Concentration fluctuations and mutual diffusion

The decay of concentration fluctuations in a two-component mixture is described by Pick s Law. Consider the solution to be characterized by a local concentration, c(r,f). The time rate of change of the concentration at position r is governed by the spatial gradient of the concentration flux vector, ], [r,t)  

The concenfrafion-flux vector is proportional to the concentration gradient  

The derivation of a microscopic expression for the mutual-diffusion coefficient uses Equahon 5.44. The relevant force is the osmotic force due to a gradient in the chemical potenhal of the solution  

Under steady-state conditions, the concentration flux vector is  

The mutual-diffusion coefficient is then identified by inspection. It is customary to convert the parhal derivative to an expression involving the osmotic pressure  

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