Understanding Knudsen Diffusion in Mass Transfer Operations
Molecular diffusion involves the movement of individual molecules through a substance due to their thermal energy. Knudsen diffusion occurs in very fine pores at low pressure where the molecule's mean free path exceeds the pore diameter, affecting diffusion rates. The Knudsen number is used to measure this phenomenon, with values >1 indicating its significance. Knudsen diffusion is crucial for gases but not as relevant for liquids due to shorter mean free paths.
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(Prof.) D.K.MEHTA, ASSISTANT PROFESSOR, CHEMICAL ENGINEERING DEPARTMENT, L.E.COLLEGE-MORBI
TOPIC:- Concept of Knudsen diffusivity, its significance and industrial application SUBJECT:-Mass Transfer Operation-I SUBJECT CODE:-3150501
Molecular diffusion Molecular diffusion is concerned with the movement of individual molecules through a substance by virtue of their thermal energy. The molecules moves in zigzag path and it also collides with another molecules where it changes its direction and magnitude The average distance the molecule travels between collisions is it mean free path.
What is Knudsen diffusion If gas diffusion occurs in a very fine pore, particularly at very low pressure, the mean free path of a molecule may be larger than diameter of the passage. Then the collision with the wall becomes more frequent than collision with the other molecules. Then diffusion rate depends on concentration gradient, molecular velocity and diameter of passage. This is known as Knudsen diffusion.
Knudsen Number (Kn):- It is the ratio of free mean path to the diameter of the Pore . = Kn d pore Knudsen Diffusivity(DAA*):- 3 8 u 3 NT = = D * AA M A
But if Kn >1, then d d 8 NT T pore 3 pore 3 = = = 4850 D u d KA pore M M A A If both Knudsen and molecular diffusion exist, then y D N + =1 1 1 1 = + A D D Ae AB KA with B N A For non-cylindrical pores, we estimate = ' 2 D D Ae Ae
Significance The Knudsen number is a good measure of the relative importance of Knudsen diffusion. A Knudsen number much greater than one indicates Knudsen diffusion is important. In practice, Knudsen diffusion applies only to gases because the mean free path for molecules in the liquid state is very small, typically near the diameter of the molecule itself.
Industrial application It becomes important when particle size is below 50 nm. It is occurs commonly for intra-particle transport in a catalyst containing fine pores.
