Molecular diffusion

Июль 22, 2022

Главная
Медицина
Molecular diffusion

Содержание

2. 2.1 FICK’S LAW Adolf Fick in 1955 first described the molecular diffusion in an isothermal, isobaric
3. Where, JA is the molar flux of component A in the Z direction. CA is the
4. 2.2 Diffusion coefficient The proportionality factor of Fick’s law is called diffusivity or diffusion coefficient which
5. Diffusivity decreases with increase in pressure (DAB∝1/p for moderate ranges of pressures, up to 25 atm)
6. The diffusivity increases with increase in temperature (DAB∝T1.5) because random thermal movement of molecules increases with
7. Diffusivity of gas, liquid, and solid The diffusivity is generally higher for gases (in the range
8. Diffusion is almost impossible in solids (in the range of 10-13 m2/s) because the particles are
9. Three models of diffusion process in gas, liquid, and solid phase The density of gas is
10. 2.3 Ratio between heat and molecular diffusivity (Le) The Le number of gas is generally about
11. 2.3 Measurement of gas-phase diffusion coefficient (a) Twin-bulb method
12. Two bulbs are connected by a narrow tube. In the beginning two bulbs are evacuated and
13. where, a is cross sectional area of the connecting tube. If pA1 and pA2 are partial
14. Applying the above boundary conditions, the Equation is integrated to obtain the expression of DAB as
15. (b) Stefan tube method (Diffusion coefficient of steam)
16. Stefan tube consists of a T-tube, placed in a constant temperature bath. Air pump supply air,
17. where, partial pressure of A at liquid surface, pA1 is equal to vapor pressure at the
18. 2.4 Estimation of gas diffusion coefficient where, T is temperature in K MA, MB are molecular
19. Atomic diffusion volume Molecular diffusion volume
20. Please calculate the molecular diffusion coefficient of n-butanol C4H10O (B) diffusing through air (A) at 298.9K
21. Stokes-Einstein Equation Liquid diffusivity varies linearly with absolute temperature and inversely proportional to viscosity of the
22. Semi-empirical Equation: Wilke-Chang Equation
23. 2.6 Diffusion in porous media Porous materials in nature and industry: sand stone, porous rock, filter
24. types of pores –open pores: surface ~, column ~, hollow ~ –isolated pores: inclusion ~
25. Pore size: (generally pore width): the distance between two opposite walls of the pore –Micropores (
26. Diffusion phenomena in porous solids Molecular diffusion Knudsen diffusion Surface diffusion –not of technical importance Configurational
28. Molecular diffusion (Collision principle) The probability of collision between molecules and molecules is very high, while
29. The following table lists some typical values for air at different pressures at room temperature.
30. Knudsen diffusion (Collision principle) Surface diffusion (Adsorption principle) Adsorption balance is established in the walls. The
31. Configurational diffusion –pore diameter within molecular dimensions (0.3-1 nm) as for zeolites –diffusion coefficients are smaller
33. Скачать презентацию

Слайд 2

2.1 FICK’S LAW
Adolf Fick in 1955 first described the

molecular diffusion in an isothermal, isobaric binary system of components A and B. According to his idea of molecular diffusion, the molar flux of a species relative to an observer moving with molar average velocity is proportional to the concentration gradient in a certain direction..

Слайд 3

Where, JA is the molar flux of component A in the

Z direction. CA is the concentration of A and Z is the distance of diffusion. The proportionality constant, DAB is the diffusion coefficient of the molecule A in B. This is valid only at steady state condition of diffusion. The diffusivity of A in B equals the diffusivity of B in A, i.e., DAB=DBA

Слайд 4

2.2 Diffusion coefficient
The proportionality factor of Fick’s law is called

diffusivity or diffusion coefficient which can be defined as the ratio of the flux to its concentration gradient and its unit is m2/s. It is a function of the temperature, pressure, nature and concentration of other constituents.

Слайд 5

Diffusivity decreases with increase in pressure (DAB∝1/p for moderate ranges

of pressures, up to 25 atm) because number of collisions between species is less at lower pressure. But the diffusivity is hardly dependent on pressure in case of liquid.

Relationship between diffusivity and pressure

Слайд 6

The diffusivity increases with increase in temperature (DAB∝T1.5) because random

thermal movement of molecules increases with increase in temperature.

