Media multiphase

Note that filter aid selection must be based on planned laboratory tests. Guidelines for selection may only be applied in the broadest sense, since there is almost an infinite number of combinations of filter media, filter aids, and suspensions that will produce varying degrees of separation. The hydrodynamics of any filtration process are highly complex filtration is essentially a multiphase system in which interaction takes place between solids from the suspension, filter aid, and filter medium, and a liquid phase. Experiments are mandatory in most operations not only in proper filter aid selection but in defining the method of application. Some general guidelines can be applied to such studies the filter aid must have the minimum hydraulic resistance and provide the desired rate of separation an insufficient amount of filter aid leads to a reduction in filtrate quality — excess amounts result in losses is filtration rate and it is necessary to account for the method of application and characteristics of filter aids. 

In PEMFCs, the membrane electrode assembly (MEA, Eig. 15.2a) is a multilayer sandwich composed of catalytic layers (CLs) where electrochemical reactions take place, gas-diffusion media providing access of gases to the CLs, and a proton exchange membrane (PEM) such as Nafion . The CL is a multiphase multicomponent medium comprising ... 

If the amount of fluid within a fully saturated permeable medium is known as a function of position, the spatially resolved porosity distribution can be determined. If the medium is saturated with two fluids, and the signal from one can be distinguished, the fluid saturation can be determined. In this section, we will develop a method to determine the amount of a single observed fluid using MRI, and demonstrate the determination of porosity. In Section 4.1.4.3, we will demonstrate the determination of saturation distributions for use in estimating multiphase flow functions. 

The system of equations for gas phase was obtained by Favre averaging the system of multicomponent multiphase medium. The modified k-e model is used to describe the behavior of the gas phase. The generalization of this model will... 

The term "heterogeneous" as applied to the atmosphere refers to chemistry that occurs in or on ambient condensed phases that are in contact with the gas phase aerosols, clouds, surface waters, etc. It is important to distinguish between heterogeneous processes that occur on the surface of the solid, and multiphase chemical reactions that take place in the bulk of the liquid medium. In the latter case, it is assumed that the reaction takes place after the molecule has been incorporated in the bulk liquid medium, such as occurs by wet deposition, where a species is ultimately removed from the atmosphere, especially in the troposphere. 

Bobrov also used this model of a syntactic foam to calculate hydrostatic strengths164). At the same time, he showed that this parameter cannot be obtained theoretically for a syntactic foam using traditional micromechanical, macromechanical, or statistical approaches, as they are unsuitable for these foams. The first approach requires a three-dimensional solution of the viscoelasticity boundary value problem of a multiphase medium, and this is very laborious. The second and third methods assume the material is homogeneous overall, and so produce poor estimates for syntactic materials. 

The enthalpy conservation equation of the multiphase medium, obtained from the sum of the appropriate balance equations of the constituents includes the heat effects due to phase changes and hydration (dehydration) process, as well as the convectional and latent heat transfer,... 

An interesting from studies of nearby starbursts is that the mass outflow rate is of the same order of magnitude as the star formation rate. This result is also motivated by a multiphase interstellar medium in which supernova explosions... 

Emulsion Polymerization in a CSTR. Emulsion polymerization is usually carried out isothermally in batch or continuous stirred tank reactors. Temperature control is much easier than for bulk or solution polymerization because the small (. 5 Jim) polymer particles, which are the locus of reaction, are suspended in a continuous aqueous medium as shown in Figure 5. This complex, multiphase reactor also shows multiple steady states under isothermal conditions. Gerrens and coworkers at BASF seem to be the first to report these phenomena both computationally and experimentally. Figure 6 (taken from ref. (253)) plots the autocatalytic behavior of the reaction rate for styrene polymerization vs. monomer conversion in the reactor. The intersection... 

Slurry Reactors Slurry reactors are akin to fluidized beds except the fluidizing medium is a liquid. In some cases (e.g., for hydrogenation), a limited amount of hydrogen may be dissolved in the liquid feed. The solid material is maintained in a fluidized state by agitation, internal or external recycle of the liquid using pipe spargers or distributor plates with perforated holes at the bottom of the reactor. Most industrial processes with slurry reactors also use a gas in reactions such as chlorination, hydrogenation, and oxidation, so the discussion will be deferred to the multiphase reactor section of slurry reactors. 

The structure of a multiphase medium can be specified by the spatial distribution of the phases that form the medium. This spatial distribution can be generally represented by the phase function or, in specific situations, by the equivalent pore-network diagram, by the spatial distribution of particles or other constituents, and by the probability density function. Examples of the representation of the porous media are shown in Fig. 2. 

In a practical implementation, the domain on which the phase volume functions are specified is typically a cubic grid of Nx x Ny x Nz voxels, which corresponds to real dimensions of Lx — hNx, Ly - hNy, and Lz — hNz, where h is the voxel size. We will further call this region of real space the computational unit cell. The relationship between the unit cell and the multiphase medium of interest depends on the absolute dimensions of the medium and on the spatial resolution at which the medium is represented (feature dimensions). The unit cell can either contain the entire medium and some void space surrounding it, as in the case of virtual granules described in Section IV.D below, or be a sample of a much larger (theoretically infinite) medium, as in the case of transport properties calculation, described in Section II.E below. 

Once a spatially 2D or 3D image of the multiphase medium of interest has been obtained, it is desirable to characterize the image by a set of morphological descriptors, which can then be correlated with effective properties of the medium or their evolution followed in time when a structure-transformation process (e.g., dissolution) takes place in the medium. Let us now review some morphological descriptors most commonly used for the characterization of porous and multiphase media. 

In spatially evolving multiphase media (e.g., during dissolution of a porous medium, or phase separation in a polymer blend), the mean curvature of the interface between two phases is of interest. Curvature is a sensitive indicator of morphological transitions such as the transition from spherical to rod-like micelles in an emulsion, or the degree of sintering in a porous ceramic material. Furthermore, important physicochemical parameters such as capillary pressure (from the Young-Laplace equation) are curvature-dependent. The local value of the mean curvature K — (1 /R + 1 /Ri) of an interface of phase i with principal radii of curvature Rx and R2 can be calculated as the divergence of the interface normal vector ,... 

In mathematical terms, given the porosity and suitable morphological characteristics, we want to construct the replica of the porous/multiphase medium... 

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