(37g) On the Derivation of Damped Wave Diffusion and Relaxation Equation from Stokes-Einstein Theory

The damped wave diffusion and relaxation equation where the Fick's law of mass diffusion is a special case when the relaxation time is zero is derived. The derivation used to obtain the Stokes-Einstein formula for the diffusion coefficients in liquids is revisited. The acceleration of the molecules prior to reaching the steady velocity is considered. This lends itself to the generalized Fick's law of mass diffusion and relaxation. An expression for the relaxation time is also obtained along the way. It can be seen that the velocity of mass is 1/3 of the root mean square velocity of the molecule derived from kinetic representation of pressure for ideal gases. The manifestation of the expression obtained for the relaxation time for low pressure fluid systems was studied. An exact well bounded Fourier series solution for the hyperbolic PDE was obtained by the method of separation of variables. The solution was found to be bifurcated. When the pressure was low for ideal gases, P