Collision molecule-wall

When Che diameter of the Cube is small compared with molecular mean free path lengths in che gas mixture at Che pressure and temperature of interest, molecule-wall collisions are much more frequent Chan molecule-molecule collisions, and the partial pressure gradient of each species is entirely determined by momentum transfer to Che wall by mechanism (i). As shown by Knudsen [3] it is not difficult to estimate the rate of momentum transfer in this case, and hence deduce the flux relations. 

The Stefan-Maxwell equations have been presented for the case of a gas in the absence of a porous medium. However, in a porous medium whose pores are all wide compared with mean free path lengths it is reasonable to guess that the fluxes will still satisfy relations of the Stefan-Maxwell form since intermolecular collisions still dominate molecule-wall collisions. 

As a first approximation, we can introduce wall collisions by simply introducing separate effectiveness parameters for molecule-molecule and molecule-wall collisions, in which fV3il can be described through kinetic theory as... 

Table 4.2 gives decomposition lifetimes extracted from the flow tube data. Keep in mind that these kinetic data are for conditions in which a combination molecule-buffer gas, molecule-molecule, and molecule-wall collisions occur. The wall surface in the flow tube was quartz, and the slight discoloration observed indicates that there was initially some decomposition on the walls. Note, however, that there was no build-up of material on the walls beyond the initial transparently thin carbonaceous coating, and no products (e.g., polymer fragments) were observed that might be expected from reaction on the walls, or from bimolecular reactions. It appears that the decomposition is dominated by true unimolecu-lar reactions however, collisions with the walls are undoubtedly important in energizing the molecules for dissociation. 

Instead, we must turn to the kinetic molecular theory of gases for an estimate of the frequency with which molecules collide with a solid surface. We shall not be misled, however, if we anticipate that this pressure is low. Example 9.6 is a numerical examination of gas collisions with walls. 

A collision between a gas molecule and a surface sometimes leads to a heterogeneous reaction. We will obtain an expression for the rate of molecule-wall collisions. 

For simulation, a 3-D random walk algorithm was developed to study diffusion-controlled mixing phenomena [160]. Several assumptions were made, i.e. only EOF carries out fluid transport, only neutral and point-like analytes are present and the transport in each dimension is fully independent. An elastic collision mechanism was applied for molecule-wall collisions. The analyte was introduced as a stream of 200 molecules ms-1. 

Diffusion in macropores occurs mainly by the combined effects of bulk molecular diffusion (as in the free fluid) and Knudsen flow, with generally smaller contributions from other mechanisms such as surface diffusion and Poiseuille flow. Knudsen flow, which has the characteristics of a diffusive process, occurs because molecules striking the pore wall are instantaneously adsorbed and re-emitted in a random direction. The relative importance of bulk and Knudsen diffusion depends on the relative frequency of molecule-molecule and molecule-wall collisions, which in turn depends on the ratio of the mean free path to pore diameter. Thus Knudsen flow becomes dominant in small pores at low pressures, while in larger pores and at higher pressures diffusion occurs mainly by the molecular mechanism. Since the mechanism of diffusion may well be different at different pressures, one must be cautious about extrapolating from experimental diffusivity data, obtained at low pressures, to the high pressures commonly employed in industrial processes. 

Continuum diffusion (Kn 1). Hie different species of a mixture move relative to each other under the influence of concentration gradients (ordinary or concentration diffusion), temperature gradients (thermal diffusion) or external forces (forced diffusion). Here molecule-wall collisions are neglected. 

Viscous flow of a pure fluid (Kn 1). The gas acts as a continuum fluid driven by a pressure gradient, and both molecule-molecule collisions and molecule-wall collisions are important. This is sometimes called convective or bulk flow. 

The difference between the DGM and BFM is in the description of molecule-wall collisions. In contrast to the DGM, the BFM does not separate viscous flow and Knudsen diffusion. According to the BFM they are the limiting forms of the same phenomena, described by the second term in the right-hand side of Equation 3.24. For large Knudsen numbers, that is for small pressures and/or small pore sizes,... 

