1. ChE 333 : Mass transfer
Textbook: Fundamentals of Momentum, Heat and Mass transfer.
J.R.Welty, R.E.Wilson and C.E.Wicks. 5 th Edition , John Wiley (2007).
Reference: Fundamentals of Heat and Mass transfer.
Theodore L. Bergman, Adrienne S. Lavine, Frank P. Incropera and David P. DeWitt.
7 th Edition , John Wiley (2011)
Dr. Sharif Fakhruz Zaman
Department of Chemical and Materials Engineering,
Faculty of Engineering, King Abdulaziz University,
Jeddah, KSA

2. Dr. Sharif Fakhruz Zaman Assistant Professor at KAU.
About myself
Dr. Sharif Fakhruz Zaman
Assistant Professor at KAU.
PhD in Chemical and Biochemical Engineering, University of British Columbia, Vancouver Canada (2010).
MS in Chemical Engineering, KFUPM, KSA .
BSc in Chemical Engineering, BUET, Bangladesh.
Field of interest : Heterogeneous catalysis and molecular modeling of catalyst and catalytic reactions, reaction kinetics, reactor design, diffusion in zeolites etc.
Office address :
Room 216, Building 45, Department of Chemical and Materials Engineering
Faculty of Engineering, King Abdulaziz university, Jeddah, KSA. or
Phone : cell : , office : ext-68044

3. Course syllabus Major exam 1
Topic 1 : Fundamentals principles of mass transfer
Introduction to mass transfer and its industrial applications.
Week 1
Topic 2 : Diffusion coefficients; mass transfer coefficients
Molecular mass transfer, Fick's rate equation, Diffusion coefficient, Gas mass diffusivity, Liquid mass diffusivity.
Week 2
Pore diffusivity, Knudsen diffusion, Solid mass diffusivity, Convective mass transfer.
Week 3
Topic 3: Differential equations of mass transfer
Modeling mass transfer phenomena, Special form of mass transfer equation, Fick's second law.
Week 4
Commonly encountered boundary conditions, steps for modeling process involving molecular diffusion. Steps to solve mass transfer problems.
Week 5
Major exam 1

4. Topic 4 : Steady state molecular diffusion
Course syllabus
Topic 4 : Steady state molecular diffusion
One dimensional mass transfer independent of chemical reaction, Pseudo steady state diffusion.
Week 6
One dimensional system associated with reaction (heterogeneous system)
Week 7
One dimensional system associated with reaction (homogeneous system), film theory and penetration theory.
Week 8
Major exam 2

5. Course syllabus Major exam 3
Topic 5 : Unsteady state molecular diffusion
Unsteady state diffusion and Fick's law, transient diffusion in a semi-infinite medium.
Week 9
Transient diffusion in a finite medium,
Concentration time chart for simple geometric shapes
Week 10
Topic 6 : Convective mass transfer
Fundamental consideration of convective mass transfer, Significant parameters in convective mass transfer, dimensionless analysis for convective mass transfer, exact analysis of the laminar concentration boundary layer.
Week 11
Approximate analysis of the laminar concentration boundary layer. Mass transfer and momentum transfer analogy, Chilton Colburn analogy.
Week 12
Major exam 3

6. Topic 7 : Convective mass transfer correlations
Course syllabus
Topic 7 : Convective mass transfer correlations
Mass transfer for plates sphere and cylinders
Week 13
Mass transfer through pipes, wetted wall columns, mass transfer in packed and fluidized bed
Week 14
Final exam
Week 15
Class Schedule
Lectures : Sunday – Tuesday 8:00 – 9:30 am
Tutorial : Sunday : 2:30 -5:20 pm
Class Room : 220 , Building 45

7. Grading
My goal is that you to learn the material and make a high grade in the course!
Homeworks %
Midterm I and II and III %
Weekly in-lecture quizzes + projects %
{ Based on class content or core homework problems + Diffusion lab experiment report}
Written final exam %

8. Mass Transfer
When a system consists of two or more components whose concentration vary from
point to point , there is a natural tendency of mass transfer minimizing the concentration
difference within the system.
The transport of one constituent from one region of higher concentration to that of a
lower concentration is called mass transfer.
What happens if a lump of sugar added to a cup of black coffee.
Sugar will eventually dissolve
diffuse uniformly throughout the coffee.
How long it will take to have uniform concentration of sugar in the coffee cup??
It depends up on the process
- 1) Quiescent (being at rest/ quite / still)
-2) Mechanically agitated by a spoon.
Mechanism of mass transfer
Depends on the dynamics of the system in which it occurs

9. Depends on the dynamics of the system in which it occurs.
Mechanism of mass transfer
Depends on the dynamics of the system in which it occurs.
Random molecular motion in quiescent fluid.
Transferred from a surface into a moving fluid aided by the dynamic
characteristics of the flow.
Mass transfer
Molecular mass transfer.
Convective mass transfer.

