Hydrodynamic dispersion, description

Modeling of hydrodynamics in gas/vapor/liquid-liquid contactors includes an appropriate description of axial dispersion, liquid holdup, and pressure drop. The correlations giving such a description have been published in numerous papers and are collected in several reviews and textbooks (e.g., Refs. 65 and 66). Nevertheless, there is still a need for a better description of the hydrodynamics in catalytic column internals this is being reflected by research activities in progress (67). 

For this description of PCS, it is evident that, for mono-disperse systems, the technique can provide an absolute measurement of hydrodynamic size knowledge of the density or refractive index of the particles is not required, and no calibration or correction is needed. With the advent of digital correlators and microprocessors, PCS has also become a very fast and precise technique. Recent studies of latex using PCS include adsorbed layers (8), particle sizes (16), surface characterization (17) and aggregation (181- ... 

Reactive absorption processes present essentially a combination of transport phenomena and reactions taking place in a two-phase system with an interface. Because of their multicomponent nature, reactive absorption processes are affected by a complex thermodynamic and diffusional coupling which, in turn, is accompanied by simultaneous chemical reactions [14—16], Generally, the reaction has to be considered both in the bulk and in the film region. Modeling of hydrodynamics in gas-liquid contactors includes an appropriate description of axial dispersion, liquid hold-up and pressure drop. 

Attempts to describe the unlimited increase of the viscosity of dispersions and emulsions observed when their concentrations approach the maximum values (tPmax) meet great theoretical difficulties. Various approaches were developed to overcome these difficulties. Thus, for example, Russel et al. [58] suggested that account should be taken of the Brownian motion of particles in colloidal dispersions in the form of a hydrodynamic contribution. They showed that this contribution which is to be taken into account in considering a slow flow (with slow shear rates y), increases considerably with increasing dispersion concentration. For a description of the dependence of viscosity on concentration the above authors obtained an exact equation only in the integral form. At low shear rates it gives the following power series ... 

A field-flow fractionation (FFF) channel is normally ribbonlike. The ratio of its breadth b to width w is usually larger than 40. This was the reason to consider the 2D models adequate for the description of hydrodynamic and mass-transfer processes in FFF channels. The longitudinal flow was approximated by the equation for the flow between infinite parallel plates, and the influence of the side walls on mass-transfer of solute was neglected in the most of FFF models, starting with standard theory of Giddings and more complicated models based on the generalized dispersion theory [1]. The authors of Ref. 1 were probably the first to assume that the difference in the experimental peak widths and predictions of the theory may be due to the influence of the side walls. 

Moving up into the reactor level, effects of convection, dispersion and generation are described in the conservation equations for mass and energy. The momentum balance describes the behavior of pressure. The interface between the reactor and the catalyst level is described by the external mass transfer conditions, most often represented in a Fickian format, i.e., a linear dependence of the rate of mass transfer on the concentration gradient. In cases where an explicit description of mixing and hydrodynamic patterns is required, the simultaneous integration of the Navier-Stokes equations is also conducted at this level. I f the reaction proceeds thermally, the conversion of mass and the temperature effect as a result of it are described here as well. 

In recent years a lot of attention has been devoted to the application of electroacoustics for the characterization of concentrated disperse systems. As pointed out by Dukhin [26,27], equation (V-51) is not valid in such systems because it does not account for hydrodynamic and electrostatic interactions between particles. These interactions can typically be accounted for by the introduction of the so-called cell model, which represents an approach used to model concentrated disperse systems. According to the cell model concept, each particle in the disperse system is inclosed in the spherical cell of surrounding liquid associated only with that individual particle. The particle-particle interactions are then accounted for by proper boundary conditions imposed on the outer boundary of the cell. The cell model provides a relationship between the macroscopic (experimentally measured) and local (i.e. within a cell) hydrodynamic and electric properties of the system. By employing a cell model it is also possible to account for polydispersity. Different cell models were described in the literature [26,27]. In each case different expressions for the CVP were obtained. It was argued that some models were more successful than the others for characterization of concentrated disperse systems. Nowadays further development of the theoretical description of electroacoustic phenomena is a rapidly growing area. 

Let us compare the fluxes of the disperse particles and molecular impurities on the bubble surface assuming that the hydrodynamic field is described by the Stokes equation. It enables to use Eq. (8.152) for the description of the impurity flux. This equation can be transformed into an analogue of the capture efficiency. 

Considering that FIA is based on sample injection, controlled dispersion of the injected sample zone, and reproducible timing and that it is physically embodied in the system shown in Fig. 2.4, it becomes evident that none of the papers published until 1975 conforms with that description. Closest to this principle was undoubtedly the work of Nagy et al. [7.1], who suggested a novel approach to hydrodynamic voltammetry, based on the injection of a small sample volume into a supporting elec-... 

The overall description (model) of a reactor is obtained through process synthesis by combining models of reactor hydrodynamics, mass transfer and heat exchange with an appropriate cell (subcellular) or population model ( 1).Description of a population should take into consideration possible dispersed or aggregated (the distinct morphological appearances of a culture pellets, mycelium, flocks, growth on reactor wall in the form of microbial film) forms of population. Biomass support particles are gaining appreciable importance in aerobic (40) as well as in anaerobic processes. 

But this is not a simple task theoretically (especially since the hydrodynamic interactions that are important for higher concentrations are very difficult to account for), and even for the second-order term B quite different values can be found in the literature (e.g., 6.2 [26] and 14.1 [27]). However, for the description of concentrated dispersions, such a virial expression is not really very useful because it would require a fairly large number of coefficients that are theoretically not easily accessible. For spheres that are not correlated spatially the hydrodynamic interactions can be taken into consideration and yield the... 

Thus, the disperse nanofiller particles aggregation in elastomeric matrix can be described theoretically within the framewoiks of a modified model of irreversible aggregation particle-cluster. The obligatory consideration of nanofiller initial particles size is a feature of the indicated model application to real systems description. The indicated particles diffusion in polymer matrix obeys classical laws of Newtonian liquids hydrodynamics. The offered approach allows to predict nanoparticles aggregates final parameters as a function of the initial particles size, their contents and other factors number. 

Description of the dispersing process for a turbulent flow of two-phase systems, in relation to the hydrodynamic mode of operation of tubular diffuser-confusor devices, can be simplified by the introduction of the volume-surface diameter of dispersed phase droplets d 2 [9, 60, 61, 76, 77] ... 

This article delineates fundamental principles germane to a new method of hydrodynamic description for a special class of disperse systems that is widespread in various industrial technological processes. Hydrodynamic description implies, first... 

In engineering practice viscosity is considered a constant of materials. In available literature the value of viscosity has large dispersion, and often differs even in several orders (Goldin, 2002). Obviously this situation is related to the different scales at which deformation and fracture take place. At tectonic scale level deformation and relaxation proceed slowly, and the value of viscosity is large. But at meso-microlevels viscosity has a low value. For example, under pressure higher than 100-200 Gpa, hydrodynamic approximation is rational in description of the propagation of a shock wave. But under pressure in the diapason 1-10 Gpa, viscosity plays a decisive role in the formation of the profile of a shock wave. 

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