12: General transport equations and Fick’s First Law

Before we move from Fick’s First Law to his (creatively named) Second Law, it is worth noting that Fick’s Law is really just one of several “transport equations” that all have a common form. In these equations, J stands for transport (of particles, charge, or heat). So you can see that the same equation that we have been learning about is applicable in almost the exact same form in several different fields!


where J is the flux, D is the diffusion coefficient, C is the concentration of particles, and x is the distance.


For Charge

where V is voltage, so the flux of ions (J) is directly proportional to the difference in voltage (the voltage potential), and σ (also called electrical conductivity) is a coefficient that relates to the properties of the medium the charge is traveling

For Energy (heat)

where T is temperature (Kelvin), so that heat transfer (J) is directly proportional to the difference
in temperatures, and k is called the coefficient of thermal conductivity.