10. Molecular mass transfer examples Biological process
oxygenation of blood
Transportation of ions across membranes
within kidney
(2) Chemical processes
Chemical vapor deposition
Aeration of waste water
Purification of ores and isotopes
(3) Chemical separation processes
Adsorption
Crystallization
Absorption
Liquid liquid extraction
Component remains
at the interface
Component penetrates
to the interface and the
transfer to the bulk of the 2nd phase.
We will talk little about interface mass transfer : Chapter 29

11. Molecular mass transfer
First observed by Parrot 1815.
A gas mixture contains two or more molecular species whose relative concentration varies from point to point, an apparently natural process which tends to diminish any inequalities of composition.
This microscopic transport of mass, independent of any convection within the system is called molecular mass transfer.
Kinetic theory of gases can explain mass transfer in gaseous mixture in specific case.
At temperature above absolute zero, individual molecules are in a state of continual yet random motion.
Within dilute gas mixture each solute molecule behaves independently of the other solute molecule, since it seldom encounters them.
Collision between solute and solvent molecules are continually occurring. As a result of collision the solute molecules move along a zigzag path sometime towards a region of higher concentration sometime towards a lower concentration.

12. Mass transfer refers to mass in transit due to a species concentration
gradient in a mixture.
Must have a mixture of two or more species for mass transfer to occur.
The species concentration gradient is the driving potential for transfer.
Mass transfer by diffusion is analogous to heat transfer by conduction.
Physical Origins of Diffusion:
Transfer is due to random molecular motion.
Consider two species A and B at the same T and p,
but initially separated by a partition.
Diffusion in the direction of decreasing
concentration dictates net transport of
A molecules to the right and B molecules
to the left.
In time, uniform concentrations of A and
B are achieved.

13. Homework
Chapter 24 (WWWR) : 1,8,12,13,15,22
Tutorial
Chapter 24 (WWWR) : 3,4,11,13,17,21,22
Example
Chapter 24 (WWWR) : 1,2,3,4,5,6,7,8

14. Definitions Molar concentration of species i.
Mass density (kg/m3) of species i.
Molecular weight (kg/kmol) of species i.
Molar flux of species i due to diffusion.
Transport of i relative to molar average velocity (v*) of mixture.
Absolute molar flux of species i.
Transport of i relative to a fixed reference frame.
Mass flux of species i due to diffusion.
Transport of i relative to mass-average velocity (v) of mixture.
Absolute mass flux of species i. : i n
Transport of i relative to a fixed reference frame.
Mole fraction of species i
Mass fraction of species i

15. Mass transfer occurs in mixtures, so it is important to evaluate the effect
of each component in the transfer process. To explain the role of a component
in the mixture we will use the following definitions.
Concentration :
In multi component mixture , the concentration of a molecular species can
be expressed in many ways.
Mass concentration also known as density (gm/cm3)
Mass fraction , ωA:

16. Molecular concentration:
Mole fraction:
(liquids,solids) , (gases)
For GAS only
For gases,
Velocity:
mass average velocity,
molar average velocity,
Velocity of a particular species relative to mass/molar average is the diffusion velocity.

