1. Theories of Mass Transfer

2. Theories of Mass Transfer
Film Theory
Penetration Theory
Boundary-layer Theory
Surface-renewal Theories
Combination Film–Surface-renewal Theory
Two Film Theory (very important)

3. 1. Film Theory (or Film Model)

5. The Film Theory

6. The Film Theory

7. 2. Penetration Theory (Higpie,1935)
Basic assumptions:

8. 2. Penetration Theory (Higpie,1935)
Time of exposure ‘’ is too short and constant for all the eddies;
No possibility of formation of concentration gradient;
Liquid particle is subjected to unsteady state diffusion; hence,

9. 2. Penetration Theory (Higpie,1935)
The conditions are CA = CA0 at t = for all Z;
CA = CAi at Z = t  0;
CA = CA0 at Z =  for all t
Solving the equation
kL,av is proportional to (DAB)0.5 for different solutes under the same circumstances. The range of exponents on D varies from 0 to 0.8 or 0.9

10. Surface Renewal Theory( Danckwerts, 1951)
In reality, all eddies are exposed for varying lengths of time.
If ‘S’ is the fractional rate of replacement of the elements, then
‘kL is proportional to (DAB)0.5
Combination of Film – Surface renewal Theory (Dobbins, 1956,1964)
If ‘Zb’ is of finite length, then the B.C becomes
CA = CA0 at Z = Zb for all 
Case i) For rapid penetration & rate of surface renewal is small, ‘k’ follows
Film Theory
Case ii) For slow penetration & rapid surface renewal, k’ follows surface
renewal Theory

13. Slope m
Gas film resistance
Over all resistance
Liquid film resistance

14. Slope = -kx/ky
Slope M
Slope m
Liquid film resistance
Gas film resistance
Over all resistance

15. Slope = -kx/ky
Slope M

16. Slope = -kx/ky
Slope M
Slope m

17. Example 1
In the dilute concentration region, equilibrium data for SO2 distributed between
Air and water can be approximated by
Where the partial pressure of SO2 in the vapor is expressed in atmosphere. For
An absorption column operating at 10 atm, the bulk vapor and liquid concentrations at one point in the column are yA1 = 0.01 and xA1 = 0.0 The mass transfer coefficient for this process are:
Find the overall mass transfer? And vapor and liquid mole fraction at the interface

18. m =2.5

19. Slope = -kx/ky

20. =0.0067

21. Example 2
KG= Ky