In low pressure regions

Fig. XVII-1. Adsorption of N2 on rutile temperatures indicated are in degrees Kelvin. (a) Low-pressure region (b) high-pressure region. (From Ref. 1.).

From the earliest days, the BET model has been subject to a number of criticisms. The model assumes all the adsorption sites on the surface to be energetically identical, but as was indicated in Section 1.5 (p. 18) homogeneous surfaces of this kind are the exception and energetically heterogeneous surfaces are the rule. Experimental evidence—e.g. in curves of the heat of adsorption as a function of the amount adsorbed (cf. Fig. 2.14)—demonstrates that the degree of heterogeneity can be very considerable. Indeed, Brunauer, Emmett and Teller adduced this nonuniformity as the reason for the failure of their equation to reproduce experimental data in the low-pressure region. 

If micropores are introduced into a solid which originally gave a standard Type II isotherm, the uptake is enhanced in the low-pressure region and the isotherm is correspondingly distorted. The effect on the t-plot is indicated in... 

As will be demonstrated in Chapter 4, an isotherm which is reversible and of Type II is quite compatible with the presence of micropores. If such pores are present, the isotherm will be distorted in the low-pressure region, the value of c will be greatly enhanced, and the specific surface derived by the BET procedure will be erroneously high. In particular, a BET specific surface in excess of - 500m g" should be taken as a warning that... 

More often, however, microporosity is associated with an appreciable external surface, or with mesoporosity, or with both. The effect of microporosity on the isotherm will be seen from Fig. 4.11(a) and Fig. 4.12(a). In Fig. 4.11(a) curve (i) refers to a powder made up of nonporous particles and curve (ii) to a solid which is wholly microporous. However, if the particles of the powder are microporous (the total micropore volume being given by the plateau of curve (ii)), the isotherm will assume the form of curve (iii), obtained by summing curves (i) and (ii). Like isotherm (i), the composite isotherm is of Type II, but because of the contribution from the Type 1 isotherm, it has a steep initial portion the relative enhancement of adsorption in the low-pressure region will be reflected in a significantly increased value of the BET c-constant and a shortened linear branch of the BET plot. 

Fig. 2.3. Experimental determination of shock-stress versus volume compression from propagating shock waves is accomplished by a series of experiments carried out at different loading pressures. In the figure, the solid lines connect individual pressure-volume points with the initial condition. These solid straight lines are Rayleigh lines. The dashed line indicates an extrapolation into an uninvestigated low pressure region. Such extrapolation is typical of much of the strong shock data.

With the intake valve open, the piston movement to the right creates a low pressure region in the cylinder, which causes air and fuel to flow through the intake valve to fill the cylinder. 

Figure 10-102B. Maximum boiling rate in the low pressure region. (Used by permission Cichelli, M. T. and Bonilla, C. E. Transactions. AlChE, V. 41, No. 6, 1945. American Institute of Chemical Engineers. All rights reserved.)...

The extrapolation to zero pressure may be effected if two measurements of pv at small pressures have been made, provided the gas satisfies equation (1). If this is not the case (e.g., hydrogen chloride, carbon dioxide), a number of points must be fixed on the curve, especially in the low pressure region. 

Similar phenomena have also been observed in the combustion of composite propellants. Eisel (El) has observed that there is a unique frequency-pressure relation in a low-pressure region where nonacoustic instability results. He speculates that this preferred frequency is related to the periodic appearance and depletion of the aluminum particles on the propellant surface. High-speed pictures confirm the periodic sluffing of aluminum, but its relation to the preferred frequency is still not clear. 

Using a value of 1.40 for y in this low pressure region, and writing ... 

For systems with large density differences, the dominating mechanism for coalescence is accumulation of the low-density fluid in the low-pressure regions. 

In a stirred tank reactor, these low-pressure regions are behind the impeller blades, in the trailing vortices leaving the impeller blades, behind the baffles, and at the center of the large turbulent eddies. 

In quiescent liquids and in bubble columns, buoyancy-driven coalescence is more important. Large fluid particles with a freely moving surface will also have a low-pressure region at the edge of the particle where the velocity is maximum. This low-pressure region will not only allow the bubble to stretch out and form a spherical cap but also allow other bubbles to move into that area and coalesce. Figure 15.14 shows an example of this phenomenon. 

The low density of gases makes it more difficult to keep the bubbles dispersed. The bubbles will move to the low-pressure areas, that is, behind the impellers, in the trailing vortices close to the impeller, behind the baffles, and at the inner side after a bend. The bubbles will coalesce in these areas with high gas holdup. It is very difficult to design reactors without low-pressure regions where the low-density fluid will accumulate. One such reactor is the monolith reactor for multiphase flow [32, 33]. 

On the other hand, as shown in Figure 4, the isotherm of Cs2.2 (72 m g"l) was of Type I [27], where most of the adsorption took place at the very low pressure region, indicating that these salts have only micropores (according to the lUPAC definition, the pore diameter is less than 20 A) [28]. Cs2.1 also gave the Type I... 

The low-pressure region displays the electroneutrality equation approximation [e ] = 2[Vx ]. Electrons predominate so that the material is an n-type semiconductor in this regime. In addition, the conductivity will increase as the partial pressure of the gaseous X2 component decreases. The number of nonmetal vacancies will increase as the partial pressure of the gaseous X2 component decreases, and the phase will display a metal-rich nonstoichiometry opposite to that in the high-pressure domain. Because there is a high concentration of anion vacancies, easy diffusion of anions is to be expected. 

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