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Model particle

A combination of equation (C2.6.13), equation (C2.6.14), equation (C2.6.15), equation (C2.6.16), equation (C2.6.17), equation (C2.6.18) and equation (C2.6.19) tlien allows us to estimate how low the electrolyte concentration needs to be to provide kinetic stability for a desired lengtli of time. This tlieory successfully accounts for a number of observations on slowly aggregating systems, but two discrepancies are found (see, for instance, [33]). First, tire observed dependence of stability ratio on salt concentration tends to be much weaker tlian predicted. Second, tire variation of tire stability ratio witli particle size is not reproduced experimentally. Recently, however, it was reported that for model particles witli a low surface charge, where tire DL VO tlieory is expected to hold, tire aggregation kinetics do agree witli tire tlieoretical predictions (see [60], and references tlierein). [Pg.2684]

For basic studies it is very advantageous to use suitable model particle systems which are much better reproducible and can be performed in a much shorter time. The best comprehension can be derived from studies under technical flow conditions in real bioreactors and partial comparison with experiences with biological cultures. [Pg.38]

The use of suitable model particle systems is recommended for the comparative test of bioreactors and their operating conditions. They permit faster, more reproducible and thus more cost-effective optimisation of technical relevant reactors [27,42-52]. [Pg.49]

Model particle systems have to have the following properties ... [Pg.49]

Since in the case of turbulent stress the ratio of particle diameter dp to length scale of turbulence qp is decisive for the stress regime (see Fig. 1) the model particle systems must have properties which guarantee dp/qp values which are in the same range as for the biological particle systems. [Pg.49]

Recommended model particle systems are enzymes immobilised on carriers ([27,44,45,47,49]), oil/water/surfactant or solvent/water/surfactant emulsions ([27, 44, 45] or [71, 72]) and a certain clay/polymer floccular system ([27, 42-52]), which have proved suitable in numerous tests. The enzyme resin described in [27,44,47] (acylase immobilised on an ion-exchanger) is used on an industrial scale for the cleavage of Penicillin G and is therefore also a biological material system. In Table 3 are given some data to model particle systems. [Pg.50]

The comparison of biological material systems and model particle systems in Fig. 2 shows that, under the operating conditions relevant for bioreactors, the... [Pg.51]

The investigations [27,44-49] carried out with model particle sytems allow the characterisation of many technical and model reactors and their comparison. Some of the results given there are summarised here since they contain the most important, systematic knowledge about stress in reactors existing so far. [Pg.52]

Table 5. Special reactors used with model particle systems... Table 5. Special reactors used with model particle systems...
It could be shown (see Sect. 6) that in stirred vessels with baffles and under the condition of fully developed turbulence, particle stress can be described by Eqs. (2) and (4) alone. The turbulent eddys in the dissipation range are decisive for the model particle systems used here and many biological particle systems (see Fig. 2), so that the following equation applies to effective stress ... [Pg.71]

A few exemplary results obtained with biological systems are discussed in the following and compared with the above-mentioned basic results of model particle systems. [Pg.72]

Figure 22 shows a comparison of results from model particle systems and h-terature data with biological systems in stirred vessels. The dependency of particle diameter on maximum energy dissipation dp of yeast and BHK... [Pg.72]

Fig. 22. Dependency of average particle diameter dp on maximiun energy dissipation of impeller systems with baffles by stirring of biological and model particle systems explanations see Tables 3 and 4... Fig. 22. Dependency of average particle diameter dp on maximiun energy dissipation of impeller systems with baffles by stirring of biological and model particle systems explanations see Tables 3 and 4...
With the knowledge of the basic tests on particle stress in model particle systems [45] and [47], Jiisten [60] selected similar stirrer types and operating conditions for his tests on stress on the myceUal microorganism, Penicillium chrysogenum. These experiments were carried out with sufficient oxygen supply so that the results may only be interpreted as due to different stress. [Pg.73]

The possibility of correlating these fermentation parameters with the turbulent stress equation shows again that obviously similar relationships exist for both the biological systems and the model particle systems used here. [Pg.74]

