Equimolar Counter Diffusion Of A and B (NA =-NB) | Mass Transfer - Chemical Engineering PDF Download

Equimolar counter-diffusion of A and B (NA =-NB) 
  → Gas phase                (3.19)
 → Liquid phase                                        (3.20)

For gas phase diffusion we know, 
                                                                                     (3.21)

Equating Equation (3.19) and Equation (3.21),
                                                                                                     (3.22)

Again,

                                                        (3.23)

Equating Equation (3.19) and Equation (3.23),
                                                                                                     (3.24)
Also,
                                                          (3.25)
Equating Equation (3.19) and Equation (3.25),
                                                                                                       (3.26)

For liquid phase diffusion the flux can be written as
                                                                         (3.27)
Equating Equation (3.20) and Equation (3.27),                   (3.28)
Also, 
                                           (3.29)
                                                                                                    (3.30)

Equating Equation (3.8) and Equation (3.17),
Conversions:     

Example problem 3.1:
Hydrochloric acid (A) diffuses through a thin film of water (B) 4.0 mm thick at 283 K. The concentration of HCl at point 1 on one boundary of the film is 12 wt% and on the other boundary, at point 2 is 4 wt%. The diffusivity of HCl in water is 2.5 x 10^-9 m²/s. Calculate the flux of HCl considering water to be stagnant. Density of the solutions at points 1 and 2 are 1060.7 kg/m³ and 1020.15 kg/m³ respectively.

Solution 3.1: Molecular weight of HCl, M_A = 36.5 and M_B = 18
At point 1, mole fraction of HCl
 Therefore, x_B1 = 1- 0.0629 = 0.9371
Average molecular weight at point 1


At point 2, mole fraction of HCl 

Average molecular weight at point 2 

z = 4 mm = 0.004 m
Flux of HCl,


3.2 Mass transfer under laminar flow condition 
Mass transfer coefficient does not play a big role in laminar flow condition as molecular diffusion exists there. In laminar flow regime, the average liquid phase mass transfer coefficient, k_L,av is correlated with Sherwood number (Sh) and D_AB as follows:
                                                                                         (3.31)
                                                                                    (3.32) 

3.3 Mass transfer under turbulent flow past solids
Mass transfer under flow past solid is a practically useful situation. Several theories have attempted to clarify the behavior of mass transfer coefficients. All the theories have some assumptions and some drawbacks. Hence, these are revised frequently. In turbulent flow medium, small fluid an element of different sizes, called eddies, move randomly. These eddies form, interact among others and disappear in the flow path. The total molar flux of a solute ‘A’ due to molecular diffusion and eddy diffusion, J_A is as follows:
                                                                            (3.33)
where D_E is eddy diffusivity. Eddy diffusivity depends on intensity of local turbulence.