1. Mass Transfer

2. Mass Transfer Fick’s First Law Flux Expression Typical mass transfer
model

3. Mass Transfer Flux due to diffusion NA DZ Flux due to bulk molar flow
Gas B
Diffusion Plane
Liquid A
Stagnant gas film
Gas insoluble in Liquid
Equilibrium at interface

4. Mass Transfer

5. Mass Transfer

6. Diffusion Coefficients
Gas Phase cm2 /s
Liquid Phase E-5 cm2 /s
Solid Phase – 1.0E-8 cm2 /s

7. Gas Diffusion
Kinetic Theory of Gases
R 3/2 T 3/2
DAB =
MA1/2 dA P

8. Gas Model (Fuller)

10. Gas Diffusion Example
Determine the diffusion coefficient of n-pentane in air at 30 F
and P = 1 atm.

11. Multi-component Gas Diffusion

12. Liquid Diffusion
Eyring / Stokes Einstein Theory
K T
DAB =
6pr mB

13. Dilute Liquid Diffusion (Wilke-Chang)

15. Liquid Diffusion Example
Determine the diffusion coefficient of a dilute concentration of
n-pentane in water at 40 F.

16. Concentrated Liquids (Vignes)

17. Two Resistance Theory xAi Bulk Gas yAG Gas Film Liquid Film
Bulk Liquid
xAL
yAi
Interface

18. Controlling Resistance
Gas Film
Liquid Film
Interface

19. Two Resistance Theory (Dilute Solution)
y = m x
yAG
yAi
yA*
xAL
xAi
xAL*

20. Dilute Solution Example
Ammonia is being absorbed in a solvent stream. The overall gas phase coefficient (Ky) is lbmol NH3 / hr ft2 atm. The bulk gas phase ammonia concentration is 8 mole % and the liquid bulk phase concentration is mole / ft3. T = 68 F and P = 1 atm. 85 % of the mass transfer resistance in in the gas phase. The Henry’s law constant is atm ft3 / lbmol NH3.
Find: kx, ky, Pai and Cai

21. Two Resistance Theory (Flux Expression - General Case)

22. Two Resistance Theory (Overall Coefficients - General Cases)

23. Concentrated Solution Example
A wetted wall absorption tower (2.54 cm diameter) is fed water and an ammonia-air mixture. At a particular level in the tower, the ammonia concentration in the bulk gas is 0.80 mole fraction and the mole fraction in the bulk liquid is The temperature is 26.7 ºC and the pressure is 1 atm. The rates of flow are such that the local mass transfer coefficient in the liquid is kL= 2.87 X 10-5 kmol /m2 s (kmol/ m3). The local Sherwood number for the gas is 40. The diffusivity of ammonia in air is X 10-5 m2 /s
Compute the local mass transfer flux for the ammonia absorption.

24. Mass / heat / momentum analogies
Laminar
Reynolds
Turbulent
Prandtl
Von Karman

25. Mass / heat / momentum analogies
Chilton-Colburn “j” factor
Friction factor (f) vs Re for pipe flow

26. Empirical Models
Wetted Wall Tower

27. Empirical Models
Laminar
Turbulent
Transition
Flat Plate

28. Empirical Models
Single Sphere

29. Example
Water is stored in a buffalo bladder that has a diameter of 0.3 meters.
The temperature of the water is 25C. Air at 25 C and a relative humidity
of 20 % flows over the outside of the bladder at a velocity of
0.1 meter / sec. Calculate the time needed to cool the water from
25 C to 22 C.

30. Non-Steady State Mass Transfer

31. Non-Steady State Mass Transfer
Sphere – constant surface concentration

32. Non-Steady State Mass Transfer
Figure 3.11 Concentration profiles for un-steady state diffusion in a sphere.

33. Non-Steady State Mass Transfer
Figure 3.9 Average concentrations for non-steady state diffusion.

34. Non-Steady State Mass Transfer
Sphere – convective mass transfer at surface

35. Non-Steady State Mass Transfer

36. Example
A deadly black widow spider is 1 foot away from my toe moving at
0.1 ft / sec when I spray it with Raid. I spray enough Raid on the spider
to coat its outside shell to a concentration of 1 kgmol / m3. Raid
researchers have found that the spider will die when the Raid concentration at the center of the spider reaches 0.56 kgmol/m3. Should I call 911 ???
Data:
DRaid-Bug = 1.0 E-6 m2 / sec
Diameter of spider = 0.01 m

37. 10 Minute Problem
A spherical 3 mm diameter pellet containing insulin is immobilized in the lower intestine. The insulin is quickly transferred from the pellets surface such that the surface concentration is maintained at zero. Determine the time required to reduce the average insulin concentration in the pellet from 2 kgmol / m3 to 0.2 kgmol/m3.
Deff = 3.0 X 10 –7 cm2 /sec