Ceramic membrane is the nanoporous membrane which has the comparatively higher permeability and lower separation fector. And in the case of mixed gases, separation mechanism is mainly concerned with the permeate velocity. The velocity properties of gas flow in nanoporous membranes depend on the ratio of the number of molecule-molecule collisions to that of the molecule-wall collision. The Knudsen number Kn Xydp is characteristic parameter defining different permeate mechanisms. The value of the mean free path depends on the length of the gas molecule and the characteristic pore diameter. The diffusion of inert and adsorbable gases through porous membrane is concerned with the contributions of gas phase diffusion and sur u e diffusion. 

Knudsen diffusion, dominated by molecule-wall collisions. This mechanism is prevailing at low pressures or high temperatures. 

Basic mechanisms involved in gas and vapor separation using ceramic membranes are schematized in Figure 6.14. In general, single gas permeation mechanisms in a porous ceramic membrane of thickness depend on the ratio of the number of molecule-molecule collisions to that of the molecule-wall collisions. In membranes with large mesopores and macropores the separation selectivity is weak. The number of intermolecular collisions is strongly dominant and gas transport in the porosity is described as a viscous flow that can be quantified by a Hagen-Poiseuille type law ... 

Molecules are assumed to be widely separated point masses that interact only during collisions, move randomly with a distribution of speeds, and experience elastic collisions with walls... 

Rates of molecule-wall and molecule-molecule collisions from the kinetic theory of gases depend on the average molecular speed u. 

Collisions with Walls -> Consider molecules traveling only in one dimension x with an... 

Molecular diffusion is significant in large pores and imder high pressures. In these cases, the effects of molecule-molecule collisions dominate over those of molecule-wall collisions. However, compared to molecular diffusion in the free bulk phase, molecular diffusion in pores is hindered by the pore walls and may be slower or even much slower. 

Knudsen diffusion becomes predominant when the mean-free path of the molecular species considered is larger than the pore diameter and hence, when the effects of the molecule-wall collisions become important. In liquid chromatography, Knudsen diffusion is negligible. 

In a gas sample the molecules are very far apart and do not attract one another significantly. Each kind of gas molecule acts independently of the presence of the other kind. The molecules of each gas thus collide with the walls with a frequency and vigor that do not change even if other molecules are present (Figure 12-11). As a result, each gas exerts a partial pressure that is independent of the presence of the other gas, and the total pressure is due to the sum of all the molecule-wall collisions. 

To describe the combined bulk and Knudsen diffusion flrrxes the dusty gas model can be used [44] [64] [48] [49]. The dusty gas model basically represents an extension of the Maxwell-Stefan bulk diffusion model where a description of the Knudsen diffusion mechanisms is included. In order to include the Knudsen molecule - wall collision mechanism in the Maxwell-Stefan model originally derived considering bulk gas molecule-molecule collisions only, the wall (medium) molecules are treated as an additional pseudo component in the gas mixture. The pore wall medium is approximated as consisting of giant molecules, called dust, which are uniformly distributed in space and held stationary by an external clamping force. This implies that both the diffusive ffrrx and the concentration gradient with respect to the dust particles vanish. 

Bulk diffusion that are significant for large pore sizes and high system pressures in which gas molecule-molecule collisions dominate over gas molecule-wall collisions. 

When the mean free path length of the molecule is large compared with the diameter of the pore and molecule-wall collisions dominate over molecule-molecule collision, the flow is called Knudsen diflPusion. Molecules of different species move entirely independent of each other. This occurs at low density of the gas (low pressure) or in fine pores. 

In this type of flow the mean free path of the molecule is very small compared to the pore diameter and molecule-molecule collision dominates over molecule-wall collision. The mixture becomes like a single gas and the driving force for the continuum fluid is the pressure gradient. 

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