Why do materials tend to move from an area of high concentration to low concentration?

Answer 1

In one word, diffusion.

But that raises the question, why does diffusion happen? Imagine that all atoms, ions, and molecules are balls (billiard balls, baseballs - whatever takes your fancy) flying about a vast room (representing the container) in three dimensions. The balls are tiny compared to the space between them.

They are always traveling in straight lines until they hit something, either the side of the container or another ball. In a collision a ball rebounds at the appropriate angle and continues in a new straight line.

Now, to simulate a high concentration of a substance we need a lot of molecules of that substance in one corner of the room. Think of them as a cluster of yellow balls. All the other substances are gray, so we can easily see what is happening to our substance. Yellow balls that bounce off other balls may rebound into their corner, but the ones on the outside of the group will gradually invade the rest of the space.

Inevitably, after a time the yellow balls will have spread evenly throughout the space. No scheming, plotting, mutual antagonism, or other trickery on the part of the molecules. It is just an inevitable result of all matter being in motion except at a temperature of absolute zero.