What is Diffusion coefficient/ Diffusivity

Diffusion coefficient/ Diffusivity

• Diffusivity is defined as the ratio of the flux to the corresponding concentration gradient.

• The diffusivity of any component is a measure of its diffusive mobility.
• Diffusivity increases with a decrease in pressure and increases with increase in temperature
• The SI unit is m²/s and dimensions of diffusivity are L²/θ 
• It is denoted by D_AB for component A diffusing through B

Diffusivity in gases

• Wikle -Lee gives an equation for a mixture of gases as follows

• According to equation D∝ 1/P, D ∝ Tⁿ (where n ranges from 1.5 to 1.8),D ∝ 1/ (M)^1/2
• where

               D_AB = diffusivity

             T = absolute temperature,K

             M_A, M_B = molecular weight of A and B, kg/kmol

             p_t = absolute pressure, N/m²

             r_AB = molecular separation at collision,nm = (r_A + r_B)/2

            ε_AB = energy of molecular attraction= (ε_Aε_B)^1/2

             k = Boltzmann's constant

             f(kT/ε_AB) = collision function

Diffusivity in liquids

• In liquids, diffusion occurs very slow
• For dilute solutions, Wilke and chang equation as follows

• According to this equation, we can conclude that D∝ T and D ∝ (1/ μ)
• where

            D_AB⁰ = diffusivity of A in very dilute solution in solvent B, m²/s

              M_B = molecular weight of solvent, kg/kmol

                 T = temperature, K

                 μ = solution viscosity, kg/m.s

                υ_A = solute molal volume at normal boiling point, m³/kmol 0.0756 for        

                         water as a solute

                φ = association factor for solvent

                    =2.26 for water as a solvent

                    =1.9 for methanol as a solvent

                    =1.5 for ethanol as a solvent

                    =1.0 for unassociated solvent, eg benzene, and ethyl ether