The document discusses various mechanisms of mass transfer including molecular diffusion in gases and liquids, mass transfer in turbulent and laminar flow, and interphase mass transfer. Molecular diffusion is the movement of molecules due to a concentration gradient. Fick's law describes the rate of diffusion. Mass transfer in fluids occurs across a boundary layer near the surface via molecular diffusion or eddies. Interphase transfer theories include the two film theory, penetration theory, and surface renewal theory which describe mass transfer across interfaces.

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
11
 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
14
 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
18
 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
19
 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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