Diffusion is a molecular-scale process wherein molecules of one type migrate through molecules that are predominantly of another type. At the molecular scale, all molecules can be seen to have constant motion known as thermal energy. Temperature and pressure arise from this motion even if the bulk material is stationary. If molecules of two type are well mixed, then their random motions do not have statistically significant chances to unmix them; but if they are in an unmixed state but free to mix, then the random movements will act to mix them.

Fick’s Law of diffusion says that the rate at which molecules of one type will diffuse through molecules of another type depends on the local concentration gradient and a system-descriptive coefficient called the diffusion coefficient. So if there is no gradient as in the well-mixed case, diffusion will be zero. If there is a big concentration difference in a short distance, diffusion will be rapid.

The diffusion coefficient is a measure of how easily molecules can move past each other. That depends on what molecules they are, but in a broad sense we know that diffusion will depend on the temperature (faster moving molecules will move past other fast moving molecules more quickly! duh), and on the viscosity (substances that are less-fluid have more intermolecular forces to overcome, so it is harder for diffusing molecules to penetrate between those connections). The temperature dependence of diffusion is described by the Arrhenius equation, if you’re interested. A lot of small ions that diffuse through water have diffusion coefficients around 1E-9 square meters/second. Multiplying by a concentration gradient like (kg/m3-m) gives kg/m2-s - a mass movement rate per area or a “flux”.

Although we start out imagining diffusion happening in some big container, the fact is that big containers are full of convection - random currents in the bulk material due to mechanical mixing or temperature-caused density differences. It is only at the microscopic scale that we see diffusion exert controlling influence. Bulk fluids are mixed by turbulence, but at boundaries, where the molecules are up against another phase, the currents do not reach. How thick is the “boundary layer”? We can sometimes estimate it, but also sometimes we approximate and use a measured “effective diffusion coefficient” that incorporates the diffusion through an um-measurable boundary thickness, along with some diffusion into tiny pores and channels in an adsorbent surface.