depends only on the intrinsic properties of the liquid (composition, temperature, etc.), not on its geometry. For example, if the frame had a more complicated shape, the ratio , with the length of the movable side and the force required to stop it from sliding, is found to be the same for all shapes. We therefore define the surface tension as The reason for the is that the film has two sides (two surfaces), each of which contributes equally to the force; so the force contributed by a single side is .

In terms of energy Surface tension of a liquid is the ratio of the change in the energy of the liquid to the change in the surface area of the liquid (that led to the change in energy). This can be easily related to the previous definition in terms of force: if is the force required to stop the side from starting to slide, then this is also the force that would keep the side in the state of sliding at a constant speed (by Newton's second law). But if the side is moving to the right (in the direction the force is applied), then the surface area of the stretched liquid is increasing while the applied force is doing work on the liquid. This means that increasing the surface area increases the energy of the film. The work done by the force in moving the side by distance is ; at the same time the total area of the film increases by (the factor of 2 is here because the liquid has two sides, two surfaces). Thus, multiplying both the numerator and the denominator of by , we get

This work is, by the usual arguments, interpreted as being stored as potential energy. Consequently, surface tension can be also measured in SI system as joules per square meter and in the cgs system as ergs per cm2. Since mechanical systems try to find a state of minimum potential energy, a free droplet of liquid naturally assumes a spherical shape, which has the minimum surface area for a given volume as first pointed out by Gibbs.Josiah Willard Gibbs (1928). Collected Works, Longmans, Green & Co. The equivalence of measurement of energy per unit area to force per unit length can be proven by dimensional analysis.

Effects

Water Several effects of surface tension can be seen with ordinary water:

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). Surfactants actually reduce the surface tension of water by a factor of three or more. Emulsions are a type of colloidal dispersion in which surface tension plays a role. Tiny droplets of oil dispersed in pure water will spontaneously coalesce and phase separate. The addition of surfactants reduces the interfacial tension and allow for the formation of oil droplets in the water medium (or vice versa). The stability of such formed oil droplets depends on many different chemical and environmental factors.

Surface curvature and pressure

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:

where: is the pressure difference, known as the Laplace pressure. is surface tension. and are 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.)

+ for water drops of different radii at STP Droplet radius 1 mm 0.1 mm 1 μm 10 nm (atm) 0.0014 0.0144 1.436 143.6

Floating objects

When an object is placed on a liquid, its weight depresses the surface, and if surface tension and downward force become equal then it is balanced by the surface tension forces on either side , which are each parallel to the water's surface at the points where it contacts the object. Notice that small movement in the body may cause the object to sink. As the angle of contact decreases, surface tension decreases. The horizontal components of the two arrows point in opposite directions, so they cancel each other, but the vertical components point in the same direction and therefore add up to balance . The object's surface must not be wettable for this to happen, and its weight must be low enough for the surface tension to support it. If denotes the mass of the needle and acceleration due to gravity, we have

Liquid surface

To find the shape of the minimal surface bounded by some arbitrary shaped frame using strictly mathematical means can be a daunting task. Yet by fashioning the frame out of wire and dipping it in soap-solution, a locally minimal surface will appear in the resulting soap-film within seconds.Aaronson, Scott (March 2005) NP-complete Problems and Physical Reality . ACM SIGACT News

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.In a mercury barometer, the upper liquid surface is an interface between the liquid and a vacuum containing some molecules of evaporated liquid. 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.