Models PSD

Increases in etch pit formation have been translated into weathering rates by Macinnis and Brantley (1993) using a pit-size-distribution model (PSD) that considers the number of pits n as an inverse exponential function of the pit width W (cm) divided by the growth rate G (m s ) such that... 

Fig. 7 Stationary water-content profiles at various current densities for the model psd (4), cf. Table 1.

Low-Angle X-Rav Diffraction Measurements. Low-angle X-ray diffraction measurements were obtained by a Kiessig low-angle camera from Richard Seifert, Germany. Ni filtered Cu radiation was used and the reflections determined by Tennelec Position Sensitive detector system (Model PSD-1100). 

Model psds with varying values of and Xm are shown in Figure 2.2. At zero eurrent and other operating eonditions as speeified in the figure, capillary equilibrium exists in pores with radius = 5.5 nm. 

Using the simple model psd in Eq. (2.79) and the assumption of fast proton transport, a full solution of the system of conservation equations in Section 2.6 could be found, providing the pressure distributions p z), q z),p z), the capillary pressure p z) = p z) + q z) + p — p z), the current density distribution j z), and the overall relation between overpotential and total current density, r o(/b)- This solution highlights several vital functions of CCLs for the fuel cell water balance. 

The roughness design can be performed by virtual alteration of the surface roughness properties, approximated by analytical model PSD functions. Several PSD models exist for the description of surface roughness characteristics [15]. The fractal model, for example, is applied if roughness characteristics are assumed to be self-affine ... 

The models of Matranga, Myers and Glandt [22] and Tan and Gubbins [23] for supercritical methane adsorption on carbon using a slit shaped pore have shown the importance of pore width on adsorbate density. An estimate of the pore width distribution has been recognized as a valuable tool in evaluating adsorbents. Several methods have been reported for obtaining pore size distributions, (PSDs), some of which are discussed below. 

Thus, while models may suggest optimal pore spuctures to maximize methane storage, they give no indication or suggestion as to how such a material might be produced. On the other hand, simple measurement of methane uptake from variously prepared adsorbents is not sufficient to elucidate the difference in the pore structure of adsorbents. Sosin and Quinn s method of determining a PSD directly from the supercritical methane isotherm provides an important and valuable link between theoretical models and the practical production of carbon adsorbents... 

The general form of the population balance including aggregation and rupture terms was solved numerically to model the experimental particle size distributions. While excellent agreement was obtained using semi-empirical two-particle aggregation and disruption models (see Figure 6.15), PSD predictions of theoretical models based on laminar and turbulent flow considerations... 

On the other hand, very few ncdels for nulticonponent systans have been reported in the literature. Apart from models for binary systems, usually restricted to "zero-one" systans (5) (6), the most detailed model of this type has been proposed by Hamielec et al. (7), with reference to batch, semibatch and continuous emilsion polymerization reactors. Notably, besides the usual kinetic informations (nonomer, conversion, PSD), the model allows for the evaluation of IWD, long and short chain brandling frequencies and gel content. Comparisons between model predictions and experimental data are limited to tulK and solution binary pwlymerization systems. 

In this work, a comprehensive kinetic model, suitable for simulation of inilticomponent aiulsion polymerization reactors, is presented A well-mixed, isothermal, batch reactor is considered with illustrative purposes. Typical model outputs are PSD, monomer conversion, multivariate distritution of the i lymer particles in terms of numtoer and type of contained active Chains, and pwlymer ccmposition. Model predictions are compared with experimental data for the ternary system acrylonitrile-styrene-methyl methacrylate. 

Research on the modelling, optimization and control of emulsion polymerization (latex) reactors and processes has been expanding rapidly as the chemistry and physics of these systems become better understood, and as the demand for new and improved latex products increases. The objectives are usually to optimize production rates and/or to control product quality variables such as polymer particle size distribution (PSD), particle morphology, copolymer composition, molecular weights (MW s), long chain branching (LCB), crosslinking frequency and gel content. 

Table II. Recent Work on the Modelling of PSD s in Emulsion Polymerization Reactors...

Note that each environment in the micromixing model will have its own set of concentrations can and moments mkn, reflecting the fact that the PSD is coupled to the chemistry and will thus be different at every SGS point in the flow. The PD algorithm is applied separately in each environment to compute the weights (wmn) and abscissa (lmn) from the quadrature formula as follows ... 

The importance of chemical-reaction kinetics and the interaction of the latter with transport phenomena is the central theme of the contribution of Fox from Iowa State University. The chapter combines the clarity of a tutorial with the presentation of very recent results. Starting from simple chemistry and singlephase flow the reader is lead towards complex chemistry and two-phase flow. The issue of SGS modeling discussed already in Chapter 2 is now discussed with respect to the concentration fields. A detailed presentation of the joint Probability Density Function (PDF) method is given. The latter allows to account for the interaction between chemistry and physics. Results on impinging jet reactors are shown. When dealing with particulate systems a particle size distribution (PSD) and corresponding population balance equations are intro-... 

Figure 9.25 Models of granules of monodisperse particles characteristic psds (pore size distributions) are given below (a) uniform packing (b) bidisperse packing of aggregates of particles of similar sizes (c) same as (b) but the size of aggregates vary in a wide range.

The first model of porous space as a 2D lattice of interconnected pores with a variation of randomness and branchness was offered by Fatt [220], He used a network of resistors as an analog PS. Further, similar approaches were applied in a number of publications (see, e.g., Refs. [221-223]). Later Ksenjheck [224] used a 3D variant of such a model (simple cubic lattice with coordination number 6, formed from crossed cylindrical capillaries of different radii) for modeling MP with randomized psd. The plausible results were obtained in these works, but the quantitative consent with the experiment has not been achieved. 

The cumulative PSD will accurately predict the calibration curve for the column set if a simple model for retention applies (13) ... 

For PSDs measured by GPC, we expect a greater degree of success with the simple model for retention (eq. 5). Halasz noted that the PSDs he measured were always broader than corresponding PSDs from porisimetry and capillary condensation. This is in keeping with the convolution model (eq. 7) and indicates that the PSDs measured by GPC already contain the convolution between Kqpq and the classical PSD. If this is the case, then the "effective PSDs" provided by the GPC method should be useful for the direct prediction of calibration curves. 

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