An Introduction About Diffusion Concept in Mass Transfer

Diffusion it is a phenomena which deal the microscopic movements of the molecules in all the phases, learning and studying the concept of diffusion will help to understand mass transfer operations, chemical reaction engineering and transportation concepts. Kinetic Theory of gases supports the diffusion occurrence in a system,

Diffusion is understood as a process of movement of particles from higher concentration section to lower concentration section of the system. Diffusion of the component is caused by this concentration difference which is called as the concentration gradient. For example when a bottle containing perfume is opened the smell is sensed as the molecules diffuse into the air due the concentration difference, so till the equilibrium is attained these molecules will move all over the room if  a exit fan is present at  top of the room and  push out  the air with some constant flow rate and the with the same flow rate the molecule will  transferred into the system from the bottle.

This concept of molecule behavior is used in separation operation and purification operations as distillation, extraction, absorption, reverse osmosis etc. Diffusion can also be occurred by pressure gradient even with temperature gradient or even with external force field which they act as the activity gradient. Mostly diffusion concept is developed by the physical properties of the molecules. For a system at equilibrium no net diffusion occurs. which is explained as when a molecule diffuse from one phase to another phase in a system containing two phases through an interface,

than at the same time another molecule will diffuse from opposite direction which the net diffusion is set to zero due to the cancellation of the opposite direction, as said this occurs at equilibrium only.


Classification: 
1. Molecular diffusion 
2.Eddy or Turbulent diffusion


Importance of Molecular diffusion:


Due to the thermal energy in a molecule it gains ability to move through another set of molecules in a system is known to be thermal diffusion. So in the same way molecules will tend to travel due to the driving force of concentration difference. To understand this let us discuss with an example which we involve regularly during the rush hour.

Let us consider a road which you want to cross from one side, say ‘A’ at the same time there are group of people waiting to cross the same from the opposite side, say ‘B’. Now when the traffic is halted by the traffic signal, all the sudden you start to move toward the zebra crossing and diffuse into the mass of people who are in hurry as you, things to be considered are:
You cannot move without colliding (facing each other) with any one
You cannot move in straight line, you have to take some zig-zig turn into the gaps between the people,
Finally you will reach the point ‘B’ let us compare to some physical phenomena

  • You will move with some rate i.e. speed
  • The distance you covered is less than the displacement
  • Opposite people also move with some speed or rate
  • Your body weight also will affect the speed you travel, the heavy you are the slow you will move
Finally we have some options from above which could be compared to molecular level,
You will be replaced by the one molecule of the solute in solution ‘A’(which contain high concentration of solute A) and other mass of people will take the position of the solvent molecules present in the solution ‘B’, as you and opposite people cross the road in the same way solute molecule will cross the interface and move into the solution B, at the same time solvent molecules (of solution B which are on opposite side) will cross the interface and move towards the solution A.

Molecule will have the rate as you have so it also cover a distance in zig-zig mode colliding with other molecules, the distance travelled per second will be the rate of diffusion, when certain fixed area is considered along the path which the molecule move than the rate become as the flux which is moles/ (area X time) and this rate depend on the molecular weight also and the number of molecule present which we say as concentration, the rate will exist till the molecule reaches the destination, that is the space in solution B to be occupied sufficiently and saturated with molecules of B, this state is called equilibrium.


Diffusivities (cm2/s) of gases at standard atmospheric pressure, (101.325 KPa), T in Kelvin
  Gas mixture system diffusivity are used for mass transfer calculations and to design the unit operation which involve in handling mass transfer like distillation, absorption etc.
s.no
System
200
273.15
293.15
373.15
473.15
573.15
673.15
1
Ar-CH4
-
-
-
0.306
0.467
 0.657
   0.876
2
Ar-CO

 0.168
0.187
0.290
0.439
 0.615
 0.815
3
Ar-CO2

0.129
0.078
0.235
0.365
0.517
 0.689
4
Ar-H2

0.698
0.794
 1.228
1.876
2.634
3.496
5
Ar-He
0.381
0.645
0.726
1.088
1.617
2.226
2.911
6
Ar-Kr
0.064
0.117
0.134
0.210
0.323
0.456
0.605
7
Ar-N

0.168
0.190
 0.290
 0.439
0.615
0.815
8
Ar-Ne
0.160
0.277
 0.313
 0.475
0.710
 0.979
 1.283
9
Ar-O2

