Kinetic particle theory and surface phenomena

Dip the edge of a paper towel into water. The wet patch creeps upwards even though gravity pulls the water down. What lifts the water, and why will it eventually stop rising?

Remember: a gas is easy to compress, but water is not. Water flows, whereas ice keeps its shape. One model connects these observations: matter consists of particles that move continuously and attract and repel one another. These are the three main ideas of kinetic particle theory. In a liquid, particles are close together but change neighbours. To explain the shape of water, we therefore need both particle motion and particle interactions.

Why is a small, freely falling drop almost spherical? Particles at the surface have different surroundings from those inside. Creating more surface takes energy, so a liquid tends to reduce its surface area while keeping the same volume. A sphere has the smallest area for that volume. This is an effect of surface tension. The model applies when gravity and other external effects distort the drop only slightly: gravity noticeably flattens a large drop resting on a table.

Now place equal drops on clean glass and on wax. Water spreads out more on the glass and beads up on the wax. This spreading is called wetting. Contact changes the interfaces between the liquid, solid and air; the final shape depends on interactions at all these interfaces. So water is not simply a liquid that “wets everything”: the material, cleanliness and condition of the surface matter.

Look closely at water beside the wall of a glass: the surface rises at the edge. This curved surface is called a meniscus. Water wets clean glass, and surface forces hold the curve against gravity. With a non-wetting liquid, the edge dips instead. The meniscus shape therefore gives a clue to whether the level will rise or fall in a narrow tube.

Place a narrow, clean glass tube in water. Surface forces at its wall have a net upward component that lifts the liquid. As the column grows, however, its mass and weight increase. The rise stops when the weight balances the surface force. The rise or fall of liquid in narrow channels is called capillary action. Equilibrium does not stop the thermal motion of individual particles.

Why does water rise higher in a narrower tube? Halving the radius halves the length of the boundary at the wall, but reduces the column's cross-sectional area to one quarter. The surface force decreases less than the weight of a column of the original height, so balance is reached higher up. The height h, measured in metres, is the vertical difference between the levels in the tube and the wide container. This comparison requires the same liquid, wetting conditions and temperature.

A paper towel replaces a single tube with many winding, narrow gaps between fibres. If water wets the fibres, it spreads through these channels, including upwards. This explains our first observation and part of the movement of water through porous soil. Capillary action also plays a part in plants, but a single-tube model cannot explain a tall tree: evaporation from the leaves and continuous columns of water are also essential.

Two clean glass tubes are dipped into the same water. One has half the radius of the other. In which tube will the water be higher at equilibrium?

Both tubes contain the same water and have clean glass walls. We compare only their radii, keeping temperature and wetting conditions unchanged.

In the tube with half the radius, the boundary at the wall is half as long and the column's cross-sectional area is one quarter as large. The surface force is therefore greater relative to the weight of a column of the same height.

The water must rise higher in the narrow tube for its weight to balance this force. For ideal narrow, circular capillaries, the height is inversely proportional to the radius.

The water rises higher in the narrower tube: its smaller weight per unit height allows a taller column to be supported.

Drops and menisci take their shape because particles interact and the liquid tends to reduce its surface energy.

Wetting depends on the combination of liquid and surface; contamination can change the result.

Water rises in a capillary until surface forces and weight balance. This does not violate conservation of energy.

Thermal motion depends on temperature. Next we will distinguish temperature from an object's total internal energy.