Abstract:

Diffusion is a process in which particles (atoms, molecules) spontaneously disperse in space – from areas of higher concentration to areas of lower concentration. It is used in many sectors, such as in technical fields (desalination, gas dilution), pharmacology (pharmacokinetics), or medicine (transport of drugs and pollutants).

Diffusion is usually experimentally demonstrated in high schools by dropping ink or food colorant into a glass of water. Unfortunately, in this experiment, diffusion is not the main cause of the mixing. The water molecules on the surface evaporate and this cools down the water that is closer to the surface. Colder water is denser, so it begins to move downwards. This creates a flow that is largely responsible for mixing the water and dye. Unlike diffusion, this process is relatively fast, and the water in the container is usually completely colored with ink within a few ten of minutes. On the other hand, it takes days or even weeks to diffusion to mix well the two liquids, depending on the sample size. It is possible to observe both the fast flow-caused mixing of the liquids and the slow diffusion by using the time-lapse video while exposing the sample to different conditions. In this way, one can distinguish different phenomena causing the mixing of liquids. In the article, we show what must be avoided during diffusion experiments, what one should watch out for, and how it is possible to quantitatively describe diffusion using a very simple experiment with a laser.

The experiment is based on the refraction of laser light in the medium. If two liquids have different refractive indices and begin to mix due to diffusion, each vertical position in the container will have a different refractive index - a gradient is created. We can measure the index of refraction using a light beam incident perpendicularly on the sample. If we measure the refraction for different heights in the sample and repeat this experiment at different times, we can see how the refractive index of each vertical position changes as the diffusion progresses. The refractive index, therefore, depends on the vertical position, or in other words on the height at which the beam enters the sample. To make our work easier, we will not move the light beam up or down, but we will spread it in a section of the plane so that it passes through the sample at an angle of 45°. It will therefore have a different height at each x-position. We then observe the curved line profile on the screen behind the sample. The deviation from a straight line decreases with the time (and thus diffusion) progression. Both the data we measured and the script which was used for the analysis are available online.

When analyzing this experiment, it is necessary to combine knowledge from computer science, mathematics, and physics. Given that relatively little space is usually devoted to diffusion in secondary schools and that students often do not understand this topic sufficiently, the described experiment is suitable for supplementing this knowledge.

Keywords:

Diffusion, laser.