Why a drop of ink after diffusion in water will not automatically gather?
In everyday life, diffusion is a very common phenomenon. For example, put a drop of black ink into a cup of clean water, ink, and clean water completely mixed after some time. The clear, colorless clear water has turned into slightly stained steam. Or place the opened perfume bottle in a room with closed doors; soon, the smell of perfume spread throughout the room.
Diffusion is caused by the chaotic thermal motion of the molecule. When a small drop of ink enters a clean glass of water, ink molecules first gather at an area’s location, later due to the violent collision movement between the ink molecule and the water molecule. The ink is evenly distributed throughout the space area of the cup. The diffusion of perfume molecules is the same. The diffusion phenomena tell us that the final diffusion is a spontaneous transformation from a relatively ordered state (such as ink and clear water with a certain interface) to a disorder state self (as the two types of matter are completely mixed).
Why is the diffuse regularity still spontaneous from orderly turn into disorder? It turned out that the probability of a state of disorder is numerous. To illustrate this nature of diffusion, let’s assume there is a closed box, the left half of the box contains three gas molecules, the right half has no gas molecule.
Due to the gas molecule’s chaotic movement, the distribution of those three molecules throughout the box has eight types of possibilities. Of these eight types of possibilities, the ordered state of all three molecules is in the left half or the right half only two types; while the relative disorder is one of the three molecules in the left half (or the right part) the other two molecules in the other half have six types. Therefore, in three molecules, the probability of an unordered state is three times the probability of an ordered state. It is clear that the greater the number of molecules, the greater the probability of an evenly distributed state of disorder. The number of molecules contained in a drop of ink or a perfume reaches over a hundred billion. Therefore, when those molecules are diffused, the probability of a uniform distribution is much greater than the probability of gathering to a particular location. That explains why all kinds of diffusion phenomena that we normally observe are ultimately still about the uniform distribution, about the state of disorder.
Theoretically, since it was a chaotic heat movement, there must be a moment when the diffused ink molecules still gather together, restoring the ink droplet shape. But the actual calculations show that the time people wait for this kind of probability to appear greatly exceeds the age of the Universe. Therefore, a drop of ink after diffusing in water, in fact, can not automatically be gathered.