‫جامعه فاروس‬
‫كلية الهندسة‬
‫قسم البتروكيماويات‬
Pharos University
Faculty of Engineering
Petrochemical Department
MASS TRANSFER
LECTURE (4)
1.SOLID MASS DIFFUSIVITY:
The diffusion of atoms within solids underlies the synthesis of many engineering
materials. In semiconductor manufacturing processes, "impurity atoms," commonly
called dopants, are introduced into solid silicon to control the conductivity in a
semiconductor device. The hardening of steel results from the diffusion of carbon and
other elements through iron. Vacancy diffusion and interstitial diffusion are the two
most frequently encountered solid diffusion mechanisms.
In vacancy diffusion, the transported atom jumps from a lattice position of the solid into
a neighboring unoccupied lattice site or vacancy. The atom continues to diffuse through
the solids by a series of jumps into other neighboring vacancies that appear to it from
time to time. This normally requires a distortion of the lattice. An atom moves in
interstitial diffusion by jumping from one interstitial site to a neighboring one. This
normally requires a dilation or distortion of the lattice. The solid phase diffusion
coefficient has been observed to increase with increasing temperature according to an
Arrhenius equation of the form:
DAB = DO
Or
ln (DAB)
= * + ln (DO)
Where:




DAB: Solid diffusion coefficient for the diffusing species A within solid B.
DO: Proportionality constant of units consistent with DAB.
Q: Activation energy (J/mol)
R: Thermodynamic constant (8.314 J/ mol.K).
 T: Absolute temperature (K).
The following two tables show the diffusion data needed to evaluate DAB by the previous
equation for self diffusion in pure metals and interstitial solutes in iron.
Table (1): Data for self diffusion in pure metals
Structure
fcc
fcc
fcc
fcc
bcc
bcc
Metal
Au
Cu
Ni
Fe (γ)
Fe (α)
Fe (δ)
Do(mm2/s)
10.7
31
190
49
200
1980
Q (kJ/mole)
176.9
200.3
279.7
284.1
239.7
238.5
Table (2): Data for diffusion parameters for interstitial solutes in iron:
Structure
bcc
bcc
bcc
fcc
Solute
C
N
H
C
Do(mm2/s)
2
0.3
0.1
2.5
Q (kJ/mole)
84.1
76.1
13.4
144.2
EXAMPLE (1):
The case hardening of mild steel involves the diffusion of carbon into iron. Estimate the
diffusion coefficient for carbon diffusing into fcc iron and bcc iron at 1000K.
SOLUTION:
Case (I):
Carbon in fcc iron at 1000 K:
By applying the following equation:
DAB = DO
Do =2.5*10-6 (m2/s)
Q =144.2 (kJ/mole)
DAB =2.5*10-6 *
= 7.34*10-10 m2/s
Case (II):
Carbon in bcc iron at 1000 K:
By applying the following equation:
DAB = DO
Do =2*10-6 (m2/s)
DAB =2*10-6 *
Q =84.1 (kJ/mole)
= 8.09*10-9 m2/s
Note: The DAB in case of bcc iron is higher than in fcc one.
2. CONVECTIVE MASS TRANSFER:
Mass transfer between a moving fluid and a surface or between immiscible moving fluids
separated by a mobile interface (as in a gas/liquid or liquid/liquid contactor) is often
aided by the dynamic characteristics of the moving fluid. This mode of transfer is called
convective mass transfer, with the transfer always going from a higher to a lower
concentration of the species being transferred. Convective transfer depends on both the
transport properties and the dynamic characteristics of the flowing fluid.
As in the case of convective heat transfer, a distinction must be' made between two types
of flow. When an external pump or similar device causes the fluid motion, the process is
called forced convection. If the fluid motion is due to a density difference, the process is
called free or natural convection.
The rate equation for convective mass transfer, generalized in a manner analogous to
Newton's "law" of cooling as follows:
NA = kc ∆cA
Where:
 NA: is the molar mass transfer of species A measured relative to fixed spatial
coordinates.
 ∆cA: is the concentration difference between the boundary surface concentration
and the average concentration of the fluid stream of the diffusing species A (CAsCA∞).
 kc: is the convective mass transfer coefficient.
As in the case of molecular mass transfer, convective mass transfer occurs in the
direction of a decreasing concentration. The reciprocal of the coefficient, 1/kc represents
the resistance to the transfer through the moving fluid.
Kc, in general, is a function of system geometry, fluid and flow properties, boundary
conditions, and the concentration difference ∆cA. From our experiences in dealing with a
fluid flowing past a surface, we can recall that there is always a layer, sometimes
extremely thin, close to the surface where the fluid is laminar, and that fluid particles next
to the solid boundary are at rest. As this is always true, the mechanism of mass transfer
between a surface and a fluid must involve molecular mass transfer through the stagnant
and laminar flowing fluid layers. The controlling resistance to convective mass transfer is
often the result of this "film" of fluid and the coefficient, kc, is accordingly referred to as
the film mass-transfer coefficient .It is important to recognize the close similarity
between the convective mass-transfer coefficient and the convective heat-transfer
coefficient.
EXAMPLE (2):
Air flows over a solid slab of frozen carbon dioxide (dry ice) with an exposed cross
sectional surface area of 1*10-3 m2. The carbon dioxide sublimes into the 2 m/s flowing
stream at a total release rate of 2.29*10-4 mol/s. The air is at 293 K and 1.013*105 Pa
pressure. At that temperature, the diffusivity of CO2 in air is 1.5*10-5 m2/s and the
kinematic viscosity of the air is 1.55*10-5 m2/s. Determine the value of the mass transfer
coefficient of CO2 subliming into the flowing air under the conditions of the experiment.
SOLUTION:
By applying the previous equation:
NA = kC ∆cA
NA= kc (CAs- CA∞)
kc =
=
At 293 K and 1.013*105 Pa:
CAs=
=
= 1.946 mol/m3
If we assume CA∞ = 0:
kc =
=
= 0.118 m/s.