Mass Transfer

1. Mass Transfer
Presented by:
Mr. E. D. Ahire M.S. PHARM
Assistant Professor,
Divine Collage of pharmacy

2. Contents
2
 Introduction
 Molecular Diffusion
 In Gases
 In Liquid
 Mass Transfer in turbulent & laminar flow
 Interphase Mass Transfer
 Two film theory
 Penetration theory
 Surface Renewal Theory

3. Introduction
3
 Transfer of material from one homogeneous phase to
another with or without phase change
 Complex phenomenon occurs almost in all unit operations
Extraction – transfer of solute
Humidification – transfer of water molecule
Evaporation
Drying
Distillation
simultaneous heat &
mass transfer
 Occurs through different mechanisms such as molecular
diffusion, convection / bulk flow & turbulent mixing

4. Mass Transfer
4
 Movement of the molecule occurs due to
concentration gradient known as molecular
diffusion.
Molecular
Diffusion
LiquidsGases

5. Molecular diffusion in gases
5
partition
 Gas A moves towards chamber B and gas B movestowards chamber
A
 Concentration of A with distance towards chamber B &B
towards A, variation in concentration of component with
distance in the system called concentration gradient
 Movement of molecule A or B occurs due to concentration
gradient known as molecular diffusion
Gas A Gas B
dx
CA decreasing
CB decreasing

6.  Fick’s law:
where,
DAB DBA = diffusivity of A in B & diffusivity of B in A respectively
( cm2/sec)
NA & NB = rate of diffusion (gm.moles/cm2/sec)
dX
(negative sign, as concentration decreases with distance)
NA 
dCA
NA  DAB
dCA
dX
NB  DBA
dCB
dX
For moleculeA For molecule B
6

7. a) Equimolecular Counter diffusion
7
If molecular diffusion is the only mechanism of mass transfer then,
NA = -NB
Consider dPAand dPB are changes in partial pressure of A & B over
element dx. As we assumed that there is no bulk flow, we can say ,
For an ideal gas,
PAV= nA RTwhere,
PA= partial vapor pressure
nA = no. of moles in volume V at temperature T.
R = gas constant
dX d X
dPA

dPB
RT
PA= CA RT ( as CA = nA/ V )
CA 
PA

8. similarly for gas B
BA(as DAB = D =D)
where,
PA1 & PA2 are partial pressures of A at distance X1 & X2
RT dX
NB  
DBA dPBDAB dPA
NA  
RT dX
But for equimolecular counter diffusion NA = -NB, therefore,
NA 
DA B dPA
 
DB A dPB
RT d X RT d X
NA
D X 2
dPA
RTX 1
dX
RT X2  X1
8
D PA2  PA1
NA 

9. b) Diffusion through stationary, non-
diffusing gas
9
 Movement of molecules from liquid or film on drying solids,
occurs to a non-diffusing gas
 Molecule A is moving from the surface to atmosphere due to
conc. gradient in partial pressure but B is not moving towards the
surface
 Therefore, rate of mass transfer of A takes place bymolecular
diffusion & bulk flow

10. c) Molecular diffusion in liquids
10
where,
CA1 & CA2 = concentration of A at point x1 &x2
Diffusivity of liquid are much lesser than diffusivity of gases.
e.g.
diffusivity of gaseous ethanol in air = 0.119 cm2/sec
diffusivity of liquid ethanol in water = 1 × 10-5 cm2/sec
X2 X1
CA2 CA1
NA D
dX
For equimolar counter diffusion,
According to Fick’s law, for diffusion in liquid
NA D
dCA

11. Mass transfer in turbulent &
laminar flow
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 Explained by boundary layer or film theory
 when fluid flows adjacent to the surface forms the
boundary layer
 Considers two regions
 boundary layer
 bulk
• If bulk flows in laminar fashion – rate of mass transfer
given by molecular diffusion equation
• If bulk flow is turbulent – mass transfer depends upon
transfer rate across the boundary layer

