Quick Surface tension is abbreviated by σs. The effect of surface tension is also called surface energy.
Details
It is often observed that a drop of blood forms a hump on a horizontal glass; a drop of mercury forms a near-perfect sphere and can be rolled just like a steel ball over a smooth surface; water droplets from rain or dew hang from branches or leaves of trees; water droplets from rain or dew hang from branches or leaves of trees; a liquid fuel injected into an engine forms a mist of spherical droplets; water dripping from a leaky faucet falls as spherical droplets; a soap bubble released into the air forms a spherical shape; and water beads up into small drops on flower petals. Some insects can land on water or even walk on water and that small steel needles can float on water. These phenomena are made possible by surface tension that balances the weights of these objects.
In these and other observances, liquid droplets behave like small spherical balloons filled with the liquid, and the surface of the liquid acts like a stretched elastic membrane under tension. The pulling force that causes this tension acts parallel to the surface and is due to the attractive forces between the molecules of the liquid. The magnitude of this force per unit is called surface tension σs and is usually expressed in the unit N/m (or lbf/ft in English units). This effect is also called surface energy and is expressed in the equivalent unit of Nm/m2 or J/m2. In this case, σs represents the stretching work that needs to be done to increase the surface area of the liquid by a unit amount.
To visualize how surface tension arises, we present a microscopic view in the figure by considering two liquid molecules, one at the surface and one deep within the liquid body. The attractive forces applied on the interior molecule by the surrounding molecules balance each other because of symmetry. But the attractive forces acting on the surface molecule are not symmetric, and the attractive forces applied by the gas molecules above are usually very small. Therefore, there is a net attractive force acting on the molecule at the surface of the liquid, which tends to pull the molecules on the surface toward the interior of the liquid. This force is balanced by the repulsive forces from the molecules below the surface that are being compressed. The resulting compression effect causes the liquid to minimize its surface area. This is the reason for the tendency of the liquid droplets to attain a spherical shape, which has the minimum surface area for a given volume.
To understand the surface tension effect better, consider a liquid film (such as the film of a soap bubble) suspended on a U-shaped wire frame with a movable side as shown. Normally, the liquid film tends to pull the movable wire inward in order to minimize its surface area. A forceF needs to be applied on the movable wire in the opposite direction to balance this pulling effect. The thin film in the device has two surfaces (the top and bottom surfaces) exposed to air, and thus the length along which the tension acts in this case is 2b. Then a force balance on the movable wire gives F = 2bσs, and thus the surface tension can be expressed as:
σs =
F
2b
Note that for b = 0.5 m, the force F measured (in N) is simply the surface tension in N/m. An apparatus of this kind with sufficient precision can be used to measure the surface tension of various fluids.
In the U-shaped wire, the force F remains constant as the movable wire is pulled to stretch the film and increase its surface area. When the movable wire is pulled a distance Δx, the surface area increases by ΔA = 2b Δx, and the workW done during this stretching process is:
W = force × distance = F Δx = 2bσs Δx = σs ΔA
since the force remains constant in this case. This result can also be interpreted as the surface energy of the film is increased by an amount σs ΔA during this stretching process, which is consistent with the alternative interpretation of σs as surface energy. This is similar to a rubber band having more potential (elastic) energy after it is stretched further. In the case of liquid film, the work is used to move liquid molecules from the interior parts to the surface against the attraction forces of other molecules. Therefore, surface tension also can be defined as the work done per unit increase in the surface area of the liquid.
The surface tension varies greatly from substance to substance, and with temperature for a given substance as shown here, for example, the surface tension is 0.073 N/m for water and 0.440 N/m for mercury surrounded by atmospheric air. Mercury droplets form spherical balls that can be rolled like a solid ball on a surface without wetting the surface. The surface tension of a liquid, in general, decreases with temperature and becomes zero at the critical point (and thus there is no distinct liquid–vapor interface at temperatures above the critical point). The effect of pressure on surface tension is usually negligible.
Impurities
The surface tension of a substance can be changed considerably by impurities. Therefore, certain chemicals, called surfactants, can be added to a liquid to decrease its surface tension. For example, soaps and detergents lower the surface tension of water and enable it to penetrate through the small openings between fibers for more effective washing. But this also means that devices whose operation depends on surface tension (such as heat pipes) can be destroyed by the presence of impurities due to poor workmanship.
Surface tension is spoken of for liquids only at liquid–liquid or liquid–gas interfaces. Therefore, it is important to specify the adjacent liquid or gas when specifying surface tension. Also, surface tension determines the size of the liquid droplets that form. A droplet that keeps growing by the addition of more mass will break down when the surface tension can no longer hold it together. This is like a balloon that will burst while being inflated when the pressure inside rises above the strength of the balloon material.
A curved interface indicates a pressure difference (or "pressure jump") across the interface with pressure being higher on the concave side. The excess pressure ΔP inside a droplet or bubble above the atmospheric pressure, for example, can be determined by considering the free-body diagram of half a droplet or bubble. Noting that surface tension acts along the circumference and the pressure acts on the area, horizontal force balances for the droplet and the bubble give:
For a droplet:
(2πR)σs = (πR 2)ΔPdroplet → ΔPdroplet = Pi − Po =
2σs
R
For a bubble:
2(2πR)σs = (πR 2)ΔPbubble → ΔPbubble = Pi − Po =
4σs
R
where Pi and Po are the pressures inside and outside the droplet or bubble, respectively. When the droplet or bubble is in the atmosphere, Po is simiply atmospheric pressure. The factor 2 in the force balance for the bubble is due to the bubble consisting of a film with two surfaces (inner and outer surfaces) and thus two circumferences in the cross section.
The excess pressure in a droplet (or bubble) also can be determined by considering a differential increase in the radius of the droplet due to the addition of a differential amount of mass and interpreting the surface tension as the increase in the surface energy per unit area. Then the increase in the surface energy of the droplet during this differential expansion process becomes:
δWsurface = σs dA = σs d(4πR 2) = 8πRσs dR
The expansion work done during this differential process is determined by multiplying the force by distance to obtain:
δWexpansion = Force × Distance = F dR = (ΔPA) dR = 4πR 2 ΔP dR
Equating the two expressions above gives ΔPdroplet = 2σs/R, which is the same relation obtained before and given in the equation for a droplet above. Note that the excess pressure in a droplet or bubble is inversely proportional to the radius.