Phase transitions - 5
Channel: bhadeshia123
Date: 2022-10-27

Diffusion is often described as "the spreading of things" but it can in fact involve "un-spreading" if the dependence of chemical potential on the composition is appropriate. We begin with a consideration of Brownian motion and the root mean square distance achieved during a random walk. This distance is found to change with the square root of time, rather than a linear dependence. The difference between Brownian motion and diffusion is that the latter can be directed (oriented), i.e, non-random motion. This leads to Fick's first law of diffusion, which is used widely, for example in considering the passage of medical drugs through cell membranes. 

Fick's first law relies on a flux that is proportional to a constant concentration gradient, with the proportionality constant being the diffusion coefficient. When the gradient is not constant, the concentration at any point should change with time. This leads to Fick's second law of diffusion, with the classical exponential solution (e.g., the penetration of lithium into copper) and to the error function solution (e.g. the penetration of chloride ions into concrete.

We note finally that an effective diffusion coefficient suffices when dealing with heterogeneous substances, such as the cell membrane or concrete, both of which contain structure.

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https://www.phase-trans.msm.cam.ac.uk/2022/EMS523U_book.pdf