12.  Boundary layer consist of 3 sub layers
 Laminar sub layer adjacent to surface
 Buffer / transient sub layer
 Turbulent region towards the bulk of fluid
Turbulent layer : eddies move under inertial forces causing
mass transfer. The rate of mass transfer is high and conc.
gradient is low
Buffer layer : Combination of eddy and molecular diffusion
responsible for mass transfer
Laminar sub layer : molecular diffusion is the only
mechanism of mass transfer. Concentration gradient is
high and rate of mass transfer is low
 The rate of mass transfer can be estimated by considering a
film which offers the resistance equivalent to boundary layer.12

13. Let,
PAi = partial pressure of A at surface
PAl
= partial pressure of A at laminar sub layer
According to Fick’s law for diffusion,
We know, therefore
where, CAi & CAb concentration of A on either side of the film.
X'
of thickness X
PAb= partial pressure of A at the edge of
boundary layer.
conc.gradient=
PAi – PAb
.
13
RT X'
D PAi – PAb
NA 
X’ is not known , hence kg constant known as mass transfer coefficient isintroduced.
RT
CA 
PA
NA  kg.CAi CAb

14. Interphase Mass Transfer
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 Involves two phase mass transfer
e.g. distillation, liquid-liquid extraction
 Different theories involved
 Two film theory
 Penetration theory
 Surface Renewal theory

15. Two film theory
15
 Theory has been developed by Nernst, Lewis and Whitman
 Postulates that two non-turbulent fictitious films are present
on either side of the interface between the film
 Mass transfer across these films purely occurs
molecular diffusion
 Total resistance for mass transfer is summation of
resistance of two films

16. Let,
pAg = partial pressure of A in the bulk of gas
pAi = partial pressure of A in gas at the interface
CAi = concentration of A in liquid at interface
CAl = concentration of A in the bulk of liquid
kg & kl = mass transfer coefficients of individual
films of gas & liquid respectively
But difficult to know pAi and CAi.
Hence concept of overall mass transfer coefficient
is used.
pAe = gas phase partial pressure of A equilibrium
with conc. of A in the bulk of liquid (CAl)
CAe = conc. Of A in the liquid phase equillibrium
with partial pressure of A bulk gas (pAg )
16
KG and KL are overall mass transfer coefficient , by applying Fick’slaw,
or
pA = H CA + b
where, H & b are constant.
NA  KGpAg  pAe  NA  KLCAe CAl 
Equilibrium between two phases ,

17. and process becomes liquid phase controlled.
If A is highly soluble in liquid ( i.e. H is very low ) then KG ≈
kg and process is gas phase controlled
According to this theory, mass transfer is directly proportional to
molecular diffusivity of solute in the phase into which it is going and
inversely proportional to thickness of films
By considering individual film transfer equations and overall mass
transfer equations, equilibrium equations can be developed between
overall and individual phase mass transfer coefficients
1

1

H
KG kg kl
KL HKG Hkg kl

1

1 1

1
kl
17
 If A is less soluble in liquid ( i.e. H is very large ) then KG 
H

18. Penetration theory
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 This theory proposed by Higbie
 considers unsteady state at interface
 Fluid eddies travel from bulk to interface by convection &
remain there for equal but limited period of time
 When eddies comes at interface, solute moves into it by
molecular diffusion & get penetrated into bulk when eddies
moves to bulk
 According to this theory, rate of mass transfer directly
proportional to square root of molecular diffusion and
inversely proportional to exopsure time of eddies at
interface.

19. Surface renewal theory
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 This theory proposed by Dankwort
 Each eddies gets equal exposure time at interface
 Continuous renewal of interface by fresh eddies which
have composition of that bulk
 Turbulent eddies remain at interface for time varying from 0
to ∞ and taken back into bulk phase by convection current
 According to this theory, rate of mass transfer is directly
proportional to square root of molecular diffusivity.

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