The comparison of the results obtained from model particle systems with experience of biological systems shows a similar tendency on many points. Therefore it proved to be very advantageous for the basic investigations, especially for the comparison of different reactor types, to use suitable model particle systems with similar properties to those of biological material systems. This permitted the performance of test series under technically relevant operating conditions, similar to those prevailing in bioreactors, in a relatively short time. The results are more reproducible than in biological systems and therefore permit faster and more exact optimization of reactors. [Pg.79]

For reactors with free turbulent flow without dominant boundary layer flows or gas/hquid interfaces (due to rising gas bubbles) such as stirred reactors with bafQes, all used model particle systems and also many biological systems produce similar results, and it may therefore be assumed that these results are also applicable to other particle systems. For stirred tanks in particular, the stress produced by impellers of various types can be predicted with the aid of a geometrical function (Eq. (20)) derived from the results of the measurements. Impellers with a large blade area in relation to the tank dimensions produce less shear, because of their uniform power input, in contrast to small and especially axial-flow impellers, such as propellers, and all kinds of inclined-blade impellers. [Pg.80]

For a model particle, titanium dioxide (Ti02, Nippon Aerosil, P-25) having its primary size of 21nm was used, which was normally impossible to be uniformly fluidized. [Pg.486]

The simplest case for modeling particle dissolution is to assume that the particles are monodisperse. Under these conditions, only one initial radius is required in the derivation of the model. Further simplification is possible if the assumption is made that mass transport from a sphere can be approximated by a flat surface or a slab, as was the case for the derivation for the Hixson-Crowell cube root law [70], Using the Nernstian expression for uniaxial flux from a slab (ignoring radial geometry or mass balance), one can derive the expression... [Pg.150]

Precisely owing to the continuum description of the dispersed phase, in Euler-Euler models, particle size is not an issue in relation to selecting grid cell size. Particle size only occurs in the constitutive relations used for modeling the phase interaction force and the dispersed-phase turbulent stresses. [Pg.170]

Lagrangian mixing models Particle-field estimation... [Pg.12]

Wottrich R, Diabate S, Krug HF (2004) Biological effects of ultrafine model particles in human macrophages and epithelial cells in mono- and co-culture. Int J Hyg Environ Health 207 353-361... [Pg.454]

The motion of polydispersed particulate phase is modeled making use of a stochastic approach. A group of representative model particles is distinguished. Motion of these particles is simulated directly taking into account the influence of the mean stream of gas and pulsations of parameters in gas phase. Properties of the gas flow — the mean kinetic energy and the rate of pulsations decay — make it possible to simulate the stochastic motion of the particles under the assumption of the Poisson flow of events. [Pg.228]

A great amount of real particles (for instance, liquid droplets) is modeled by an ensemble of model particles (their number is of the order of thousands). Each model particle is characterized by a vector of values, representing its location, velocity, mass, and other properties. The following vector, determined for each model particle, is introduced ... [Pg.228]

Modeling the particles phase, therefore, is split into two stages. The first stage is to evaluate the vector (14.12) for each model particle. The second stage is to evaluate the particle s phase volumetric share, a2 = 1 — a, and fluxes M/.,... [Pg.228]

Here d is the model particle diameter Nu is the Nusselt number. The Nusselt number for the th particle is determined as... [Pg.229]


See other pages where Model particle is mentioned: [Pg.156]    [Pg.663]    [Pg.709]    [Pg.489]    [Pg.35]    [Pg.36]    [Pg.49]    [Pg.50]    [Pg.52]    [Pg.506]    [Pg.2]    [Pg.149]    [Pg.64]    [Pg.407]    [Pg.257]    [Pg.301]    [Pg.447]    [Pg.700]    [Pg.446]    [Pg.371]    [Pg.228]    [Pg.228]    [Pg.229]    [Pg.229]   
See also in sourсe #XX -- [ Pg.906 ]




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A model for the craze-flow stress of particle-toughened polystyrene

A stochastic model for surface reactions including energetic particle interactions

