An Introduction To Diffusion Concept in Mass Transfer | Mass Transfer — Introduction to Chemical and Biological

Diffusion is a phenomenon that deals with the microscopic movements of 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. The Kinetic Theory of gases supports the diffusion that occurs in a system,

Diffusion is understood as a process of movement of particles from a higher concentration section to a lower concentration section of the system. Diffusion of the component is caused by this concentration difference which is called the concentration gradient. For example, when a bottle containing perfume has opened the smell is sensed as the molecules diffuse into the air due to the concentration difference, so till the equilibrium is attained these molecules will move all over the room if an 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 transfer into the system from the bottle.

This concept of molecule behavior is used in separation operation and purification operations such as distillation, extraction, absorption, reverse osmosis, etc. Diffusion can also be occurred by a pressure gradient even with a temperature gradient or even with an external force field that acts 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 diffuses from one phase to another phase in a system containing two phases through an interface, then at the same time another molecule will diffuse from the 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 the 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 an example in which we involve regularly during rush hour.

Let us consider a road that you want to cross from one side, say ‘A’ at the same time there are a 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 anyone
You cannot move in a straight line, you have to take some zig-zig turns into the gaps between the people,
Finally, you will reach point ‘B’ let us compare to some physical phenomena

You will move at 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 at you travel, the heavy you are slow you will move

Finally, we have some options from above which could be compared to the molecular level,
You will be replaced by the one molecule of the solute in solution ‘A’(which contains a high concentration of solute A) and another mass of people will take the position of the solvent molecules present in 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 the opposite side) will cross the interface and move towards the solution A.

The molecule will have the rate you have so it also covers a distance in zig-zig mode colliding with other molecules, the distance traveled per second will be the rate of diffusion, when a certain fixed area is considered along the path which the molecule move then the rate become as the flux which is moles/ (area X time) and this rate depending 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 is used for mass transfer calculations and to design the

the unit operation which involves 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