17. Example # 1
mol

20. Flux: Isothermal, Isobaric system
A vector quantity denoting amount of a particular species that passes per given time through a unit area normal to the vector, given by Fick’s First Law, for basic molecular diffusion.
Flux can be expressed in different ways , three different expression
(1) Flux reference to a coordinate that are fixed in space (Total/absolute flux)
nA = Mass flux and NA = molar flux.
(2) Flux reference to a coordinate that are moving with the mass average velocity (jA).
(3) Flux reference to a coordinate that are moving with the molar average velocity (JA).
Fick’s first law defines the molar flux relative to molar average velocity.
or, in the z-direction,
JA,z = Molar flux of component A in z direction relative to molar average velocity.
DAB = Proportionality factor, Mass diffusivity, diffusion coefficient for component A diffusing through component B .
Isothermal,
Isobaric system

21. For a general relation in a non-isothermal, isobaric system,
Mass flux relative to Mass average velocity, jA,z.
Concentration gradient
in terms of mass fraction
Initial experimental investigation were unable to verify Fick’s 1st law
Why??
Since mass is transferred by two means: (1) concentration differences (concentration gradient) and (2) convection differences from density differences (bulk motion)

22. For binary system with constant average velocity in z direction Vz,
Thus,
Rearranging to
Molar average velocity
Which substituted, becomes
Multiply by cA and rearrange
Defining molar flux, N as flux
relative to a fixed coordinate,
Finally
Generalized Eqn.
Concentration gradient contribution
Bulk motion contribution

23. Average velocity
Stairs : Fixed coordinate
Escalator : Moving coordinate

25. Related molecular mass transfer
Defined in terms of chemical potential, molar diffusion velocity:
Nernst-Einstein relation
Mobility of component A

26. Diffusion Coefficient
Fick’s law proportionality/constant
Similar to kinematic viscosity, n (momentum transfer) m2/s
and thermal diffusivity, a (heat transfer) m2/s

27. Gas mass diffusivity {Sutherland – Jeans – Chapman - Cowling}
Theoretical expression for gas mass diffusivity for low density gas mixture
Based on Kinetic Gas Theory
Assumptions
Rigid sphere
No intermolecular forces
Elastic collision
l = mean free path length, u = mean speed
Species ‘A’ diffusing through its isotopes ‘A*’
MA = molecular weight ( gm/mol)
N = Avogadro’s number = x molecules/mole
P = system pressure (atm)
T = absolute temperature (K)
k = Boltzmann constant ( 1.38 x erg/mol)
σ AB = Lennard Jones diameter of the spherical molecule

28. Hirschfelder’s equation: For Non polar and Non reacting molecule.
For binary gas mixture
P in atm
Diffusivity
in cm2/s.
Collision diameter
A Lennard Jones parameter (Å)
Collision integral
Temperature in
Kelvin
Molecular
weight
(periodic Table)
Gas phase diffusion coefficient , DAB = f(P,T)
Diffusion coefficient for gases: DAB = DBA

29. for binary systems, (non-polar, non-reacting)
Lennard-Jones parameters s and e from tables, or from empirical relations
for binary systems, (non-polar, non-reacting)
ΩD = f(T, intermolecular potential field for one molecule of A and one molecule of B). From Table : K-1;
Extrapolation of diffusivity up to 25 atmospheres
Temperature and
Pressure correction
of diffusivity
Quick estimation
Temperature dependency of collision integral is very nominal/small.

30. Binary gas-phase Lennard-Jones “collision integral”

31. If Lennard Jones parameter values are not reported :
Empirical relation to estimate Lennard Jones parameter for PURE COMPONENT.
Vb = Molecular volume at normal
boiling point (cm3/g mol); Table 24.4
Tc = Critical temperature(K)
Pc = Critical pressure (atm)
Vc = Critical volume (cm3/g mol)
Tb = Normal boiling point temperature (K)

34. Unit conversion of pressure
Gas constant R or Rg :
(14) L atm K−1 mol−1
(34) cal K−1 mol−1
(34)×10−3 kcal K−1 mol−1
(75)×107 erg K−1 mol−1
(75) L kPa K−1 mol−1
(75) m3 Pa K−1 mol−1
(75) cm3 MPa K−1 mol−1
(75)×10−5 m3 bar K−1 mol−1
×10−5 m3 atm K−1 mol−1
cm3 atm K−1 mol−1
Unit conversion of pressure
Convert from these to pascals (Pa)
multiply by
standard atmosphere (atm)
bar (bar)
kilopascal (kPa)
1 000
megapascal (MPa)
millibar (mbar)
100
std centimeter of mercury (cmHg)
millimetre of mercury (mmHg)
Unit conversion of viscosity (μ)
1 poise = dyne·s/cm² = g/cm·s = 1/10 Pa·s
1 Pa·s = 1 N·s/m² = 1 kg/m·s
1 cP = 1 mPa·s = Pa·s/1000 = poise/100
Unit of work or energy
1 erg = 10-7 J = 10-7 N-m

35. Interpolation If you know the atomic wt. you should be able to
calculate the molecular wt if you know the correct
chemical formula. Periodic Table – keep one with you.

