Particle property model

Details of the particle property model may be found in Kiparissides et al M,2] and Chiang and Thompson [3]. Following an approach used by Dickinson [4J and Gorber [5], the development was based on an age distribution analysis in which the classes of particles born between any time, t and T+dt, were followed through the reactor. The result was a series of differential equations in the total particle size properties (diameter, area and volume), the number of particles, conversion and the initiator and emulsifier levels in the reactor. 

Saunders B R and Vincent B 1999 Microgel particles as model colloids theory, properties and applications Adv. Colloid Interface Sol. 80 1 -25... 

The model is able to predict the influence of mixing on particle properties and kinetic rates on different scales for a continuously operated reactor and a semibatch reactor with different types of impellers and under a wide range of operational conditions. From laboratory-scale experiments, the precipitation kinetics for nucleation, growth, agglomeration and disruption have to be determined (Zauner and Jones, 2000a). The fluid dynamic parameters, i.e. the local specific energy dissipation around the feed point, can be obtained either from CFD or from FDA measurements. In the compartmental SFM, the population balance is solved and the particle properties of the final product are predicted. As the model contains only physical and no phenomenological parameters, it can be used for scale-up. 

Gertlauer, A., Mitrovic, A., Motz, S. and Gilles, E.-D., 2001. A population balance model for crystallization processes using two independent particles properties. Chemical Engineering Science, 56(7), 2553-2565. 

Although both of these models provide a reasonable description of the precipitation polymerization process, they do not illustrate the relationship between the reactor variables and the polymer particle properties. 

Spin densities determine many properties of radical species, and have an important effect on the chemical reactivity within the family of the most reactive substances containing free radicals. Momentum densities represent an alternative description of a microscopic many-particle system with emphasis placed on aspects different from those in the more conventional position space particle density model. In particular, momentum densities provide a description of molecules that, in some sense, turns the usual position space electron density model inside out , by reversing the relative emphasis of the peripheral and core regions of atomic neighborhoods. 

The relation between electrophoretic mobility y and the surface properties of the particle (usually modeled as an ionic double layer for aqueous systems) is a classical problem in colloid science. 

The further development of accurate models to predict the above parameters (including the effects of particle properties and duct diameter) is being pursued currently, and considerable effort still is required before such models can be applied solely in design practice (i.e., without the need for experience or comparative data). 

It is also salutary to note figure 2, which reminds us that agreement and correctness are not always linked. [This figure is from the on-line dBase of particle properties http //pdg.lbl.gov.] Systematic errors always exist, and may be much larger in amplitude than expected. In general, deducing from uncertain data that a model is acceptable is not useful scientific progress. One learns from the failure of models, not from their successes. 

It should be noted that the magnitude of the predicted forcing is quite sensitive to treatment of relative humidity (RH) in the model because of the effects on particle size and optical properties (e.g., Haywood and Shine, 1995 Haywood and Ramaswamy, 1998 Ghan and Easter, 1998 Haywood et al., 1998a Penner et al., 1998). For example, in the calculations by Penner et al. (1998), when the particle properties were held fixed at the values for 90% RH for 90-99% RH, the predicted direct radiative forcing for sulfate particles decreased from - 1.18 W m-2 to -0.88 W m 2 for the Northern Hemisphere and from -0.81 to -0.55 W m-2 globally. 

Thiele(I4>, who predicted how in-pore diffusion would influence chemical reaction rates, employed a geometric model with isotropic properties. Both the effective diffusivity and the effective thermal conductivity are independent of position for such a model. Although idealised geometric shapes are used to depict the situation within a particle such models, as we shall see later, are quite good approximations to practical catalyst pellets. 

For size quantification of these particle systems, the underlying LII model has to be extended taking into consideration the optical metal particle properties (Vander Wal et al., 1999 Kreibig and Vollmer, 1995) on the one hand side and the contact surface area, on the other hand. The optical metal properties, which are in particular determined by the high imaginary part of the complex refraction index, show low absorption coefficients. 

We will discuss three cold dark matter candidates which are well-motivated , i.e. that have been proposed to solve problems in principle unrelated to dark matter and whose properties can be computed within a well-defined particle physics model. The three candidates we discuss are (1) a heavy active neutrino with standard model interactions, (2) the neutralino in the minimal super-symmetric standard model, and (3) the axion. Examples of other candidates that can be included in this category are a sterile neutrino (See e.g. Abazajian, Fuller, Patel (2001)) and other supersymmetric particles such as the grav-itino (See e.g. Ellis et al.(1984)) and the sneutrino (see, e.g.,Hall, Moroi Murayama( 1998)). 

