Jorge H. Sánchez, UPB
Chapter 6
Introduction to Convective and
Interphase Mass Transfer
Jorge H. Sánchez, UPB
Introduction
Convective mass transfer involves the transport of material between a boundary surface and a moving fluid.
When the mass transfer involves a solute dissolving into a moving fluid, we can define a convective mass
transfer coefficient by an equation analogous to Newton’s law of cooling:
N A = kc ( c A,i − c A, )
Where cA,i is the composition of the solute in the fluid of
interest at the interface (in equilibrium at T and P), and cA,
represents the composition at some point within the fluid phase.
Jorge H. Sánchez, UPB
Introduction
Consider the mass transfer of a solute A from a solid to a fluid flowing past the surface of the solid
c A,i − c A,
The mass transfer at the surface is by molecular diffusion
y
c A,i − c A = f ( y )
Concentration boundary layer
N A = kc ( c A,i − c A, )
N A = − DAB
dc A
dy
y =0
Therefore, combining the equations we obtain
kc =
− DAB ( dc A dy ) y =0
(c
A,i
− c A , )
Jorge H. Sánchez, UPB
Individual mass transfer coefficients
Table shown below provides the definitions of the most often encountered individual-phase mass
transfer coefficients, based on the phase and the dependent variable used to describe the masstransfer driving force.
Jorge H. Sánchez, UPB
Dimensional Analysis
 v Lc
Re =

 gL3c 
Gr =
2

Sc =
 DAB
Sh =
kc Lc
DAB
Forced convection
Natural convection
Sh = f ( Re,Sc )
Sh = f ( Gr,Sc )
Reynolds number
Grashof number
Schmidt number
Sherwood number
Jorge H. Sánchez, UPB
Boundary layer theory
c A
+   ( c A v m ) = DAB 2c A + RA
t
c A
 cA
m c A
v
+ vy
= DAB
x
y
y 2
2
m
x
Sh x = 0.332 Re1x 2 Sc1 3


Sh L = 0.664 Re1 2 Sc1 3
 Re c = 5  105 


 Sc  1.0

Jorge H. Sánchez, UPB
Example
In a manufacturing process, an organic solvent (methyl ethyl ketone, MEK) is used to dissolve a thin coating of a
polymer film away from a nonporous flat surface of length 20 cm and width 10 cm, as shown in the figure. The
thickness of the polymer film is initially uniform at 0:20 mm (0.02 cm). In the present process, a volumetric flow rate
of 30 cm3/s of MEK liquid solvent is added to an open flat pan of length 30 cm and width 10 cm. The depth of the
liquid MEK solvent in the pan is maintained at 2.0 cm. It may be assumed that the concentration of dissolved polymer
in the bulk solvent is essentially zero even though in reality the concentration of dissolved polymer in the solvent
increases very slightly from the entrance to the exit of the pan. It may also be assumed that the change film thickness
during the dissolution process does not affect the convection mass transfer process. Let A = polymer (solute), B =
MEK (liquid solvent).
Jorge H. Sánchez, UPB
Log-mean concentration difference
When the driving force change along the mass
transfer surface, the log-mean concentration
difference should be used to calculate the total
mass flow rate:
ÑA
(y
A,i
− y A ) LM =
total
(y
= S ky
A,i
(y
A,i
− y A ) LM
− y A )bottom − ( y A,i − y A ) top
 ( y A,i − y A )

bottom 
Ln 
 ( y A,i − y A ) top 


Jorge H. Sánchez, UPB
Interphase mass transfer
In the previous topics we have discussed the transfer of mass within a single phase. Many mass-transfer operations,
however, involve the transfer of material between two contacting phases. These phases may be a gas stream contacting a
liquid, two liquids streams if they are immiscible, or a fluid flowing past a solid.
Equilibrium – Transport of mass by either molecular or convective
transport mechanism depends upon the concentration gradient of the
diffusing species. Transfer between two phases requires a departure from
equilibrium of the average or bulk concentration within each phase.
Raoult’s law (liquid phase is ideal)
p A = x A p Av
Henry’s law (dilute solutions)
Distribution law (immiscible liquids)
p A = Hc A
c A,1 = Kc A,2
Jorge H. Sánchez, UPB
Two-resistance theory
Interphase mass transfer involves three steps:
1. Transfer from the bulk of one phase to the
interfacial surface,
2. Transfer across the interface into the second
phase, and
3. Transfer to the bulk of the second phase.
Initially suggested by Lewis and Whitman (1924) has
two principal assumptions:
1. The rate of mass transfer is controlled by the rates
of molecular transport through two stagnant films
on each side of the interface.
2. No resistance is offered to the transfer of the
diffusing component across the interface.
Jorge H. Sánchez, UPB
Overall mass transfer coefficients
Individual mass-transfer coefficients
N A = k y ( y A − y A,i )
N A = k x ( x A,i − x A )
k x y A − y A,i
− =
k y x A − x A,i
Overall mass-transfer coefficients
(
(x
)
)
N A = K y y A − y *A
NA = Kx
*
A
− xA
1
1
m

=
+
 K
ky
kx
y

Total resistance gas film resistance liquid film resistance
 1
1
1
=
+

 K x mk y k x
Jorge H. Sánchez, UPB
Example
In an experimental study of the absorption of NH3 by water
in a wetted-wall column, the value of KG was found to be
2.7810-4 kmol/(m2satm). At one point in the column, the
gas contained 8 mol% NH3 and the liquid phase
concentration was 0.14 mol/m3 of solution. The temperature
was 20ºC, and the total pressure was 1 atm. 85% of the total
resistance to the mass transfer was found to be in the gas
phase.
If Henry’s constant is 0.004 atm/(mol NH3/m3 of solution),
calculate the individual film coefficient and the interfacial
compositions.
Jorge H. Sánchez, UPB
Example
Consider the waste treatment operation proposed in the figure below. In this process, wastewater containing a TCE concentration of 50
gmol/m3 enters a clarifier, which is essentially a shallow, well-mixed tank with an exposed liquid surface. The overall diameter is 20 m
and the maximum depth of the liquid in the tank is 4 m. The clarifier is enclosed to contain the gases (often quite odorous) that are
emitted from the wastewater. Fresh air is blown into this enclosure to sweep away the gases emitted from the clarifier and is then sent to
an incinerator. The TCE content in the effluent gas is 4.0 mol%, whereas the TCE content in the effluent liquid phase is 10 gmol
TCE/m3 liquid. The clarifier operates at 1.0 atm and a constant temperature of 20ºC.
In independent pilot plant studies for TCE, the liquid film mass transfer coefficient for the clarifier was, kx = 200 gmol/m2s, whereas
the gas film mass transfer coefficient for the clarifier was ky = 0.1 gmol/m2s. Equilibrium data for the air–TCE–water system at 20ºC
are represented by Henry’s law in the form pA = HxA with H = 550 atm. The molar density of the effluent liquid is 66 gmol/m3.
a. What is the overall mass-transfer coefficient based on the liquid phase, KL?
b. What is the flux of TCE from the clarifier liquid surface?
c. What is the inlet volumetric flow rate of wastewater, in units of m3/h, needed to ensure that the liquid effluent TCE
concentration is 10 gmol TCE/m3?