Momentum transfer mixture

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. 

A good exposition of the momentum transfer arguments is given by Present [9], but for our purpose it is necessary only to quote the result. For a binary mixture this takes the form... 

Maxwell obtained equation (4.7) for a single component gas by a momentum transfer argument, which we will now extend essentially unchanged to the case of a multicomponent mixture to obtain a corresponding boundary condition. The flux of gas molecules of species r incident on unit area of a wall bounding a semi-infinite, gas filled region is given by at low pressures, where n is the number of molecules of type r per... 

Dry etching techniques permit etch processes to be carried out in various modes. These can be described as purely chemical, purely physical, and a mixture of chemical and physical. With plasma etching and RIE, we have concentrated on chemical and ion assisted processes. In this section, etching methods that depend either solely or primarily on physical processes (momentum transfer) will be discussed briefly. 

Several guns have been used to produce the primary beam to bombard the FABMS target (12). These beams are composed of fast neutral atoms or ions, or a mixture of the two. It does not appear that the charge state is critical, because desorption is produced by momentum transfer. Some of the guns and the characteristics of the beams are examined in this section. 

In order to take into account the effect of both mechanisms, more complicated models have been proposed [1,2,11,43-45]. Overviews have been given by Uhlhorn et al. [21] and more recently by Veldsink [46]. The models differ in the way the different mechanisms cire combined and which coupling terms are taken into account. The most important coupling effects are the occurrence of drag effects in mixtures and of momentum transfer between different species. Drag effects on molecular species a and b occur in isobaric binary mixtures a-b due to differences in molecular velocities between species a and b, which induce internal pressure differences causing a net flow of the mixture which has to be superimposed on the diffusive fluxes of a and b. 

The Dusty Gas Model (DGM) is one of the most suitable models to describe transport through membranes [11]. It is derived for porous materials from the generalised Maxwell-Stefan equations for mass transport in multi-component mixtures [1,2,47]. The advantage of this model is that convective motion, momentum transfer as well as drag effects are directly incorporated in the equations (see also Section 9.2.4.2 and Fig. 9.12). Although this model is fundamentally more correct than a description in terms of the classical Pick model, DGM/Maxwell-Stefan models )deld implicit transport equations which are more difficult to solve and in many cases the explicit Pick t)q>e models give an adequate approximation. For binary mixtures the DGM model can be solved explicitly and the Fickian type of equations are obtained. Surface diffusion is... 

In the DGM model as presented by Mason and Malinauskas [11a] all the different contributions to the transport are taken into accoimt. The wall of the porous medium is considered as a very heavy component and so contributes to the momentum transfer. The model is schematically represented in Fig. 9.12 for a binary mixture (in analogy with an electriccd network). As can be seen from this figure, the flux contributions by Knudsen diffusion /k, and of molecular (continuum) diffusion of the mixture /m,i23re in series and so are coupled. The total flux of component i (i = 1,2) due to these contributions is /j km- Note that /k = /m,i2- The contribution of the viscous flow and of the surface diffusion are parallel with / km J d so are considered independent of each other (no coupling terms, e.g. no transport interaction between gas phase and surface diffusion). 

The elementary modeling of the diffusion force is outlined in the sequel. For dilute multicomponent mixtures only elastic binary collisions are considered and out of these merely the unlike-molecule collisions result in a net transfer of momentum from one species to another. The overall momentum is conserved since all the collisions are assumed to be elastic (see sect 2.4.2), hence the net force acting on species s from r per unit volume, equals the momentum transferred from r to s per unit time and unit volume [77] (sect 4-2). The diffusion force yields ... 

Chemical engineering processes involve the transport and transfer of momentum, energy, and mass. Momentum transfer is another word for fluid flow, and most chemical processes involve pumps and compressors, and perhaps centrifuges and cyclone separators. Energy transfer is used to heat reacting streams, cool products, and run distillation columns. Mass transfer involves the separation of a mixture of chemicals into separate streams, possibly nearly pure streams of one component. These subjects were unified in 1960 in the first edition of the classic book. Transport Phenomena (Bird et al., 2002). This chapter shows how to solve transport problems that are one-dimensional that is, the solution is a function of one spatial dimension. Chapters 10 and 11 treat two- and three-dimensional problems. The one-dimensional problems lead to differential equations, which are solved using the computer. 

Fig. 5.9 The recoil of helium isotopes in a mixture of He and He (MARI, ISIS) [21]. The lines trace the maximum scattering of each isotope. Note that the momentum transfer is unconventionally given in A. ...

Most three atom ion-molecule reactions that exhibit direct mechanism behaviour do not proceed solely by a spectator stripping mechanism since product ions exist far beyond the critical energy. The migration mechanism is an attractive candidate for the direct mechanism since it contributes to the simultaneous occurrence of forward scattering, large momentum transfer to the product atom and stability to the product ion far beyond the critical energy of the spectator stripping model. It is, of course, clear that the actual mechanism is a mixture of a number of direct processes. 

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