37. Atomic diffusion volume
For binary gas mixture
With no reliable s or e, we can use the Fuller-Schettler and Giddings correlation,
Careful about addition of structural correction; i.e. aromatic ring, for calculation of diffusion volume from atomic volume.
Calculation of volume of benzene (C6H6) [vapor/gas phase] from table 24.3.
Atomic diffusion volume : C = 16.5; H = 1.98
Diffusion volume = 16.5* *6 +aromatic ring correction
= =
Atomic diffusion volume
(Table 24.3) cm3/g mol
Gas Diffusivity
in cm2/s
Pressure in atm

38. Calculation of volume of benzene (C6H6) [vapor/gas phase] from table 24.3.
Atomic diffusion volume : C = 16.5; H = 1.98
Diffusion volume = 16.5* *6 +aromatic ring correction
= =

39. Example of polar gases:
For binary gas mixture containing POLAR component
where
Suggested by Brokaw (1969)
Hirschfelder equation is valid but need to estimate the collision integral (ΩD) in a
different way.
For binary gas with polar compounds, we calculate W by
Problem Exercise 24-11
μb = dipole moment, Debye.
Vb = Liquid molar volume of the specific
compound at its boiling point,
cm3/g mol, Table 24-4 and 24-5.
Tb = Normal boiling point in K.
Example of polar gases:
NH3 , SO2, H2S, PH3

40. For gas mixtures with several components (multiple components),
Calculate D1-2, D using any empirical equation or you can get it from literature i.e values reported in Appendix J-1. You may need to perform temperature correction of the diffusivity value if you use the value from the App. J.1.
In appendix J.1 : diffusivity values are reported in the form of => DAB.P [cm2 .atm/s]
you need to divide the value with the system pressure to get the
actual value at the reported temperature.
yn’= Mole fraction of component ‘n’ in the
gas mixture evaluated on a component -1-free basis.

41. 2

42. Liquid mass diffusivity
No rigorous theories
Diffusion as molecules or ions
Eyring theory
Hydrodynamic theory
Stokes-Einstein equation
Equating both theories, we get Wilke-Chang equation
Non electrolyte solute in low
concentration solution
Association parameter
for solvent, B
A = solute
B = solvent
Molar volume at
Normal boiling point
Viscosity in centipoises (cP) unit
1 cP = 10−2 P = 10−3 Pa·s = 1 mPa·s

43. If data for computing the molar volume of solute at its normal boiling point, VA is not available, Tyne and Calus (1975) recommended the following correlation :
Vc = critical volume of species A in cm3/g. mol. Values are tabulated in literature {Reid, Prausnitz and Sherwood, 1977}.

44. Molar volume of ethanol

47. Liquid diffusion coefficient in concentrated solution:
For infinite dilution of non-electrolytes in water, W-C is simplified to Hayduk-Laudie eq.
Scheibel’s equation eliminates FB, simplified form of W-C
Exceptions:
for benzene as a solvent, if VA < 2VB , use K = 18.9x10-8.
For other organic solvents, if VA < 2.5 VB, use K = 17.5x 10-8.
Liquid diffusion coefficient in concentrated solution:
Combine the infinite dilution coefficient DAB and DBA =>
Where, DAB = infinitely dilute diffusion coefficient of A in solvent B.
For associating compound , i.e alcohols,

48. polyvalent salt solution
As diffusivity changes with temperature, extrapolation of DAB is by
Tc = Critical temperature of solvent B in Kelvin. Temperatures are in Kelvin unit.
n = Exponent related to the heat of vaporization of solvent(B), ΔHv, at its normal boiling point temperature {Text book page table for the value of n}.
For diffusion of univalent salt in dilute solution, we use the Nernst equation:
DAB = Diffusion coefficient based on the molecular concentration of A in cm/s2.
R = Gas constant Joules/K/g mol.
F = faraday’s constant coulombs/g equivalent
= Limiting ionic conductance in (amp/cm2 )(volt/cm)(g equivalent/cm3)
polyvalent salt solution
Replace the constant 2 in the univalent salt diffusion equation with
where n+ and n- are the valances of the cation and anion of the polyvalent salt.