Abstract. Surface pressure/area isotherms of monolayers of micro- and nanoparticles at fluid/liquid interfaces can be used to obtain information about particle properties (dimensions, interfacial contact angles), the structure of interfacial particle layers, interparticle interactions as well as relaxation processes within layers. Such information is important for understanding the stabilisation/destabilisation effects of particles for emulsions and foams. For a correct description of II-A isotherms of nanoparticle monolayers, the significant differences in particle size and solvent molecule size should be taken into account. The corresponding equations are derived by using the thermodynamic model of a two-dimensional solution. The equations not only provide satisfactory agreement with experimental data for the surface pressure of monolayers in a wide range of particle sizes from 75 pm to 7.5 nm, but also predict the areas per particle and per solvent molecule close to the experimental values. Similar equations can also be applied to protein molecule monolayers at liquid interfaces. 

The deposition variables are the process parameters most suited to regulate the particle composite content within the limits set by the particle properties and plating bath composition. Particle bath concentration is the most obvious process variable to control particle codeposition. Within the limits set by the metal plating process and the practical feasibility also current density, bath agitation and temperature can be used to obtain a particular composite. Consequently the deposition process variables are the most extensively investigated parameters in composite plating. The models and mechanisms discussed in Section IV almost exclusively try to explain and model the relation between these process parameters and the particle codeposition rate. 

The model presents an improvement of Guglielmi s model, but it also suffers from the same limitations. Process parameters, like bath agitation and particle properties, are not taken into account and even more fit parameters have been introduced. The reduction of adsorbed ions again leads to some debatable assumptions. Inherently the reduction of adsorbed... 

Dynamic light scattering (DLS) techniques measure the fluctuations in the scattered light intensity caused by the random Brownian motion of the dispersed particles. The use of a theoretical model of particle Brownian motion enables us to extract particle size from DLS data. Other dynamic light scattering techniques such as electrophoretic light scattering (ELS) study collective particle motions. Theoretical interpretation of ELS data leads to other particle properties such as electrophoretic mobility fi and zeta potential f. These techniques will be discussed in more detail in subsequent sections. 

We have also conducted adhesion measurements between real CMP abrasive particles (not model particles) and various surfaces as well as particle hardness and elastic modulus measurements, using colloidal AFM and nanoindentation AFM, respectively, in an attempt to correlate CMP defectivity with mechanical and adhesion properties of CMP abrasives [77,78]. For example, in a carefully designed experiment, we have been able to demonstrate that softer particles, indeed, result in fewer scratches [78]. 

The effects of gas and coal/char feeds and reactor geometries upon these internal processes and, hence, upon the performance of the reactor, can be simulated with this numerical model. The model incorporates representations of particle-particle and particle-gas interactions which account for finite rate heterogeneous and homogeneous chemistry as well as the hydrodynamical processes associated with particle collisions and drag between the particles and the gas flow. The important influences of multicomponent gas phase properties as well as solid particle properties, such as shape and size, are included in the representations. 

Continuons emulsion polymerization is one of the few chemical processes in which major design considerations require the use of dynamic or unsteady-state models of the process. This need arises because of important problems associated with sustained oscillations or limit cycles in conversion, particle number and size, and molecular weight. These oscillations can occur in almost all commercial continuous emulsion polymerization processes such as styrene (Brooks et cl., 1978), styrene-butadiene and vinyl acetate (Greene et cl., 1976 Kiparissides et cl., 1980a), methyl methacrylate, and chloropene. In addition to the undesirable variations in the polymer and particle properties that will occur, these oscillations can lead to emulsifier concentrations too low to cover adequately the polymer particles, with the result that excessive agglomeration and fouling can occur. Furthermore, excursions to high conversions in polymer like vinyl acetate... 

In the case of fumed powders, the results of particle size analysis depend veiy strongly on the characterization method. Each method measures a different particle property, from which sphere equivalent diameters are calculated. The underlying models assume homogeneous, spherical particles, which does not apply to the porous aggregates and agglomerates of these materials. 

---