Algorithmic methods fluid particle model

Blood, discrete particle model

Catalyst particle models

Charged-particle state electron models

Colloidal dynamic modeling discrete-particles

Colloidal model particles from

Colloidal model particles from organoalkoxysilanes

Computer simulation hard particle models

Cylindrical diffusion model particles

Discrete Particle Modeling of a Wurster Coater

Discrete particle model

Discrete particle modeling

Dispersion particles model

Electron correlation expansion, independent particle model

Electronic structure methods independent-particle models

Excitons effective-particle model

Experiments on Particle Model of Matter

Extended Independent Particle model

Fine particles other models

Finite-element model, rubber particles

Fluid Particle Model

Fluid particle model, discrete-particles

Fluid-particle flow mesoscale model

Fluid-particle flow microscale model

Fluidized discrete particle modeling

Free-particle model

Granular flow particle turbulence model

Hartree-Fock method independent particle model

Hartree-Fock theory. The independent-particle model

INDEX particle model

Independent particle model

Independent-particle model, wave function

Independent-particle model, wave function calculations

Inter-particle model

KL Model for Fine Particles

KL Model for Intermediate-Size Particles

Kinetic models intra-particle diffusion, rates

Kinetics intra-particle diffusion model

Lagrangian particle model

Lagrangian properties particle models

Lagrangian single-particle model

MODELS FOR REACTIVE SOLID PARTICLES

Mathematical dynamic model development particle distribution

Mathematical models particle size distribution

Metal particle, physical model

Microscale model fluid particle

Microstructure, colloidal model particles

Model for Large Particles

Model of Two Floating Spherical Particles

Model particle size distribution, protein

Model particle size effects

Model, multi-component particle property

Modeling and Experimental Analysis of Single Electrode Particles

Modeling at the particle scale

Modeling of the particle

Modeling single particle model

Modelling of the Fly Ash Particle

Models LaGrangian particle tracking

Models independent particle, electron correlation

Models, crystallization process particle characteristics

Momentum equation, discrete particle modeling

Morphology, colloidal model particles from

Multi-particle collision model

Multiple fine particle model

Multiscale modeling discrete particle model

Nearly free particle model

Nucleation exclusion zones modeling particle growth

Nucleus, atomic alpha-particle model

Octahedral Models of Complex Particles

One-Particle Model with Square Potential-Energy Wells

Overview of Discrete, Particle Models

Partial condenser Particle model

Particle Standard model

Particle array modelling

Particle based models

Particle bed model

Particle connectivity model

Particle deposition computational models

Particle deposition models

Particle diameter-separation factor model

Particle dynamics models, dissipative

Particle formation model

Particle heating/cooling models

Particle lifetime model

Particle migration model and its limitations

Particle model basic

Particle model craze formation

Particle model experience

Particle model of light

Particle model resources

Particle model students’ misconceptions

Particle model students’ understanding

Particle model teaching

Particle model, calculation

Particle model, calculation intensity

Particle model, calculation theoretical scattered

Particle modeling, Wurster coater

Particle morphology, colloidal model

Particle property model

Particle scale modeling

Particle sedimentation model

Particle size distribution modeling

Particle size distribution population balance model

Particle surface site-binding model

Particle velocities model developing

Particle-in-a- model

Particle-in-a-box model

Particle-in-a-box model and

Particle-rotor model

Particles discrete particle modeling

Particles source apportionment, models

Physical Significance of Independent-Particle Models and Correlation

Possible Explanations of Particle Size Effects Experiments versus Models

Quantum Mechanics of Particle-in-a-Box Models

Quasi-continuum model in particle accumulation

Quasi-particle model

Reactions, colloidal model particles from

Rigid particles suspensions rheology, models

Rigid spherical particles models

Scaled discrete particle model

Scaled-particle model

Schrodinger equation independent particle model

Separation factor-particle size modeling

Shrinking Core Model for Spherical Particles of Unchanging Size

Shrinking-particle model

Shrinking-particle model system

Simplified single-particle model

Single Particle Heat Transfer Modeling for Expanded Shale Processing

Single Particle Models - Mass- and Heat-transfer Resistances

Single particle unreacted core models

Single-particle model

Single-particle shell model

Solutions of the effective-particle model

Spherical diffusion model particles

Spouted discrete particle modeling

Standard Model of elementary particles

Structured particles, modeling

Surface complexation models particle geometry

Surface complexation models particle morphology

Surface-modified Polystyrene Particles as Model Carriers

Suspension models particle shape effect

Test particle model

The Independent Particle Model

The effective-particle model

The nearly free particle model

The physical model of water-like particles in two dimensions

Theoretical Models of Gas-Liquid-Particle Operations

Two-particle model

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