49. Diffusion of molecules within pores of porous solids
Pore diffusivity
Diffusion of molecules within pores of porous solids
example
Heterogeneous catalysts are porous solids containing active material inside the pore wall. So reactants need to diffuse through the pore and reach the active metal surface to convert into products.
Separation of solute from dilute solution by the process of adsorption.
Knudsen diffusion for gases in cylindrical pores
(1)Pore diameter smaller than mean free path, and
(2) density of gas is low
Knudsen number
If Kn>>>1 then Knudsen diffusion is important.
From Kinetic Theory of Gases,

50. dpore in cm
But if Kn >1, then
If both Knudsen and molecular diffusion exist, then
with
For non-cylindrical pores, we estimate
Diffusivity
value in cm2/s
Void fraction in the solid, ε = void volume /(total volume of solid + void)

51. Types of porous diffusion. Shaded areas represent nonporous solids

52. Example 6

53. Updating the diffusivity value to a different temperature and pressure

56. Hindered diffusion for solute in solvent-filled pores
Diffusion of a solute molecule through tiny capillary pore filled with liquid solvent. A general model is
DAB0 = Liquid liquid diffusivity.
F1 and F2 are correction factors, function of pore diameter, values between 0 and 1.
If φ >1, solute molecule is greater than pore diameter, This phenomena is known as solute exclusion. It is used to separate large biomolecules such as proteins from dilute aqueous mixture.
ds = diameter of solute molecule

57. F1 is the stearic partition coefficient: geometric hindrance
F2 is the hydrodynamic hindrance factor, one equation is by Renkin, range in between 0<=φ=>0.6
Assumptions for the model:
Spherical rigid solute in straight cylindrical pore.
Ignore electrostatic or other energetic solute, solvent and pore wall interaction;
polydispersity of solute diameter and noncircular pore diameter.

58. Example 7

62. Convective Mass Transfer
Mass transfer between moving fluid with surface or another fluid
Forced convection
Free/natural convection
Rate equation analogy to Newton’s cooling equation
Surface concentration
(mol/m3)
Mass transfer coefficient
(m/s)
Bulk fluid concentration

63. Film mass transfer and film mass transfer co-efficient:
Fluid flowing past a surface, there is a thin layer close to the surface where
the fluid is laminar and the fluid particles next to the solid boundary are at rest.
Laminar boundary layer
No slip condition
Mechanism of mass transfer between the surface and stagnant and laminar layer is by molecular mass transfer.
Controlling resistance to the convective mass transfer sometime is from this laminar “film” due to molecular diffusion.
Momentum transfer
/ Fluid Mechanics h w L W L

64. Example 8

66. Diffusion in solids
Diffusion of atoms within solids. Mainly covered in the Materials Engineering
course.
Examples:
Semiconductor manufacturing process :Impurity atoms : DOPANTS are
introduced to the solid silicon to control the conductivity in a semiconductor device.
Hardening of still (i.e. Carburization) : Diffusing carbon(C) atom through iron (Fe).
Solid diffusion mechanism :
Vacancy Diffusion
Interstitial diffusion

67. Vacancy diffusion:
Transported atoms JUMPS from a lattice position of the solid into the
neighboring unoccupied solid site or vacancy.
Atoms continues to diffuse by a series of jumps into the neighboring vacancy.
This normally requires a distortion of lattice or lattice defect sites.

68. Interstitial Diffusion
the diffusing atom is not on a lattice site but on an interstice. The diffusing atom is free to move to any adjacent interstice, unless it is already occupied.
The rate of diffusion is therefore controlled only by the ease with which a diffusing atom can move into an interstice. 
Appendix J-3 : Values of binary diffusion coefficient in solids

69. There is an energy barrier to change the places of atom.
Eyring “unimolecular rate theory” concept explains the mechanism of the diffusion.
Effect of temperature :
Diffusion coefficient value increases with temperature according to
Arrhenius equation
Problem : 24.19
Do = proportionality constant
Q = activation energy , kcal/mol, J/mol etc.
R = Gas constant = J/mol/K

70. Linear Interpolation formulaX1 Y1
X known x value)
Y (unknown) X2 Y2