ON THE DIFFERENTIAL EQUATIONS OF DIFFUSION

The fundamental bases of the differential equation of diffusion are examined. From a dynamical equation defining the motion of the gas, an equation of continuity expressing the law of conservation of mass, and an equation of state giving the relation between concentration and pressure, the differential equations are derived for the interdiffusion of two gases, for the diffusion of vapors, and for the diffusion of gases and vapors through solids. For the diffusion of gases through adsorbing solids, the dynamical equation of the flow is obtained by equating the space derivative of the spreading pressure of the adsorbed film to a resistive force equal to the product of the coefficient of resistance and the velocity of the film. The differential equations derived on this assumption agree qualitatively with measurements for the diffusion of gases through metals when the adsorption can be represented by Langmuir's equation. When the adsorption follows the BET equation, qualitative agreement is found with the diffusion of water vapor through hygroscopic materials. It is also shown that Fick's law is not generally valid as the fundamental equation of diffusion.