Granular material, phases

Proprietary designs for rotary valve feeders (star valves) capable of continuous feeding of certain pelleted and granular materials into low velocity, dense phase systems, having system pressures up to 200 kPa (2 bars) have been developed. 

From isotherm measurements, usually earried out on small quantities of adsorbent, the methane uptake per unit mass of adsorbent is obtained. Sinee storage in a fixed volnme is dependent on the uptake per unit volume of adsorbent and not on the uptake per unit mass of adsorbent, it is neeessary to eonvert the mass uptake to a volume uptake. In this way an estimate of the possible storage capacity of an adsorbent can be made. To do this, the mass uptake has to be multiplied by the density of the adsorbent. Ihis density, for a powdered or granular material, should be the packing (bulk) density of the adsorbent, or the piece density if the adsorbent is in the form of a monolith. Thus a carbon adsorbent which adsorbs 150 mg methane per gram at 3.5 MPa and has a packed density of 0.50 g/ml, would store 75 g methane per liter plus any methane which is in the gas phase in the void or macropore volume. This can be multiplied by 1.5 to convert to the more popular unit, V/V. 

A contemporary of the method just described is the use of an absorbent (e.g. C-18) bonded onto granular or disk-type supports (solid-phase extraction [5]). The granular material is used in cartridge form (typically less than 5 ml), while disk forms are placed in a funnel/holder such as shown in Fig. 18.1b. A liquid (e.g. water, milk, or juice) would be passed through the cartridge (or filter disk), the analytes absorbed in the stationary matrix, the absorbent washed with water, and then the analytes of interest eluted from the absorbent with an organic solvent. This method has found limited use in the isolation of volatiles from foods but continues to find significant application in the analytical field overall [6]. 

For ideal mixtures there is a simple relationship between the measurable ultrasonic parameters and the concentration of the component phases. Thus ultrasound can be used to determine their composition once the properties of the component phases are known. Mixtures of triglyceride oils behave approximately as ideal mixtures and their ultrasonic properties can be modeled by the above equations [19]. Emulsions and suspensions where scattering is not appreciable can also be described using this approach [20]. In these systems the adiabatic compressibility of particles suspended in a liquid can be determined by measuring the ultrasonic velocity and the density. This is particularly useful for materials where it is difficult to determine the adiabatic compressibility directly, e.g., powders, biopolymer or granular materials. Deviations from equations 11 - 13 in non-ideal mixtures can be used to provide information about the non-ideality of a system. 

The study of problems concerning the flow of fluids through beds of granular material has many applications. It is indispensable to the theory of industrial filtration and water purification. The flow of ground water is controlled by soil structure and the most elementary phases of granular bed structure are fundamental to soil mechanics and soil physics. 

Then, the effective diffusivity of the macro-porous granular material is evaluated. The transport is again governed by the Fick s equation (23), but diffusion also takes place in the solid phase, which formally represents the nano-porous material, cf. Fig. 15. The diffusion coefficient in the solid phase is Dsohd = i//nanoD — 0.112D, where D is the bulk diffusivity. The concentration field in the macro-porous media is the solution of Eq. (23) with a diffusivity... 

In non-scattering systems, ultrasonic properties and the volume fraction of the disperse phase are related in a simple manner. In practice, many emulsions and suspensions behave like non-scattering systems under certain conditions (e.g. when thermal and visco-inertial scattering are not significant). In these systems, it is simple to use ultrasonic measurements to determine 0 once the ultrasonic properties of the component phases are known. Alternatively, if the ultrasonic properties of the continuous phase, 0and p2 are known, the adiabatic compressibility of the dispersed phase can be determined by measuring the ultrasonic velocity. This is particularly useful for materials where it is difficult to measure jc directly in the bulk form (e.g. powders, granular materials, blood cells). 

Thermal degradation, as outlined above, leads to production of volatile, low molecular weight products throughout the binder phase and the removal of the binder by evaporation of a liquid. Binder removal by this mechanism m.ay be quite similar to the drying of a moist granular material considered above (17.2.3.3.1). Considerable redistribution of the liquid occurs, and the evaporation front does not move uniformaly into the bodyT Instead, pore channels first develop deep in the body as liquid from the larger pores is drawn into the smaller pores. 

Figure 1 Phase diagram for typical granular material interactions.

The available continuum models for dispersed multi-phase flows thus follow one of two asymptotic approaches. The dilute phase approach is formulated based on the continuum mechanical principles in terms of the local conservation equations for each of the phases. A macroscopic model is then obtained by averaging the local equations based on an appropriate averaging procedure. In the dense phase approach, on the other hand, a kinetic theory description is adopted for the dispersed particulate phase (granular material), whereas an averaged continuum model formulation is adopted for the interstitial phase. 

The granular material closures presented in this section lead to a typical, or even the standard reference, dense phase model used for simulating fluidized bed reactor flows. 

To model the particle velocity fluctuation covariances caused by particle-particle collisions and particle interactions with the interstitial gas phase, the concept of kinetic theory of granular flows is adapted (see chap 4). This theory is based on an analogy between the particles and the molecules of dense gases. The particulate phase is thus represented as a population of identical, smooth and inelastic spheres. In order to predict the form of the transport equations for a granular material the classical framework from the kinetic theory of... 

Moreover, He Simonin [64, 65] considered the early models developed by Jenkins and Richman [69] appropriate for granular flows in vacuum, but inaccurate in the dilute zones of the bed where the interstitial gas phase fluctuations may affect the particles. He Simonin [64, 65] thus extended the kinetic theory of granular materials in vacuum to take into account the influence of the interstitial gas. 

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