Isothermal Diffusion in Solutions

As seen in the earlier discussion of Onsager s theory (section 6.2), in the classical approach diffusion is a response to a concentration gradient. If species i is diffusing then the flux of i is given by 

This is known as Pick s second law it states that the time derivative of the concentration at a given point in space is equal to the diffusion coefficient times the Laplacian of the concentration. In deriving this equation it has been assumed that the diffusion coefficient is independent of concentration. 

In a simple situation the variation of concentration only occurs in one direction in space. Then Pick s first law becomes 

This is a second-order partiai differentiai equation whose soiution gives the concentration of species i as a function of position and time, that is, of x and t. 

As seen eariier, the dimensions of the diffusion coefficient in SI units are m s Typicai diffusion coefficients in aqueous soiutions are the order of i x iO m s. On the basis of Onsager s theory the quantity ieading to the flux, that is, the force shouid have the dimensions of Newtons. On the basis of ciassicai thermodynamics this is most directiy achieved by writing Pick s iaws in terms of the chemicai potentiai rather than the concentration. This means that Pick s first law becomes 

---

Dahms-Ruff theory — For fast electron exchange processes coupled to isothermal diffusion in solution, the theoretical description and its experimental verification were given by Dahms [i] and by Ruff and co-workers [ii—v]. Ruff and co-workers studied the displacement of the centers of mass particles, which is brought about by both common migrational motion and chemical exchange reaction of the type... 

---