‫جامعه فاروس‬
‫كلية الهندسة‬
‫قسم البتروكيماويات‬
Pharos University
Faculty of Engineering
Petrochemical Department
MASS TRANSFER
LECTURE (3)
1. DIFFUSION IN GAS MIXTURES:
Mass transfer in gas mixtures of several components can be described by theoretical
equations involving the diffusion coefficients for the various binary pairs involved in
the mixture. Wilke has simplified the theory and has shown that a close approximation
to the correct form is given by the following relation:
D1-mixture=
Where:


D1-mixture: is the mass diffusivity for component 1 in the gas mixture.
D1-n: is the mass diffusivity for the binary pair, component 1 diffusing
through component n.

yn: is the mole fraction of component n in the gas mixture evaluated on a
component-1-free basis, that is:
y2’=
=
EXAMPLE (1):
In the chemical vapor decomposition of silane (SiH4) on silicone wafer, a process gas
stream rich in an inert nitrogen (N2) carrier gas has the following composition:
ySiH4= 0.0075, yH2=0.015, yN2= 0.9775
The gas mixture is maintained at 900 K and 100 Pa total system pressure. Determine the
diffusivity of silane through the gas mixture. The Lennard-Jones constants for silane are
εA/k = 207.6K and ϬA= 4.08A.
SOLUTION:
The diffusivity of silane through the gas mixture is determined by the following equation:
D1-mixture=
D1-2 (the diffusivity of silane in nitrogen) and D1-3(the diffusivity of silane in hydrogen),
they are calculated using hirchfelder equation as follows:
I) First D1-2 (the diffusivity of silane in nitrogen) is calculated as follows:
1.
ϬA= 4.08A, ϬB= 3.681A and ϬAB =
2.
εA/k = 207.6K, εB/k = 91.5K and εAB/k=
3.
KT/εAB = 6.5 so from the appendix ΩD= 0.801
= 3.88
= 137.82 K
By applying the previous values in hirchfelder equation, D1-2 (the diffusivity of silane
in nitrogen) at 900 K and 100 Pa =1.09*103 cm2/s.
II) Second D1-3 (the diffusivity of silane in hydrogen) is calculated as follows:
1.
ϬA= 4.08A, ϬB= 2.968A and ϬAB =
2.
εA/k = 207.6K, εB/k = 33.3K and εAB/k=
3.
KT/εAB = 10.8 so from the appendix ΩD= 0.67968
= 3.524
= 83.144K
By applying the previous values in hirchfelder equation, D1-3 (the diffusivity of silane
inhydrogen) at 900 K and 100 Pa = 4.06*103 cm2/s.
III) y2’=
IV) DSiH4=
=
=
=0.9849, y3’=
=
=
=
= 0.0151
= 1.10*103 cm2/s.
2. LIQUID-MASS DIFFUSIVITY:
Liquid mass diffusivity depend on concentration due to the changes in viscosity with
concentration and changes in the degree of ideality of the solution. Certain molecules
diffuse as molecules, while others that are designated as electrolytes ionize in
solutions and diffuse as ions. For example, sodium chloride, NaCl, diffuses in water
as the ions Na+ and CI-. Though each ion has a different mobility, the electrical
neutrality of the solution indicates that the ions must diffuse at the same rate;
accordingly, it is possible to speak of a diffusion coefficient for molecular electrolytes
such as NaCl. However, if several ions are present, the diffusion rates of the
individual cations and anions must be considered, and molecular diffusion
coefficients have no meaning. Needless to say, separate correlations for predicting the
relation between the liquid mass diffusivities and the properties of the liquid solution
will be required for electrolytes and non- electrolytes.
Wilke and Chang have proposed the following correlation for non-electrolytes in an
infinitely dilute solution:
Where DAB is the mass diffusivity of A diffusing through liquid solvent B, in cm2/s;
is the viscosity of the solution, in centipoises; T is absolute temperature, in K; MB is
the molecular weight of the solvent; VA is the molal volume of solute at normal
boiling point in cm3/g mol; and ɸB is the "association" parameter for solvent B.
Molecular volumes at normal boiling points, VA, for some commonly encountered
compounds, are tabulated in Table (1). For other compounds, the atomic volumes of
each element present are added together as per the molecular formulas. Table (2)
lists the contributions for each of the constituent atoms.
Table (1): Molecular volumes at normal boiling point for some commonly
encountered compounds
Table (2): Atomic volumes for complex molecular volumes for simple substances
Recommended values of the association parameter, ɸB, are given below for a few
common solvents.
EXAMPLE 2:
Estimate the liquid diffusion coefficient of ethanol, C2H5OH, in a dilute solution of water
at 10°C. At 10 °C, the viscosity of a solution containing 0.05 mol of alcohol/liter of water
is 1.45 centipoises.
SOLUTION:
The molecular volume of ethanol may be evaluated by using values from the previous
Table as follows:
VC2H5OH = 2VC + 6VH + VO
= 2(14.8) + 6(3.7) + 74 = 59.2 cm3/mol
The remaining parameters to be used are T = 283K for water = 2.26 and MB for water =
18.
Substituting these values into the following equation:
This value is in good agreement with the experimental value of 8.3 x 10 -10 m2/s
Appendix J. Let us compare this value of the liquid diffusivity of ethanol in a dilute
solution of water 7.96 x10 -6cm2/s, with the value of the gas diffusivity of ethanol in air at
10 °C and 1 atm pressure 0.118cm2/s. This emphasizes the order of magnitude difference
between the values of the liquid and gas diffusivities.
Performing a similar calculation, the liquid diffusion coefficient of water in an infinite
dilute solution of ethanol at the same 10° C temperature predicts that the diffusion
coefficient DAB is equal to 1.18 x 10-5 cm2/s. It is important to note that liquid
diffusivities DABL and DBAL are not equal as were the gas diffusivities at the same
temperature and pressure.