Model ideal

In the Ideal Model, the water content of a gas is assumed to be equal to the vapor pressure of pure water divided by the total pressure of the system. This yields the mole fraction of water in the gas and this is value converted to g water per m3[std] by multiplying by 760.4. Mathematically this is  

Plater vapor pressure of pure water Ptotai absolute pressure 

This equation yields w in g/m3[std] and the units on the two pressure terms must be the same. A slight modification results in  

Clearly, this model is very simple and should not be expected to be highly accurate except at very low pressures. 

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Figure 2.1 The idealized models used for reactor design. (From Smith and Petela, Thz Chemical Engineer, Dec. 17, 1991 reproduced by permission of the Institution of Chemical Engineers.)...

Consider now which of the idealized models is preferred for the five categories of reaction systems introduced in Sec. 2.2. 

By contrast with ideal models, practical reactors must consider many factors other than variations in temperature, concentration, and residence time. Practical reactors deviate from the three idealized models but can be classified into a number of common types. 

The performance of fluidized-bed reactors is not approximated by either the well-stirred or plug-flow idealized models. The solid phase tends to be well-mixed, but the bubbles lead to the gas phase having a poorer performance than well mixed. Overall, the performance of a fluidized-bed reactor often lies somewhere between the well-stirred and plug-flow models. 

Returning to Eq. XI-4, wiA C2 replacing 02, at low concentrations 112 will be proportional to C2 with a slope n b. At sufficiently high concentrations /I2 approaches the limiting value n . Thus is a measure of the capacity of the adsorbent and b of the intensity of the adsorption. In terms of the ideal model, nf should not depend on temperature, while b should show an exponential... 

SAMs are generating attention for numerous potential uses ranging from chromatography [SO] to substrates for liquid crystal alignment [SI]. Most attention has been focused on future application as nonlinear optical devices [49] however, their use to control electron transfer at electrochemical surfaces has already been realized [S2], In addition, they provide ideal model surfaces for studies of protein adsorption [S3]. 

A second ideal model for adhesion is that of a liquid wetting two plates, forming a circular meniscus, as illustrated in Fig. XII-13. Here a Laplace pressure P = 2yz.A (h ws the plates together and, for a given volume of liquid. 

Simulations act as a bridge in another sense between theory and experiment (see figure B3.3.2. We can test a theory using idealized models, conduct thought experiments , and clarify what we measure in the laboratory. We may also carry out simulations on the computer tliat are difficult or impossible in the laboratory (for example, working at extremes of temperature or pressure). 

The microscopic understanding of tire chemical reactivity of surfaces is of fundamental interest in chemical physics and important for heterogeneous catalysis. Cluster science provides a new approach for tire study of tire microscopic mechanisms of surface chemical reactivity [48]. Surfaces of small clusters possess a very rich variation of chemisoriDtion sites and are ideal models for bulk surfaces. Chemical reactivity of many transition-metal clusters has been investigated [49]. Transition-metal clusters are produced using laser vaporization, and tire chemical reactivity studies are carried out typically in a flow tube reactor in which tire clusters interact witli a reactant gas at a given temperature and pressure for a fixed period of time. Reaction products are measured at various pressures or temperatures and reaction rates are derived. It has been found tliat tire reactivity of small transition-metal clusters witli simple molecules such as H2 and NH can vary dramatically witli cluster size and stmcture [48, 49, M and 52]. 

Hydrogen-bonded clusters are an important class of molecular clusters, among which small water clusters have received a considerable amount of attention [148, 149]. Solvated cluster ions have also been produced and studied [150, 151]. These solvated clusters provide ideal model systems to obtain microscopic infonnation about solvation effect and its influence on chemical reactions. 

The hamionic oscillator (Fig. 4-1) is an idealized model of the simple mechanical system of a moving mass connected to a wall by a spring. Oirr interest is in ver y small masses (atoms). The harmonic oscillator might be used to model a hydrogen atom connected to a large molecule by a single bond. The large molecule is so... 

In this section we compare actual polymer chains with the perfectly flexible model discussed in the last section. There are four respects in which an actual molecule differs from the idealized model ... 

Computer simulation of the reactor kinetic hydrodynamic and transport characteristics reduces dependence on phenomenological representations and idealized models and provides visual representations of reactor performance. Modem quantitative representations of laminar and turbulent flows are combined with finite difference algorithms and other advanced mathematical methods to solve coupled nonlinear differential equations. The speed and reduced cost of computation, and the increased cost of laboratory experimentation, make the former increasingly usehil. 

Most of the assumptions are based on idealized models, indicating the limitations of the mathematical methods employed and the quantity and type of experimental data available. For example, the details of the combinatorial entropy of a binary mixture may be well understood, but modeling requires, in large measure, uniformity so the statistical relationships can be determined. This uniformity is manifested in mixing rules and a minimum number of adjustable parameters so as to avoid problems related to the mathematics, eg, local minima and multiple solutions. 

There have been many modifications of this idealized model to account for variables such as the freezing rate and the degree of mix-ingin the liquid phase. For example, Burton et al. [J. Chem. Phy.s., 21, 1987 (1953)] reasoned that the solid rejects solute faster than it can diffuse into the bulk liquid. They proposed that the effect of the freezing rate and stirring could be explained hy the diffusion of solute through a stagnant film next to the solid interface. Their theoiy resulted in an expression for an effective distribution coefficient k f which could be used in Eq. (22-2) instead of k. 

Real reactors may conform to some sort of ideal mixing patterns, or their performance may be simulated by combinations of ideal models. The commonest ideal models are the following ... 

