Pores diffusion into

Molecules larger than the pore size do not enter the pores and elute together as the first peak in the chromatogram and this is called total exclusion volume which defines the exclusion limit for a particular column. Molecules that can enter the pores diffuse into the internal pore structure of the gel to an extent depending on their size and the pore size distribution of the... 

Ksenzhek [13] treated the case where one substance diffuses in the direction of the axis of an infinite pore. Austin and Lerner [14] considered the diffusion of both oxidized and reduced species in a finite pore. Euler [15] pointed out that the longitudinal diffusion can be simulated by a constant resistance per unit pore length in the electrical analog of a pore. Diffusion into the pore from one side is discussed in this section. Supply of fuel from two sides of flooded porous structures and also forced reactant supply were analyzed by Gurevich and Bagotzky [16]. 

Metalliding. MetaUiding, a General Electric Company process (9), is a high temperature electrolytic technique in which an anode and a cathode are suspended in a molten fluoride salt bath. As a direct current is passed from the anode to the cathode, the anode material diffuses into the surface of the cathode, which produces a uniform, pore-free alloy rather than the typical plate usually associated with electrolytic processes. The process is called metalliding because it encompasses the interaction, mostly in the soHd state, of many metals and metalloids ranging from beryUium to uranium. It is operated at 500—1200°C in an inert atmosphere and a metal vessel the coulombic yields are usually quantitative, and processing times are short controUed... 

There are two mechanisms of PAN-based carbon fiber oxidation dependent on oxidation temperature ((67,68). At temperatures below 400°C, oxygen diffuses into the fiber and attacks at pores resulting in significantly increased fiber surface area. At higher temperatures impurities catalyze the oxidation reaction. 

As a reactant molecule from the fluid phase surrounding the particle enters the pore stmcture, it can either react on the surface or continue diffusing toward the center of the particle. A quantitative model of the process is developed by writing a differential equation for the conservation of mass of the reactant diffusing into the particle. At steady state, the rate of diffusion of the reactant into a shell of infinitesimal thickness minus the rate of diffusion out of the shell is equal to the rate of consumption of the reactant in the shell by chemical reaction. Solving the equation leads to a result that shows how the rate of the catalytic reaction is influenced by the interplay of the transport, which is characterized by the effective diffusion coefficient of the reactant in the pores, and the reaction, which is characterized by the first-order reaction rate constant. 

Fig. 9. Catalyst pore and reaction. The CO diffuses into a precious metal site D reacts with O2 and leaves as CO2.

The former usually involves process temperature or isolation. Sohds surface characteristics are important in that they control the extent to which an operation is diffusion-limited, i.e., diffusion into and out of the pores of a given sohds particle, not through the voids among separate particles. The size of the solids parti(des, the surface-to-mass ratio, is also important in the evaluation of surface characteristics and the diffusion problem. 

Effectiveness As a reac tant diffuses into a pore, it undergoes a falling concentration gradient and a falling rate of reaction. The concentration depends on the radial position in the pores of a spherical pellet according to... 

The rate of diffusion into the pore equals the rate of diffusion through the dead zone,... 

Fig. 19.2. The microscopic mechanism of sintering. Atoms leave the grain boundary in the neck between two particles and diffuse into the pore, filling it up.

The relationship between adsorption capacity and surface area under conditions of optimum pore sizes is concentration dependent. It is very important that any evaluation of adsorption capacity be performed under actual concentration conditions. The dimensions and shape of particles affect both the pressure drop through the adsorbent bed and the rate of diffusion into the particles. Pressure drop is lowest when the adsorbent particles are spherical and uniform in size. External mass transfer increases inversely with d (where, d is particle diameter), and the internal adsorption rate varies inversely with d Pressure drop varies with the Reynolds number, and is roughly proportional to the gas velocity through the bed, and inversely proportional to the particle diameter. Assuming all other parameters being constant, adsorbent beds comprised of small particles tend to provide higher adsorption efficiencies, but at the sacrifice of higher pressure drop. This means that sharper and smaller mass-transfer zones will be achieved. 

Dead-end Pores Dead-end volumes cause dispersion in unsteady flow (concentration profiles ar> ing) because, as a solute-rich front passes the pore, transport oceurs by molecular diffusion into the pore. After the front has passed, this solute will diffuse back out, thus dispersing. 

