Two liquids

There are two liquids, with different colours in the container. They cannot mix and their densities differ considerably. The coloured liquid is denser than the transparent one. Even if the liquids are stirred violently they do not intermingle. As a result, small balls form, but after a while they blend with the corresponding liquid.

The slow sloshing of the blue liquid is caused by the presence of the transparent liquid above it; the disturbance of the bottom liquid churns the top one. The surface of the top liquid, with air above it, sloshes in a regular manner, while the bottom liquid does not take part in this movement.

The wavy movement at the border of two liquids can explain the problems that Norwegian fishermen experience in spring. According to local folk tales, some elves awake in spring and hamper rowing so that boats do not move as fast as they usually do. In reality, a layer of fresh water of about fifteen centimetres forms on the surface of the sea as snow melts. Rowing in such a layer of light water sloshes the heavier salty water below and the boat does not move forward as fast as it is supposed to.

The waves disturbing the balance of stagnant water surface, which are formed following the impact of some outside forces, have somehow double character:


1) Gravitational, for waves created on water surface by gravitational forces, the velocity v of λ wavelength wave propagation can be calculated from the following formula:

, (1)

where g is the gravitational acceleration.

2)Capillary one, in which surface tension forces σ perform a significant function. For such waves their velocity is described by the following equation:

, (2)

in which ρ stands for the density of liquid.

Generally the velocity of capillary-gravitational waves propagation is described by this equation:

, (3)

However, this is not everything, on the boundary between two liquids, which do not mix and which have different density, waves are also formed, as the film shows. To describe the velocity of their propagation we can employ the 3rd equation, with a slight modification concerning the differences in density:

, (4)

The above analysis have been plotted on the graph showing the relation between propagation of velocity of waves and their length for gravitational waves (green line), for capillary waves (blue line), for capillary-gravitational waves (red line) and on the boundary between two liquids: oil-water (yellow line). As the graph shows, within short waves, the band capillary waves perform the main role, within long waves band - the main role is performed by gravitational waves. The waves within 0.1 do 10 cm band are of a mixed character.

The very slow rise and small absolute values of the yellow graphs for oil-water liquid explains why pouring oil on the wavy surface of the sea water calms it.