The paper (pdf) "One and a half century of diffusion: Fick, Einstein, Before and Beyond" by Jean Philibert traces the history of diffusion phenomena.

It starts with Thomas Graham (of dialysis fame) who perhaps made the first systematic observations, which were integrated into phenomenological law by German physiologist Adolf Fick in 1855, at the age of 26.

Fick observed the analogy between mass diffusion and heat conduction (now considered obvious), and piggy-backed on Fourier's law of conduction (1822). The paper cites the opening lines of Fick's work:

In 1905, Einstein integrated Robert Brown's observations of random zig-zag trajectories and Fick's phenomenological laws, with the crucial observation that it was the mean-squared displacement, and not the mean displacement that was related to diffusion.

Following Einstein's paper, the experimental work of Perrin was responsible helping the world accept the link between the microscopic (MSD is proportional to diffusivity and time) and macroscopic worlds (flux is proportional to concentration gradient).

It is always interesting to look at the chronological development of (now familiar) ideas. These uncontroversial ideas were once strongly wrestled with. It took centuries for scientists to come up with a comprehensive understanding, and to develop interesting applications based off of it.

It starts with Thomas Graham (of dialysis fame) who perhaps made the first systematic observations, which were integrated into phenomenological law by German physiologist Adolf Fick in 1855, at the age of 26.

Fick observed the analogy between mass diffusion and heat conduction (now considered obvious), and piggy-backed on Fourier's law of conduction (1822). The paper cites the opening lines of Fick's work:

A few years ago, Graham published an extensive investigation on the diffusion of salts in water, in which he more especially compared the diffusibility of different salts. It appears to me a matter of regret, however, that in such an exceedingly valuable and extensive investigation, the development of a fundamental law, for the operation of diffusion in a single element of space, was neglected, and I have therefore endeavoured to supply this omission.Next, the paper talks about the contributions of W. C. Roberts-Austen (an assistant to Thomas Graham, and successor as Master of the Mint) to quantification of diffusion in solids.

In 1905, Einstein integrated Robert Brown's observations of random zig-zag trajectories and Fick's phenomenological laws, with the crucial observation that it was the mean-squared displacement, and not the mean displacement that was related to diffusion.

Following Einstein's paper, the experimental work of Perrin was responsible helping the world accept the link between the microscopic (MSD is proportional to diffusivity and time) and macroscopic worlds (flux is proportional to concentration gradient).

It is always interesting to look at the chronological development of (now familiar) ideas. These uncontroversial ideas were once strongly wrestled with. It took centuries for scientists to come up with a comprehensive understanding, and to develop interesting applications based off of it.