0.166
0.189
 0.285
 0.430
0.600
 0.793
10
Ar-SF6
-
-
-
0.128
0.202
 0.290
0.389
11
Ar-Xe
0.052
0.095
 0.108
0.171
0.264
0.374
0.498
12
CH4-H2
-
-
0.782
1.084
1.648
2.311
 3.070
13
CH4-He
-
-
0.723
 0.992
 1.502
 2.101
 2.784
14
CH4-N2
-
-
0.220
0.317
0.480
0.671
 0.890
15
CH4-O2
-
-
0.210
0.341
0.523
 0.736
 0.978
16
CH4-SF6
-
 -

0.167
0.257
0.363
0.482
17
CO-CO2
    -
    -
0.162
0.250
 0.38


18
CO-H2
0.408
0.686
 0.772
1.162
1.743
2.423
3.196
19
CO-He
0.365
0.619
 0.698
1.052
1.577
2.188
2.882
20
CO-Kr

0.131
0.581
0.227
0.346
0.485
 0.645
21
CO-N2
0.133
0.208
 0.231
 0.336
0.491
 0.673
 0.878
22
CO-O2
-
-
0.202
0.307
 0.462
 0.643
0.849
23
CO-SF6
-
-
-
0.144
0.226
0.323
0.432
24
CO2-C3H8
-
-
0.084
0.133
0.209
--
-
25
CO2-H2
0.315
0.552
0.412
 0.964
1.470
2.066
2.745
26
CO2-H2O
 -
 -
0.162
0.292
0.496
0.741
1.021
27
CO2-He
0.300
0.513
0.400
 0.878
1.321
-
-
28
CO2-N2
-
-
0.160
0.253
0.392
0.553
0.733
29
CO2-N2O
0.055
0.099
0.113
0.177
0.276
-

30
CO2-Ne
0.131
 0.227
 0.199
 0.395
0.603
 0.847
-


s.no
System
200
273.15
293.15
373.15
473.15
573.15
673.15
31
CO2-O2


 0.159
 0.248
0.38
0.535
0.710
32
CO2-SF6



 0.099
 0.155


33
D2-H2
0.631
1.079
 1.219
 1.846
2.778
3.866
5.103
34
H2-He
0.775
1.320
1.490
2.255
3.394
4.726
6.242
35
H2-Kr
0.340
0.601
 0.682
1.053
1.607
2.258
 2.999
36
H2-N2
0.408
0.686
 0.772
1.162
 1.743
2.423
3.196
37
H2-Ne
0.572
0.982
0.317
1.684
 2.541
 3.541
4.677
38
H2-O2

0.692
0.756
1.188
 1.792
 2.497
.299
39
H2-SF6


0.208
0.649
0.998
1.400
1.851
40
H2-Xe

0.513
 0.122
 0.890
1.349
 1.885
2.493
41
H2O-N2


0.242
0.399



42
H2O-O2


0.244
0.403
 0.645
 0.882
1.147
43
He-Kr
0.330
0.559
 0.629
 0.942
 1.404
 1.942
 2.550
44
He-N2
0.365
 0.619
0.698
1.052
1.577
 2.188
2.882
45
He-Ne
0.563
0.948
1.066
1.592
2.362
3.254
 4.262
46
He-O2


0.641
0.697
1.092
1.640
 2.276
47
He-SF6



1.109
0.592
0.871
1.190
48
He-Xe
0.282
0.478
0.538
0.807
1.201
1.655
2.168
49
Kr-N2

0.131
0.149
0.227
0.346
 0.485
0.645
50
Kr-Ne
0.131
0.228
0.258
0.392
0.587
0.812
1.063
51
Kr-Xe   
0.035
0.064
0.073
0.116
0.181
0.257
0.344
52
N2-Ne


0.258
0.483
0.731
1.021
1.351
53
N2-O2


0.202
0.307
0.462
0.643
0.849
54
N2-SF6



0.148
0.231
0.328
0.436
55
N2-Xe

0.107
0.123
0.188
0.287
0.404
0.539
56
Ne-Xe
0.111
0.193
0.219
0.332
0.498
0.688
0.901
57
O2-SF6


0.097
0.154
0.238
0.334
0.441