Brownian motion, named after Scottish botanist Robert Brown, refers to any physical phenomena where some quantity is constantly undergoing small, random fluctuations. It causes the particles in a fluid to be in constant motion and prevents solid molecules in colloidal solutions (think emulsions) from settling down. Therefore one may consider diffusion to be a macroscopic version of brownian motion (albeit still on a very small scale) and hence we can simulate diffusion through the principles of brownian motion. There are a few key parts describing brownian motion which Einstein actually published a paper on during his miracle year. Let's discuss a couple of them.

1. The size of particles is inversely proportional to the speed of motion. This is because smaller and therefore less massive particles gain more speed from collisions to maintain conservation of momentum.

2. Speed of Brownian motion is inversely proportional to the viscosity of a fluid as there is a lower amount of friction between particles and hence less energy loss.