Diffusion discussion

SoUd Diffusion In the case of pore diffusion discussed above, transport occurs within the fluid phase contained inside the particle here the solute concentration is generally similar in magnitude to the external fluid concentration. A solute molecule transported by pore diffusion may attach to the sorbent and detach many times along its... 

Is the diffusion discussed on page 376 and in Problem 10 17 a fatal Raw (Him Recall what you know from general chemistry about a simple aqueous cell Zn Zrr Cir Cti.)... 

The theory of filtration is a direct application of principles of Brownian diffusion discussed previously. The objective of the theory is to provide a framework for cal-... 

The material balance on a laminar-flow reactor with negligible mass diffusion (discussed later in this chapter) is ... 

Fick diffusion takes place when the pore diameter is much greater than the mean free path of the molecule. In this case, the collisions between the molecules dominate and the collision between the molecule and the walls of the pore is negligible in Figure 2.15a. The driving force of the Fick diffusion is the concentration gradient of the gaseous species and the diffusivity discussed above. 

According to Equation (5.7) the increase in processing temperature and preform thickness leads to larger values of Valid poor density uniformity. As stated previously, CVI processes preferably operate in a chemical-reaction-controlled regime where the ratio of k/D is small. For Fick diffusion, discussed in Section2.3.1, the diffusivity D is inversely proportional to the pressure and thus operates at lower pressures. Furthermore, coarser pore structures correspond to more uniform deposition. Figure 5.5 shows the microstructures of C/SiC composites prepared at different 9 numbers. 

When >i2/ >i3 = 1 the ratio D 2/ 11 = regardless of the composition of the mixture (this corresponding to the case of three equal, or nearly equal, binary diffusivities discussed... 

We tried to avoid any detailed or complete literature review concerning the subject under discussion this would inevitably lead to vast and diffuse discussions and criticism. Instead, we attempted to point out the main problems and difficulties, to trace paths to possible solutions and to mention the achievements reached to date. 

For very narrow pores, say 10 nm, the permeability depends on molecular size. This is comparable to, but not the same as, the hindered diffusion discussed in the following section. 

Consider a powder compact in which the neck growth at the initial stage sintering occurs by lattice as well as surface diffusion. Discuss the relative importance of the two mechanisms according to particle size and sintering time. 

An other common explanation for drag reduction is that the extensional viscosity stabilizes the flow of the viscous sublayer or the organisation of the different features in a grand structure. It would also be possible to incorporate the enhanced vorticity diffusion discussed here into such an explanation. Without knowing the grand structure in Newtonian fluids this is naturally highly speculative. 

Nuclear magnetic resonance methods have become very useful in measuring diffusion coefficients, but, as in DLS, it becomes more difficult to determine what is being measured as the system gets more complex. The measured diffusivity is most often called the NMR self-diffusion coefficient, but in many instances it is the traditional diffusivity, discussed in Section 4. 

The consequences of the mechanisms of diffusion, discussed above, for the strength of the interfaces formed are further considered in Polymer-polymer adhesion models. 

A variety of solutes in the rare earth metals present a partly or total interstitial character. These solutes include beside the metalloid classical interstitials also some metallic elements, the so-called fast-diffusers, discussed in section 4. In general the study of electromigration of interstitials offers two advantages as compared to that of substitutional solutes. From the experimental point of view, the relatively high mobilities of the interstitial solutes increases the electrotransport effects often allowing to achieve steady state conditions within... 

Clearly these dispersive processes will increase in relative importance as the mobile phase flow rate increases and as the diffusion rates decrease (the opposite to the dependence for longitudinal diffusion discussed above). This is because the faster the mobile phase (and slower the inter-phase diffusion) the greater the extent to which the molecules originally far from the stationary phase interface will be swept ahead of the molecules that made it into the stationary phase and were retained there for some time. A detailed discussion (Scott http //www.chromatography-online.org/), based on that originally derived by van Deemter, of the form of this dependence of band dispersion on resistance to mass transfer, gives ... 

The type of diffusion discussed here may be termed normal" or Gaussian diffusion. It arises simply from the statistics of a process with two possible outcomes, which is attempted a very large number of times. In Section 2.1.2.7, the statistical basis of diffusion is enlarged to include random walks in continuous rather than discrete time, and also situations where different distributions of jump distances occur. 

In considering membranes for various applications, the engineer must have a means of estimating the performance of a membrane system. The fundantental laws of diffusion discussed earlier in this chapter under Transport Mechanisms apply. Mathematical solutions for compositions of residue and permeate streams have been developed for two components and are described in the literature (e.g., Lacey and Loeb, 1979). For three or more compo-... 

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