Water tends to form beads or drops. This ability of water molecules to stick together, a property known as surface tension, is due to the mutual attraction of water molecules. One side of each water molecule has a slight positive charge; the other side has a slight negative charge. The attraction of two molecules is maintained by a hydrogen bond. The high surface tension of water forms a kind of ”skin” on the top of water. Lightweight insects such as water striders can scoot across the water’s surface without sinking. I am going to elaborate surface tension below.
The surface of any liquid behaves as though it is covered by a stretched membrane. Small insects can walk on water without getting wet. The membrane is obviously quite strong: it will support dense objects, provided they are small and of the right shape – a needle, a small square of aluminium sheet, a razor blade, a container made of fine wire gauze and small insects. The strength of the surface membrane can be imagined to arise from a set of forces acting on each point of the surface, parallel to the surface, like the skin of a drum. These cohesive forces act between molecules of the substance without chemical bonding.
This tension of surfaces can be understood in terms of forces between molecules. Molecules repel each other when close, attract each other when farther away and at some in-between distance neither repel not attract. Inside a liquid, the molecules on the average usually repel each other slightly, just enough to counteract the pressure applied by the surroundings to the liquid. But molecules at the surface are farther apart than the neutral distance, and attract each other. This attraction, or surface tension, is necessary if surface molecules are to be kept from moving from the surface into bulk liquid.
Since all phenomena in mechanics can be explained in terms of either forces or energies, the predictions one makes about surfaces are the same whether one starts with the concept of surface tension or surface energy. Surface energy results from surface molecules’ having more energy than molecules in the bulk liquid; they have had, in effect, half their neighbours removed from them. Dimensionally, surface tension, often expressed as dynes-per-centimetre, is the same as surface energy, which is often expressed as ergs per square centimetre (erg/cm2 = dyne cm/cm2 = dyne/cm).
Magnitude of surface tension
Surface tension boundary conditions
Since surfaces exert forces, they force liquids into shapes and motions that differ from what they would be in the absence of surface tension. The effects can be summarised by three general rules:
- Contact angles. Where surfaces meet, the contact angle is determined by the energies of the interfaces,
- Pressures caused by curved surfaces. A curved liquid surface has higher pressure on the concave side:
- Shear forces caused by surface tension gradients. Variation of surface tension along a surface is balanced by shear forces in the bounding materials:
σ is surface tension, and R1 and R2 are the two radii of curvature necessary to specify curvature at a point on a surface.
These three statements describe the boundary conditions that surface tension imposes on liquids and, together with the equations for fluid mechanics, are sufficient to determine the shapes and motions. All but a few simple cases, however, are difficult to solve mathematically. Free-surface boundaries introduce mathematical complexity even into cases that look as though they should be very simple, such as a static hanging drop.
We have seen that surface tension arises because of the intermolecular forces of attraction that molecules in a liquid exert on one another. These forces, which are between like molecules, are called cohesive forces. A liquid, however, is often in contact with a solid surface, such as glass. Then additional forces of attraction come into play. They occur between molecules of the liquid and molecules of the solid of the solid surface and, being between unlike molecules, are called adhesive forces.
When can we disregard the influence of gravity on the shape of a raindrop? Consider a spherical raindrop of radius R falling steadily throughout the air with its weight being balanced by air drag. Since the drag force balances gravity, the condition must be that the variation in hydrostatic pressure inside the drop should be negligible compared to the pressure excess, due to surface tension.
The capillary length equals 2.7 mm for the air-water interface at 25° C. Falling raindrops are deformed by the interaction with the air and never take the familiar teardrop shape with a pointed top and rounded bottom, so often used in drawings – and even by some national meteorology offices.
References & Resources
- Boys, C. V., Soap Bubbles, 1890. Reprinted by Doubleday & Company, Inc. 1959, and by Dover Publishing Co., 1959.
- Adam, N. K., Physics and Chemistry of Surfaces, Oxford University Press, 1941.
- Levich, V. G., Psychochemical Hydrodynamics, Prentice-Hall, 1962.
- Contact Angle, Wettability and Adhesion, Advances in Chemistry No. 43, American Chemical Soc., 1964.
- Prandtl, L., Essentials of Fluid Dynamics, Hafner, 1952.
- Image and information via Haber. H., Surface Tension, University of California, Santa Cruz. Retrieved from:
- Surface Tension, Center for Nonlinear Science, Georgia Institute of Technology, Lautrup B., 1998.
- Slider image via Wikimedia Commons. Retrieved from: