Non-ideal Phenomena

The solution-difTusion model is valid only in strictly ideal systems, namely when dealing with solutions of infinite dilution. As soon as one departs from such ideal solutions, it becomes to some extent subjective what can still be considered as almost ideal and highly dilute . For the pervaporation of isobutyl alcohol, for example, a feed concentration of 50 mg kg would lead to a membrane surface concentration of 50 mg kg (according to the sorption coefficient listed in Table 3.6-2). For the same feed concentration, ethyl hexanoate would yield a membrane surface concentration about 240 times higher, namely 12 g kg which may not be considered ideal anymore. The stronger the (desired) solute-polymer affinity, the more pronounced can be the non-ideal phenomena, with the most relevant being discussed below. 

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However, in the study of thermodynamics and transport phenomena, the behavior of ideal gases and gas mixtures has historically provided a norm against which their more unruly brethren could be measured, and a signpost to the systematic treatment of departures from ideality. In view of the complexity of transport phenomena in multicomponent mixtures a thorough understanding of the behavior of ideal mixtures is certainly a prerequisite for any progress in understanding non-ideal systems. 

In many process design applications like polymerization and plasticization, specific knowledge of the thermodynamics of polymer systems can be very useful. For example, non-ideal solution behavior strongly governs the diffusion phenomena observed for polymer melts and concentrated solutions. Hence, accurate modeling of... 

Other model representations of flow mixing cases in chemical reactors are described by Levenspiel (1972), Fogler (1992) and Szekely and Themelis (1971). Simulation tank examples demonstrating non-ideal mixing phenomena are CSTR, NOSTR, TUBMIX, MIXFLO, GASLIQ and SPBEDRTD. 

Experimental non-ideality at pH extremes in isotachophoresis has been compared with theoretical models.56 The model was able to predict phenomena that are usually regarded as artifactual, including system peaks, diffuse... 

In order to get an overall idea of the effects of the above-mentioned phenomena on the response of a non-ideal calorimeter, let us now considerer a simplified model of one of the calorimeter of COURICINO (Fig. 15.7) experiment (see Section 16.6). 

This brief review attempts to summarize the salient features of chemically modified electrodes, and, of necessity, does not address many of the theoretical and practical concepts in any real detail. It is clear, however, that this field will continue to grow rapidly in the future to provide electrodes for a variety of purposes including electrocatalysis, electrochromic displays, surface corrosion protection, electrosynthesis, photosensitization, and selective chemical concentration and analysis. But before many of these applications are realized, numerous unanswered questions concerning surface orientation, bonding, electron-transfer processes, mass-transport phenomena and non-ideal redox behavior must be addressed. This is a very challenging area of research, and the potential for important contributions, both fundamental and applied, is extremely high. 

In this paper, an overview of the important phenomena is given. The supercritical combustion process employed is also known to occur in liquid propellant rocket motors (e.g. in LOX/GH2-motors), liquid propellant guns (LPG), advanced aviation gas turbines and, to a lesser extent, in internal combustion engines. Supercritical combustion is characterized by (1) injection of at least one liquid state fuel component into a chamber which is thermodynamically in the supercritical state, (2) density ratios of fuel to oxidizer near one, (3) supercritical phase transitions of fluid-particles due to combustion, (4) non-ideal properties of the fluids. Additionally a short description of pertinent design criteria is given. 

As has become clear adsorption phenomena play an important, if not, decisive role in this behaviour, and good data and modelling of adsorption are mandatory, too, to serve as the input parameters for the permeation description. This should not be l ted to the T.angmnir model, but other theories like the IAS (ideal adsorbed solution) and NIAS (non-ideal) should be considered, since they sometines work well for binary systems where the Langmuir model fails. 

Several sophisticated techniques and data analysis methodologies have been developed to measure the RTD of industrial reactors (see, for example, Shinnar, 1987). Various different types of models have been developed to interpret RTD data and to use it further to predict the influence of non-ideal behavior on reactor performance (Wen and Fan, 1975). Most of these models use ideal reactors as the building blocks (except the axial dispersion model). Combinations of these ideal reactors with or without by-pass and recycle are used to simulate observed RTD data. To select an appropriate model for a reactor, the actual flow pattern and its dependence on reactor hardware and operating protocol must be known. In the absence of detailed quantitative models to predict the flow patterns, selection of a model is often carried out based on a qualitative understanding of flow patterns and an analysis of observed RTD data. It must be remembered that more than one model may fit the observed RTD data. A general philosophy is to select the simplest model which adequately represents the physical phenomena occurring in the actual reactor. 

