# Molecular Diffusion in Solids, Liquid and Gases | Is there Diffusion in Solids

Is there diffusion in solids, like leaching, drying, etc. involving contact of fluids with solids and involving diffusion in the solid phase?

Fick's law for the steady-state diffusion can be written as

NA = - DA dCA/dz

where NA is the rate of diffusion of A per unit cross-section of solid. DA is the diffusion of A through the solid, dCA/dz is the concentration gradient in the direction of diffusion.

## Molecular Diffusion in liquid

#### Study-state equimolar counter diffusion:

We Have NA = - NB

The flux equation for steady-state equimolar counter diffusion is given by

NA = DAB/z(CA1 - CA2) = DAB/z(p/M) avg. (xA1 - xA2)

Where xA1-xA2 is the concentration difference in terms of mole fraction.

(p/M) avg. = C avg. = [p1/M1 - p2/M2]/2

C avg. is the total average concentration of A and B in kmol/m3, p1 and p2 are the average densities of the solution in kg/m3 at locations 1 and 2 respectively, and M1 and M2 are the average molecular weight of the solution at locations 1 and 2 respectively in kg/kmol.

#### Steady state diffusion of A through nondiffusioning B:

We know that NA = Constant, NB = 0

The flux is given by

NA = DAB/z.xAM(p/M) avg. (xA1 - zA2)

Where   xB, M = (xB2 - xB1) / ln (xB2/xB1).

## Molecular diffusion in Gas

For the diffusion in the z-direction and for NA and NB both constant (steady-state) we will derive equations for the flux

For an ideal gas, we have

CA/C = PA/P = yA

Where PA is the partial pressure of component A and P is the total pressure.

### Diffusivity

Diffusivity is defined as the ratio of flux to the corresponding concentration gradient. The dimensions of the diffusivity are L2/θ and its SI units are m2/s. The diffusivity of any component is a measure of its diffusive mobility and is a function of the temperature, pressure, nature, and concentration of the other components.

Diffusivity mobility is a function of the number of collisions. Therefore, diffusivity increases with a decrease in pressure because the number of collisions is less at lower pressure. However, the effects of pressure are negligible in the case of liquids. Also as the random motion of the molecules increases with an increase in temperature, diffusivity increases with an increase in temperature.

NA = JA + xA (NA + NB)