Knudsen effect

Gurgel and Grenier s results showed the bed conductivity to increase from 0.14 to 0.17 W/mK as the pressure was raised from 4 mbar (evaporating pressure) to 110 mbar (condensing pressure). The principle reason stated for this small variation is the reduction in the gas conductivity with decreasing pressure (Knudsen effect) in the macropores. The solid grain conductivity varied linearly from 0.61 to 0.65 W/mK as the methanol concentration varied from 0 to 31%. 

Collisions of molecules with the walls of the passage provide the resistance to diffusion when the mean free path, A, is appreciably greater than the diameter, d, of the passage. In experimental work the ratio, A/d, is taken as 10 or more to isolate the Knudsen effect. That investigator did experiments with small capillaries and deduced the equation... 

Diffusivity in Pores and Fick s Laws Diffusion in Gas-Filled Pores Knudsen Effect Diffusion in Liquid-Filled Pores Renkin Effect Diffusion in the Unsaturated Zone of Soils... 

In liquids, the mean free path is typically of the order of 10 10 m. Hence the Knudsen effect is not important (i.e., diffusing molecules collide with solvent molecules long before they typically arrive at a pore wall). However, diffusion is affected by a different mechanism, the viscous drag caused by the pore walls. This is known as the Renkin effect (Renkin, 1954). In essence, the ratio of pore diffusivity in the liquid-filled pore space and diffusivity in the free liquid, D(pore/D,free, is a function of the nondimensional parameter... 

This is expected to happen when the mean free path (A) of the gas becomes comparable to the space between the particles ( ) of the assemblage. Since the true size of the space between the particles is not known, we assume it to be equal to the diameter of the microparticle (d ) as a first approximation. The Knudsen effect has, however, been observed at much higher pressures where d, (32]. 

A particular example of the application in equation (2.8) is the Knudsen effect for the stationary state of the vessels with the same rarefied ideal gases at various temperatures and a small hole between the vessels. The small... 

At low gas pressures and for small pore size, the mean free path of the gas molecules may be on the order of the pore size and therefore velocity slip occurs (Knudsen effect), resulting in higher permeabilities. However, an increase in the permeability due to an increase in gas pressure has been found in some experiments. Scheidegger [24] discusses the effect of the Knudsen slip, the internal surface roughness, surface absorption, capillary condensation, and molecular diffusion on the measured permeability. By examining these effects at the pore level, it becomes clear that the measured gas and liquid permeabilities can be noticeably different. 

Trugo, L.C. C.M. Donangelo N.M.F. Trugo K.E. Bach Knudsen. Effect of heat treatment on nutritional quality of germinated legume seeds. /. Agric. Food Chem. 2000, 48, 2082—2086. 

Just as microporous foams present better properties than conventional foams, it is expected that nanoporous foams will present enhanced properties because of their lower pore size. For instance, they could have better mechanical properties, such as better toughness, higher impact energies, and strain to failure [26], In addition, they could present an improved thermal insulation behavior because of the Knudsen effect [27], More details about the expected properties of nanoporous polymer foams will be provided in the last section of this chapter. 

Reprinted from B. Notario, et ah, Experimental validation of the Knudsen effect in nanoceUu-lar polymeric foams, Polymer, 56 (2015) 57-67 with permission from Elsevier. 

For many years the direct probe for introducing samples into the spectrometer has dominated all the others. The sample is transferred into a small cup with a volume of a few microliters, made of gold, silica, or aluminum. Some of them have a cap with a small hole to exploit the Knudsen effect for controlled evaporation. The cup is placed in the tip of the removable probe. The probe is introduced into the ion source housing with the sam-... 

The effective diffusivity value determined from the numerical solution of Eq. 9.11 neglects the Knudsen effects. In general this is acceptable, if the Knudsen number (Kn), defined below, is small ... 

As the mean free path of a gas is in the order of 100 nm, Kn is small for the carbon paper GDL and the Knudsen effect can be neglected. But pore sizes inside the MPL are of the same order of magnitude as the mean free path of the gas and thus Knudsen effects have to be taken into account. The Knudsen diffusion effect in the MPL was investigated by Becker et al. by applying Bosanquet s formula " ... 

The low gas thermal conductivity Agas of aerogels in general can be explained by the Knudsen effect, expressing the gas conduction in a porous media as function of the air pressure and the characteristic pore size and written in a simplified way as follows (see also Figure 45.3) [31,69-71] ... 

Research is also ongoing to develop new high-performance thermal insulation materials, for example, nano insulation materials (NIM) [31,69,70,103-114] that utilize the Knudsen effect to achieve their low thermal conductivity without applying a vacuum in the pores. One possible pathway toward NlMs is to... 

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