The axial dispersion terms may be required to account for the mixing phenomena created by a non-ideal flow. However, the ideal plug flow model is often appropriate for packed bed reactors because the axial mixing is negligible compared to the convective flux for many processes. 

The theory of electrolyte solutions developed in this chapter relies heavily on the classical laws of electrostatics within the context of modern statistical mechanical methods. On the basis of Debye-Hiickel theory one understands how ion-ion interactions lead to the non-ideality of electrolyte solutions. Moreover, one is able to account quantitatively for the non-ideality when the solution is sufficiently dilute. This is precisely because ion-ion interactions are long range, and the ions can be treated as classical point charges when they are far apart. As the concentration of ions increases, their finite size becomes important and they are then described as point charges within hard spheres. It is only when ions come into contact that the problems with this picture become apparent. At this point one needs to add quantum-mechanical details to the description of the solution so that phenomena such as ion pairing can be understood in detail. 

Most of the solvent systems exhibit a non-ideal additive behaviour. This result can be ascribed to (a) the preferential solvation of the cybotactic region by some of the solvents present in the mixture, (b) the occurrence of strong solvent-solvent interactions that can generate complex intersolvent structures affecting solute-solvent interactions or (c) a combination of the two phenomena. 

The first pervaporation membrane reactor model which takes into account solution non-idealities was developed and validated experimentally by Zhu et al [5.90]. Prior studies [5.89, 5.91] also made note of such non-idealities, but offered no unified means for accounting for these phenomena in the description of PVMR. Since the model of Zhu et al. [5.90] appeared, other groups have also utilized similar models [5.92]. A more comprehensive analog of this model was, for example, recently presented and validated experimentally by Park [5.93], and by Lim et al. [5.94]. Zhu et al. [5.90] analyzed a tubular PVMR, in which the homogeneously catalyzed esterification reaction of acetic acid with ethanol to produce ethyl acetate and water took place. The reaction can be expressed generally as ... 

Thus, the mechanism of catalytic processes near and far from the equilibrium of the reaction can differ. In general, linear models are valid only within a narrow range of (boundary) conditions near equilibrium. The rate constants, as functions of the concentration of the reactants and temperature, found near the equilibrium may be unsuitable for the description of the reaction far from equilibrium. The coverage of adsorbed species substantially affects the properties of a catalytic surface. The multiplicity of steady states, their stability, the ordering of adsorbed species, and catalyst surface reconstruction under the influence of adsorbed species also depend on the surface coverage. Non-linear phenomena at the atomic-molecular level strongly affect the rate and selectivity of a heterogeneous catalytic reaction. For the two-step sequence (eq.7.87) when step 1 is considered to be reversible and step 2 is in quasi-equilibria, it can be demonstrated for ideal surfaces that... 

Figure 29-2 Concentration dependence of the Gibbs free energy of mixing at 38 and 52°C for regular solutions of isobutane and furfural. Non-Ideal effects are based on the van Laar model. Negative curvature [i.e., (9 A n,ixuig/9yf)r,/> < 0] within the spinodal region exists for isobutane mole fractions between 0.27 and 0.81 at 38°C, and between 0.29 and 0.78 at 52°C. This binary system exhibits upper critical solution phenomena.

This phenomenon is denoted feed-side concentration polarization and, in practice, affects mainly the fluxes of compounds of high sorption coefficient, even under turbulent hydrodynamic conditions over the membrane, as their permeability (and hence flux across the membrane) is high. It should at this point be emphasized that contrary to the non-ideal transport phenomena discussed earlier, feed-side concentration polarization is not a membrane-intrinsic phenomenon, but stems from poor design of the upstream flow conditions in practice it may in fact not be overcome owing to module design limitations (Baker et ah, 1997). 

In the second part, the possible products of kinetically controlled catalytic distillation processes are analyzed using residue curve maps. Ideal, as well as non-ideal, ternary mixtures are considered. Current research activities are presented that are focussed on reaction systems exhibiting liquid-phase splitting phenomena such as the hydration of cyclohexene to cyclohexanol at strongly acidic catalyst partides. 

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