Relationship between diffusivity and temperature

Слайд 7

Diffusivity of gas, liquid, and solid
The diffusivity is generally higher

for gases (in the range of 0.5×10-5 to 1.0 × 10-5 m2 /s) than for liquids (in the range of 10-10 to 10-9 m2 /s).

Слайд 8

Diffusion is almost impossible in solids (in the range of

10-13 m2/s) because the particles are too closely packed and strongly held together with no ‘empty space’ for particles to move through. Solids diffuse much slower than liquids because intermolecular forces in solid are stronger enough to hold the solid molecules together.

Слайд 9

Three models of diffusion process in gas, liquid, and solid phase
The

density of gas is three orders of magnitude lower than that of liquid or solid.

Слайд 10

2.3 Ratio between heat and molecular diffusivity (Le)
The Le number

of gas is generally about 1. This means that when gas undergoes transient heat and molecular diffusion, the variations of heat and molecular diffusion distribution are approximately the same. However, for liquid and solid, thermal conductivity is much faster than molecular diffusion.

Слайд 11

2.3 Measurement of gas-phase diffusion coefficient
(a) Twin-bulb method

Слайд 12

Two bulbs are connected by a narrow tube. In the

beginning two bulbs are evacuated and all the three valves [V1, V2 and V3] are kept closed. Then V2 is opened and bulb 1 is filled with pure A at a pressure P. After that V3 is opened and bulb 2 is filled with pure B at the same pressure P. Finally, V1 is opened. At steady state

Слайд 13

where, a is cross sectional area of the connecting tube. If

pA1 and pA2 are partial pressures of A in two bulbs at any time, then

From the above three equations, we have

Слайд 14

Applying the above boundary conditions, the Equation is integrated to obtain

the expression of DAB as follows:

Слайд 15

(b) Stefan tube method (Diffusion coefficient of steam)

Слайд 16

Stefan tube consists of a T-tube, placed in a constant

temperature bath. Air pump supply air, passed through the T-tube. Volatile component (A) is filled and change in the level is observed by a sliding microscope. At any time t, partial pressure of A at the top of the vertical tube is pA1 and that at the liquid surface is pA2. The diffusional flux of A is given as:

Слайд 17

where, partial pressure of A at liquid surface, pA1 is equal

to vapor pressure at the same temperature. The partial pressure of A at the top of the vertical tube, pA2 is zero due to high flow rate of B.

Слайд 18

2.4 Estimation of gas diffusion coefficient
where, T is temperature in K

MA, MB are molecular weights of A and B
P is total pressure in bar
νA, νB are atomic diffusion volume in m3.

Слайд 19

Atomic diffusion volume
Molecular diffusion volume

Слайд 20

Please calculate the molecular diffusion coefficient of n-butanol C4H10O (B) diffusing

through air (A) at 298.9K and 1.0 atm. (The measured value is 8.60×10-6 m2/s.)

Слайд 21

Stokes-Einstein Equation
Liquid diffusivity varies linearly with absolute temperature and inversely

proportional to viscosity of the medium. Hence,

2.5 Estimation of liquid-phase diffusion coefficient

Слайд 22

Semi-empirical Equation: Wilke-Chang Equation

Слайд 23

2.6 Diffusion in porous media
Porous materials in nature and industry: sand

stone, porous rock, filter paper, nano tubes….
main feature: cavities in a solid matrix, cavities are partly or fully connected, and accessible for probe molecules.
porosities are often desired and of importance in medicine, membranes, sorbents, ceramics, and catalysts.

Слайд 24

types of pores
–open pores: surface ~, column ~, hollow ~

–isolated pores: inclusion ~

Слайд 25

Pore size: (generally pore width): the distance between two opposite walls

of the pore
–Micropores (< 2 nm)
–Mesopores (2-50 nm)
–Macropores (> 50 nm)

Слайд 26

Diffusion phenomena in porous solids
Molecular diffusion
Knudsen diffusion
Surface diffusion

–not of technical importance
Configurational diffusion
–pore diameter within molecular dimensions (0.3-1 nm) as for zeolites
–diffusion coefficients are smaller by some orders of magnitude

Слайд 27

Слайд 28