Diffusion is one of several transport phenomena that occur in nature. A distinguishing feature of diffusion is that it results in mixing or mass transport without requiring bulk motion. Thus, diffusion should not be confused with convection or advection, which are other transport mechanisms that use bulk motion to move particles from one place to another. In Latin, "diffundere" means "to spread out".
There are two ways to introduce the notion of diffusion: either a phenomenological approach starting with Fick’s laws and their mathematical consequences, or a physical and atomistic one, by considering the random walk of the diffusing particles.
In the phenomenological approach, according to Fick's laws, the diffusion flux is proportional to the minus gradient of concentrations. It goes from regions of higher concentration to regions of lower concentration. Later on, various generalizations of the Fick's laws were developed in the frame of thermodynamics and non-equilibrium thermodynamics.
From the atomistic point of view, diffusion is considered as a result of the random walk of the diffusing particles. In molecular diffusion, the moving molecules are self-propelled by thermal energy. Random walk of small particles in suspension in a fluid was discovered in 1827 by Robert Brown. The theory of the Brownian motion and the atomistic backgrounds of diffusion were developed by Albert Einstein.
Now, the concept of diffusion is widely used in science: in physics (particle diffusion), chemistry and biology, in sociology, economics and finance (diffusion of people, ideas and of price values). It appears every time the concept of random walk in ensembles of individuals is applicable.
Read more about Diffusion: History of Diffusion in Physics