Experimental and theoretical study on multicomponent diffusion of gases under rarefied conditions
Final Report Abstract
Multicomponent diffusion of gases in confined geometries at microscale and nanoscale is determining both behavior and efficiency of many natural and technical processes. Consequently considerable enhancement of the performance of processes such as membrane gas separation, heterogeneous catalysis, and microelectromechanical systems requires an understanding of gaseous flows at the small scales. The smaller the scale, the more the gas is in a state referred to as rarefied where diffusion is the dominating, and hence limiting, transport mechanism. Thus the performance at macroscale can depend on gaseous rarefaction (quantified by Knudsen number, Kn), which in turn determines multicomponent diffusion. Multicomponent diffusion of gases is well known for uniform geometries as demonstrated in the socalled two-bulb-diffusion experiment of Duncan and Toor. We successfully reproduced their experiment and repeated it with tapered instead of uniform ducts which was done for the first time. It was shown that the gaseous transport in tapered ducts is reduced compared to the transport through a uniform channel with the same average cross section 𝐴̅ and length 𝐿. The diffusion delay occurs due to the change in concentration gradient along the duct. The mean driving gradient is highest when the tube is uniform and thus the gradient is linear. Consequently for gaseous diffusion in “real” pores, that are typically somehow tapered, the transport limitation is even more serious than considered so far. Basing on the Maxwell-Stefan equations a model was developed that shows very good agreement with the experimental results under non-rarefied conditions and considers the taperedness of ducts. The intended experiments of multicomponent diffusion under gaseous rarefaction were not accomplished because contamination occurred in the downscaled set-up due to degassing from plastic components. As an alternative, we developed a steady-state experiment and found that the volumetric flow rate used there is inversely proportional to the experimental duration in the transient two-bulbdiffusion experiment. The steady-state experiment was only tested under non rarefied conditions but the approach is promising for realizing the multicomponent diffusion experiments under gaseous rarefaction in the future because experimental time is reduced significantly and hence contamination problems can be avoided. For tapered ducts we also demonstrated a phenomenon which we called gas flow diode effect. In corporation with the Aix-Marseille University we found the physical explanation of this effect. The effect bases on the tangential momentum accommodation and reflection process of gas molecules colliding with the inclined walls of a tapered channel. Further we found that the effect crucially depends on the proportion of inclined walls to the overall channel inner surface. The inclination of the wall determines the strength of the diode effect meaning that the diodicity increases with the opening angle. Molar mass and internal structure of the impinging molecules have an influence on the diodicity: a high molar mass in a monoatomic structure of the gas molecules promotes the diode effect.
Publications
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(2015). Multicomponent gas diffusion in nonuniform tubes. AIChE J. 61, 1404-1412
Veltzke T, Kiewidt L, Thöming J
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(2016). A physical explanation of the gas flow diode effect. Microfluid and Nanofluid 20, 145
Graur I, Meólans JG, Perrier P, Thöming J, Veltzke T
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(2016). Delayed binary and multicomponent gas diffusion in conical tubes. Chem. Eng. Sci. 148, 93-107
Veltzke T, Pille F, Thöming J
