# Surface Tension

## Surface tension is a contractive tendency of the surface of a liquid that allows it to resist an external force.

#### Key Points

• Surface tension is responsible for the curvature of the surfaces of air and liquids.

• Surface tension is responsible for the ability of some solid objects to "float" on the surface of a liquid.

• Surface tension is responsible for the shape of the interface between two immiscible liquids.

#### Terms

• force transmitted through a rope, string, cable, or similar object (used with prepositions on, in, or of, e.g., "The tension in the cable is 1000 N", to convey that the same magnitude of force applies to objects attached to both ends)

• the shape of something curved

• a quantity that denotes the ability to do work and is measured in a unit dimensioned in mass × distance²/time² (ML²/T²) or the equivalent

• a contractive tendency of the surface of a liquid that allows it to resist an external force

#### Figures

1. ##### Diagram of Forces on Molecules in a Liquid

In the bulk of the liquid, the forces are the same in all directions, while at the surface, the net effect is "downward," into the interior.

2. ##### Resolution of Forces on a "Floating Needle"

The mass of a needle is supported by the surface tension of the liquid, with the force of the weight of the needle being balanced by the surface tension effects, Fs. Note that the forces from the surface tension are symmetrical.

3. ##### Tabulated Surface Tensions of Selected Liquids

The surface tensions of a few common liquids and solutions

## Surface Tension

This section will investigate a fundamental property of liquids: surface tension. Liquids and solids share a common attribute: a clear and discernible phase boundary that gives the sample a simple but definite shape. Liquids and solids share something else, too: most of their molecular units are in some degree of direct contact. At the same time, however, liquids, like gases, are fluids, meaning that their molecular units can move more or less independently of each other. But whereas the volume of a gas depends entirely on the pressure (and thus generally on the volume within which it is confined), the volume of a liquid is largely independent of the pressure.

The molecules of a liquid that find themselves fully in the interior volume are at a lower energy than those that are at the interface, as shown in Figure 1.

Surface tension is responsible for the shape of a liquid droplet. 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. If no force acts normal (perpendicular) 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 the surface area results in a normal force. In order for the surface tension forces to cancel out this force due to pressure, the surface must be curved. When all the forces are balanced, the curvature of the surface is a good measure of the surface tension, which is descibed by the Young-Laplace equation:

$\Delta P = \gamma \left (\frac{1}{R_{x}}+\frac{1}{R_{y}} \right )$

where P is the pressure differential across the interface, $\gamma$ is the measured surface tension, and Rn is the radius in a given direction along the surface.

This equation describes the shape and curvature of water bubbles and puddles, the "footprints" of water-walking insects, and the phenomenon of a needle floating on the surface of water, as shown in Figure 2. Even though the needle is denser than water, it floats because surface tension is a contractive tendency of the surface of a liquid that allows it to resist an external force. This property is caused by cohesion of similar molecules and is responsible for many of the behaviors of liquids.

In imagining the shape of a liquid droplet or the curvature of the surface of a liquid, one must keep in mind that the molecules at the surface are at a different level of potential energy than are those of the interior. That is to say, there is an energy difference between the interior and the surface: to move a molecule from the interior to the surface requires energy. The object of the "game" is for a droplet or surface to form that minimizes the energy at the surface. Again, since the energy at the surface is due in large part to the attractive forces between particles in the bulk and those in the interior, the surface tension is an indicator of the extent of those forces. Different liquids and solutions have different surface tensions, as seen in Figure 3.

Surface tension is expressed in units of force per unit length, or of energy per unit area. The two are equivalent, but when referring to energy per unit area, people use the term "surface energy," which is a more general term in the sense that it applies to solids as well as to liquids.

#### Key Term Glossary

curvature
the shape of something curved
##### Appears in these related concepts:
energy
a quantity that denotes the ability to do work and is measured in a unit dimensioned in mass × distance²/time² (ML²/T²) or the equivalent
##### Appears in these related concepts:
gas
Matter in a state intermediate between liquid and plasma that can be contained only if it is fully surrounded by a solid (or held together by gravitational pull); it can condense into a liquid, or can (rarely) become a solid directly.
##### Appears in these related concepts:
indicator
a halochromic chemical compound that is added in small amounts to a solution so that the pH (acidity or basicity) of the solution can be determined visually
##### Appears in these related concepts:
liquid
A substance that flows and keeps no definite shape, such as water. A substance whose molecules, while not tending to separate from one another like those of a gas, readily change their relative position, and which therefore retains no definite shape, except that determined by the containing receptacle; an inelastic fluid.
##### Appears in these related concepts:
molecule
the smallest particle of a specific element or compound that retains the chemical properties of that element or compound; two or more atoms held together by chemical bonds
##### Appears in these related concepts:
phase
Any one point or portion in a recurring series of changes, as in the changes of motion of one of the particles constituting a wave or vibration; one portion of a series of such changes, in distinction from a contrasted portion, as the portion on one side of a position of equilibrium, in contrast with that on the opposite side.
##### Appears in these related concepts:
phase boundary
the line in a phase diagram that indicates the conditions under which multiple states of matter exist at equilibrium
##### Appears in these related concepts:
potential energy
the energy possessed by an object because of its position (in a gravitational or electric field), or its condition (as a stretched or compressed spring, as a chemical reactant, or by having rest mass)
##### Appears in these related concepts:
Pressure
the amount of force that is applied over a given area divided by the size of this area
##### Appears in these related concepts:
A line segment between any point on the circumference of a circle and its center/centre.
##### Appears in these related concepts:
solid
A substance in the fundamental state of matter that retains its size and shape without need of a container (as opposed to a liquid or gas).
##### Appears in these related concepts:
solution
A homogeneous mixture, which may be liquid, gas or solid, formed by dissolving one or more substances.
##### Appears in these related concepts:
Solution
A homogeneous mixture, which may be liquid, gas or solid, formed by dissolving one or more substances.
##### Appears in these related concepts:
surface tension
a contractive tendency of the surface of a liquid that allows it to resist an external force
##### Appears in these related concepts:
tension
force transmitted through a rope, string, cable, or similar object (used with prepositions on, in, or of, e.g., "The tension in the cable is 1000 N", to convey that the same magnitude of force applies to objects attached to both ends)
##### Appears in these related concepts:
volume
A unit of three-dimensional measure of space that comprises a length, a width, and a height. It is measured in units of cubic centimeters in metric, or cubic inches or cubic feet in English measurement.