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Knudsen number sensitivity to pressure drop in a nanoscale membrane.

Ramalan, Muktar M.; Prabhu, Radhakrishna; Hashm, Idris; Ogunlude, Priscilla; Aisueni, Florence; Abunomah, Ofasa; Gobina, Edward


Priscilla Ogunlude

Ofasa Abunomah

Edward Gobina


According to the kinetic theory of gases, gas molecules are in constant random motion and frequently collide with one another and with the walls of their container. They continuously experience changes in velocity and direction. Between collisions, molecules move in a straight line at a constant velocity. The actual path length between two successful collisions of a molecule, known as a free path, cannot be established as its calculation requires the knowledge of the path of every molecule in a containment system. The average of all the path lengths between collisions is known as the mean free path (λ). Unlike free path, mean free path is measurable and it is a better measure of the random motion of gas molecules in a gaseous system which is very difficult to measure directly. However, the finding relating to pressure drop with Knudsen number (Kn) in a nanoparticle is limited. This study focuses on understanding the pressure gradient in a nonporous membrane structure and calculating the mean free path. The Knudsen number of selected gases was plotted against pressure drop at 1000C for the three gases and generated several plots. Each plot represents the profile of the respective Knudsen number of the gases in membranes with a pore size of 15nm, 200nm and 600nm respectively. The investigation established that there is an inverse relationship between Kn and Pressure. The correlation is strong as indicated by the R2 of 0.89. The three gases show a dramatic relationship of Kn with pressure in the 15nm pore membrane. The rate of change or slopes of Kn with pressure is higher for all the gases in 15nm than for the 200nm and 6000nm pore sizes. Kn for H2 has the most response to pressure in the 15nm with a response of -0.70 Kn/KPa, followed by CO2 (-0.54 Kn/KPa) and Air (-0.37 Kn/Kpa). The lowest magnitude of Kn at the extended experimental pressure 300KPa is compared and a qualitative deduction can be drawn that the Kn/KPa parameter dampens as the pore size increases.


RAMALAN, M.M., PRABHU, R., HASHM, I., OGUNLUDE, P., AISUENI, F., ABUNOMAH, O. and GOBINA, E. 2022. Knudsen number sensitivity to pressure drop in a nanoscale membrane. In Proceedings of the 2nd International congress on scientific advances 2022 (ICONSAD'22), 21-24 December 2022, [virtual conference]. Turkey: ICONSAD [online], pages 276-281. Available from:

Conference Name 2nd International congress on scientific advances 2022 (ICONSAD'22)
Conference Location [virtual conference]
Start Date Dec 21, 2022
End Date Dec 24, 2022
Acceptance Date Dec 7, 2022
Online Publication Date Dec 9, 2022
Publication Date Jan 6, 2023
Deposit Date Jan 18, 2023
Publicly Available Date Feb 21, 2023
Publisher ICONSAD (International congress on scientific advances)
Pages 276-281
Book Title Proceedings of the 2nd International congress on scientific advances 2022 (ICONSAD'22)
ISBN 9786057363954
Keywords Ceramic membrane; Pore size; Pressure; Knudsen number; Mean-free path
Public URL
Publisher URL


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