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diffusion on liquid

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Hello.
I know what is diffusion... chemical process when molecules from a material move from an area of high concentration to an area of low concentration... Typical example is ink in water. However, how it works? Molecules of water collide with molecules of ink? How it is happens from the viewpoint of molecular physics? ... If i take the ink to the warmer watter, diffusion will be faster. Can me tell why? Molecules are faster, so collisions are more frequent or why?
I heard that the pressure affects diffusion also. Why?

Thank you very much.

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