Principles of Diffusion

• Molecular diffusion of A in the direction of decreasing concentration (i.e. from left to right)
• Net diffusion of B in the opposite direction
• Diffusion continues until the concentration is uniform throughout

// Fick’s Law

The molecular diffusion flux of component A in the z-direction in a mixture of A and B, is given by Fick’s law:

[latex]J_A=-D_AB\ \ \begin dc〗_A/dz[/latex]

Where,
J_A = rate of molecule diffusion, kmol/(m².s)
D_AB = diffusion coefficient (or diffusivity) of A in a mixture of A and B, m²/s
dc_A/dz = concentration gradient of A, kmol.m^-3/m

The concentration gradient is the driving force, as temperature gradient in Fourier’s law for heat flux by conduction

For gases , Fick‟s law is expressed in terms of partial pressure of component A , pA .

The ideal gas law gives:

Corresponding to a concentration of A,

With the derivative:

// Diffusion with bulk of mass in motion

• With uniform concentration of A, the molar flux of A past a stationary observer is c_AV.

•A concentration gradient dc_A/dz gives an additional flux due to molecular diffusion, J_A, or total molar flux of A.

// Diffusion of A through a stagnant B

Also known as Stefan diffusion

At point 1, p_A1is the vapour pressure of A at the temperature of the bath, and at point 2, p_A2 may be close to zero.