Coimectivity is a term that describes the arrangement and number of pore coimections. For monosize pores, coimectivity is the average number of pores per junction. The term represents a macroscopic measure of the number of pores at a junction. Connectivity correlates with permeability, but caimot be used alone to predict permeability except in certain limiting cases. Difficulties in conceptual simplifications result from replacing the real porous medium with macroscopic parameters that are averages and that relate to some idealized model of the medium. Tortuosity and connectivity are different features of the pore structure and are useful to interpret macroscopic flow properties, such as permeability, capillary pressure and dispersion. 

In this review we consider several systems in detail, ranging from idealized models for adsorbates with purely repulsive interactions to the adsorption of spherical particles (noble gases) and/or (nearly) ellipsoidal molecules (N2, CO). Of particular interest are the stable phases in monolayers and the phase transitions between these phases when the coverage and temperature in the system are varied. Most of the phase transitions in these systems occur at fairly low temperatures, and for many aspects of the behavior quantum effects need to be considered. For several other theoretical studies of adsorbed layer phenomena see Refs. 59-89. 

Whereas chain models still allow for a relatively unified treatment of various aspects of amphiphilic systems, such as their bulk phase behavior and the properties of monolayers and bilayers, this is no longer true for the even more idealized models at the next level of coarse graining. These usually have to be adapted very specifically to the problem one wishes to study. 

Zhong G., Guioehon G. (1996) Analytieal Solution for the Linear Ideal Model of Simulated Moving Bed Chromatography, Chem. Eng. Sci. 51 4307-4319. 

The computational paradigm in an ANN is based on an idealized model of a biological unit called a neuron. The unique characteristics of this ANN model are the inputs of signal from stimulus in a training environment. It is important to note that each neuron works independently of the other neurons. The specific characteristics of ANN models that attract industrial application are ... 

A recent series of papers [18, 24, 32-34] substantially clears up the three-dimensional polymerization mechanism in the AAm-MBAA system. Direct observation of the various types of acrylamide group consumption using NMR technique, analysis of conversion at the gel-point, and correlation of the elastic modulus with swelling indicate a considerable deviation of the system from the ideal model and a low efficiency of MBAA as a crosslinker. Most of these experimental data, however, refer to the range of heterogeneous hydrogels where swelling is not more than 80 ml ml-1 [24]. 

Its main features are given by the use of a stream of inert carrier gas which percolates through a bed of an adsorbent covered with adsorbate and heated in a defined way. The desorbed gas is carried off to a detector under conditions of no appreciable back-diffusion. This means that the actual concentration of the desorbed species in the bed is reproduced in the detector after a time lag which depends on the flow velocity and the distance. The theory of this method has been developed for a linear heating schedule, first-order desorption kinetics, no adsorbable component in the entering carrier gas (Pa = 0), and the Langmuir concept, and has already been reviewed (48, 49) so that it will not be dealt with here. An analysis of how closely the actual experimental conditions meet the idealized model is not available. 

Carnie and Chan and Blum and Henderson have calculated the capacitance for an idealized model of an electrified interface using the mean spherical approximation (MSA). The interface is considered to consist of a solution of charged hard spheres in a solvent of hard spheres with embedded point dipoles, while the electrode is considered to be a uniformly charged hard wall whose dielectric constant is equal to that of the electrolyte (so that image forces need not be considered). 

Liquid crystals (LCs) are organic liquids with long-range ordered structures. They have anisotropic optical and physical behaviors and are similar to crystal in electric field. They can be characterized by the long-range order of their molecular orientation. According to the shape and molecular direction, LCs can be sorted as four types nematic LC, smectic LC, cholesteric LC, and discotic LC, and their ideal models are shown in Fig. 23 [52,55]. 

Various PIB architectures with aromatic finks are ideal model polymers for branching analysis, since they can be disassembled by selective link destmction (see Figure 7.7). For example, a monodisperse star would yield linear PIB arms of nearly equal MW, while polydisperse stars will yield linear arms with a polydispersity similar to the original star. Both a monodisperse and polydisperse randomly branched stmcture would yield linear PIB with the most-probable distribution of M jM = 2, provided the branches have the most-probable distribution. Indeed, this is what we found after selective link destruction of various DlBs with narrow and broad distribution. Recently we synthesized various PIB architectures for branching analysis. 

The binding specificity of d-[ C]glucose by the taste-papillae membranes, compared to that of control membranes isolated from epithelial tissue, has been confirmed in two studies. One inherent problem in the approach is that the stimuli, primarily carbohydrate sweeteners, are not ideal model compounds to use, as they are not active at low concentrations and do not show sufficiently high binding-constants. The use of other stimulus compounds that are at least several hundred times sweeter than sucrose, such as saccharin, dihydrochalcone sweeteners, dipeptide sweeteners, stevioside, perillartine and other sweet oximes, the 2-substituted 5-nitroanilines, and... 

However, the reality is considerably more complicated than the ideal model. Non-ideality of the system causes that segregation extends over more than one layer. Further, when the size of the atoms is not equal one has to consider it in the calculations. This all has been done by A.D.van Langeveld (10), who made the following assumptions on the Pt/Cu system i) segregation extends over the two outmost layers, ii) when the binding energy of pairs of atoms is e the non-ideality of an alloy AB is described by the parameter ... 

Within the limits of validity of the theories developed above on the basis of idealized models and of the simplifying assumptions, xi of the preceding treatment may be related to these parameters by comparing Eq. (42) with (43). Then... 

Mention of this connection is incidental only. It will not be required to identify the quantity ki — i+l/2 with the parameter %i of the theory based on an idealized model. 

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