It was shown in laboratory studies that methanation activity increases with increasing nickel content of the catalyst but decreases with increasing catalyst particle size. Increasing the steam-to-gas ratio of the feed gas results in increased carbon monoxide shift conversion but does not affect the rate of methanation. Trace impurities in the process gas such as H2S and HCl poison the catalyst. The poisoning mechanism differs because the sulfur remains on the catalyst while the chloride does not. Hydrocarbons at low concentrations do not affect methanation activity significantly, and they reform into methane at higher levels, hydrocarbons inhibit methanation and can result in carbon deposition. A pore diffusion kinetic system was adopted which correlates the laboratory data and defines the rate of reaction. 

The catalytic reaction can be subdivided into pore diffusion and chemisorption of reactants, chemical surface reaction, and desorption and pore diffusion of products, the number of steps depending upon the nature of the catalyst and the catalytic reaction. 

Glaser and Litt (G4) have proposed, in an extension of the above study, a model for gas-liquid flow through a b d of porous particles. The bed is assumed to consist of two basic structures which influence the fluid flow patterns (1) Void channels external to the packing, with which are associated dead-ended pockets that can hold stagnant pools of liquid and (2) pore channels and pockets, i.e., continuous and dead-ended pockets in the interior of the particles. On this basis, a theoretical model of liquid-phase dispersion in mixed-phase flow is developed. The model uses three bed parameters for the description of axial dispersion (1) Dispersion due to the mixing of streams from various channels of different residence times (2) dispersion from axial diffusion in the void channels and (3) dispersion from diffusion into the pores. The model is not applicable to turbulent flow nor to such low flow rates that molecular diffusion is comparable to Taylor diffusion. The latter region is unlikely to be of practical interest. The model predicts that the reciprocal Peclet number should be directly proportional to nominal liquid velocity, a prediction that has been confirmed by a few determinations of residence-time distribution for a wax desulfurization pilot reactor of 1-in. diameter packed with 10-14 mesh particles. 

Models of chemical reactions of trace pollutants in groundwater must be based on experimental analysis of the kinetics of possible pollutant interactions with earth materials, much the same as smog chamber studies considered atmospheric photochemistry. Fundamental research could determine the surface chemistry of soil components and processes such as adsorption and desorption, pore diffusion, and biodegradation of contaminants. Hydrodynamic pollutant transport models should be upgraded to take into account chemical reactions at surfaces. 

As discussed in Chapter 7, this form can provide a good fit of the data if the reaction is not too close to equilibrium. However, most reaction engineers prefer a mechanistically based rate expression. This section describes how to obtain plausible functional forms for based on simple models of the surface reactions and on the observation that aU the rates in Steps 2 through 8 must be equal at steady state. Thus, the rate of transfer across the film resistance equals the rate of diffusion into a pore equals the rate of adsorption equals the rate of reaction equals the rate of desorption, and so on. This rate is the pseudohomo-geneous rate shown in Steps 1 and 9. 

This gives the concentration profile inside the pore, a l). The total rate of reaction within a pore can be found using the principle of equal rates. The reaction rate within a pore must equal the rate at which reactant molecules enter the pore. Molecules enter by diffusion. The flux of reactants molecules diffusing into a pore of diameter dp re equals the reaction rate. Thus,... 

The catalytic reaction can be conveniently divided into a number of sequential steps, all of which impact on the overall efficiency of the reaction. First the reactants must diffuse to the catalyst surface the rate of diffusion depends on several factors including fluid density, viscosity and fluid flow rate. Whilst some reaction will take place at the external surface, the majority of reactants will need to diffuse into the internal pores. For a... 

Fig. 2 shows the liquid product distributions over catalysts. Main product over ferrierite is C5 hydrocarbon, while products were distributed over mainly C,-C, over HZSM-5. Table 4 shows the effect of mixing ratio on product distribution. While HZSM-5/PP ratio does not affect product distribution, higher amount of gas is obtained with increasing ferrierite/PP ratio. This is ascribed to the increased possibility of polypropylene diffusion into pore as the amount of ferrierite is increased. 

Figure 7. Sediment eontains derived both seavenged from the water eolumn during particle settling and contained in solid material. Ra produced in the sediments is highly soluble in pore waters and diffuses into the overlying water or is advected across the sediment-water interface by discharging groundwater. Rn is produced within the water column from dissolved Ra and within the underlying sediments.

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