Interstitial phases

Because of the inadequacies of the aforementioned models, a number of papers in the 1950s and 1960s developed alternative mathematical descriptions of fluidized beds that explicitly divided the reactor contents into two phases, a bubble phase and an emulsion or dense phase. The bubble or lean phase is presumed to be essentially free of solids so that little, if any, reaction occurs in this portion of the bed. Reaction takes place within the dense phase, where virtually all of the solid catalyst particles are found. This phase may also be referred to as a particulate phase, an interstitial phase, or an emulsion phase by various authors. Figure 12.19 is a schematic representation of two phase models of fluidized beds. Some models also define a cloud phase as the region of space surrounding the bubble that acts as a source and a sink for gas exchange with the bubble. 

This structure type with the axial ratio c/a close to 1 is an example of the Hagg interstitial phases formed when the ratio between non-metal and metal radii is less than about 0.59. The structure can be described as a 3D array of trigonal prisms of W atoms (contiguous on all the faces). Alternate trigonal prisms are centred by C atoms. Compounds belonging to this structure type are for instance IrB, OsB, RuB, MoC, WC (compare, however, with the NaCl-type phase), NbN, WN, MoP, etc. 

Interstitial phases. These are predominant in steels and ferrous-based alloys, where elements such as C and N occupy the interstitial sites of the ferrite and austenite lattices. In this case the structure of the phase can be considered as consisting of two sublattices, one occiqiied by substitutional elements, such as Fe, Cr, Ni, Mn, etc., and the other occupied by the interstitial elements, such as C or N, and interstitial vacancies (Va). As the concentration of C, N,..., etc., increases the interstitial vacancies are filled until there is complete occiqjation. The occupation of the sublattices is shown below as... 

If the dense phase expands this immediately affects the reactor model because more gas will then flow via the favourable interstitial phase. Most models readily allow for this change given that the true division of flow can be predicted. Unhappily it has so far only been possible to measure this division experimentally at fairly low flow rates, well below those employed in commercial reactors. Certainly at velocities up to about 15 cm/s much more gas flows interstitially through Geldart type A powders than minimum fluidisation flow (17). 

Considering now the consequences for chemical reaction, much of the reactant gas that ultimately forms a bubble will first enter the interstitial phase and enjoy a brief moment of intimate contact with the particles. Later it may form a cloud as in Figure 5 with limited access to particles. Hence the high reaction rates associated with the process of bubble formation and limited to the bottom layer of the bed of thickness up to twice the initial bubble diameter - a few centimeters at most. 

When nitrides are treated with carbon monoxide at moderate temperatures, two reactions occur. The first may be termed a completion reaction in which carbon enters the interstitial phase until C + N increases to about 0.5. This reaction is more rapid than the second, the substitution reaction in which carbon replaces nitrogen. Similar reactions are observed when carbides of iron (Hagg carbide or cementite) are... 

Here, n is a unit normal vector at the interstitial phase boundary Sp, if any, across which the kinematic viscosity v(r) is possibly discontinuous, whereas the generic symbol h denotes either P or j. Equation (8.15) expresses continuity of the pertinent fields across the unit cell faces dr0. In Eq. (8.15), m is to be chosen such that Rm, = Rm - I is a basic lattice vector [cf. Eq. (7.1)]. 

Section of poly-mineralic grain (scoie of interstitial phase IS slightly exaggeroted). 

Elemental analysis generally poses no problems because of the limited stability of the compounds and the formation of elemental gold in decomposition and combustion, which does not form carbides, nitrides, or other interstitial phases. Atomic absorption and inductively coupled plasma spectroscopy are presently the methods of choice for An estimation. Many organogold compounds are sufficiently volatile to allow registration of good mass spectra by gas-phase electron impact. Field desorption, fast-atom bombardment, and chemical ionization mass spectrometry have also been successfully applied. 

When the formulated solution contains essentially saline or organic solutes that crystallize easily, the interstitial phase will crystallize out abruptly as an eutectic or a mixture of eutectics. The crystallization results in an immediate hardening of the frozen system, which becomes fully rigid. At this point, the system has reached its maximum temperature for complete... 

When the formulated solution predominantly contains polyols, sugars, or polymers, the interstitial phase does not usually crystallize out upon cooling but increases progressively in viscosity as a glass-like system. In the case where the interstitial phase has effectively the structure of a glass, the frozen system becomes fully rigid once the glass transition temperature (Fg) is reached. In contrast, some amorphous systems may show no such definite transition, but they eventually become very stiff at low temperature, as shown by electrical resistance studies. 

Regardless of the freezing behavior of the formulated solution, it is essential to make sure that the temperature of the product is decreased below the temperature where complete solidification is observed. If this condition is not respected, the incompletely frozen interstitial phase will boil or induce pellet partial melting or collapse during lyophilization. 

In vitreous systems, it is to be noted that the collapse temperature, T., can exceed the glass transition temperature by several degrees or more [2]. The retention of pellet structure below arises from the fact that when the frozen solution passes through the glass transition temperature, it returns from a glass to a highly viscous amorphous material. It is only when the viscosity of this material has decreased significantly that the fluidity of the interstitial phase is sufficient to cause collapse. 

Ureilites contain a variety of trace accessory phases. Metallic spherules composed of cohenite, metal, and sulfide are included in olivine and pigeonite of a few ureilites, and metal, phosphide, and sulfide are present as interstitial phases in most. The interstitial regions also commonly contain fine-grained silicates, including low-calcium pyroxene, augite and Si-Al-alkali glass. 

Occluded skin may absorb up to 5-6 times its dry weight of water. In the idealised model of the stratum corneum shown in Fig. 9.23, L represents the lipid-rich interstitial phase and P the proteinaceous phase. If p = P /Pp (the ratio of the partition coefficients of the drug between vehicle and the L and P phases), and Dl and Dp are the diffusion coefficients of the drug in these phases, the flux through stratum corneum of average thickness (that is, 40 pm) is found to reduce to... 

Fig. 2.11 Relationship between HETP and interstitial phase velocity.

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. 

Grindability of quickly cooled clinker is good. Amber belite is ground at the last stage. J.M. Butt (1974) stated that good grindability of quickly cooled clinker is due to plenty of micropores in the interstitial phase. 

A paper by Takagi and Kawashima (1980) shows the effects of various kiln conditions on alite, belite, and interstitial phases. These authors present a clinker Character Index, a collection of parameters which, when plotted against compressive strength at 28 days, forms a sigmoidal curve. The Ono parameters figure significantly in the formulation of the Character Index, as seen in the following list of phase characteristics ... 

The fine powder fraction of clinker is rich in alite fragments. The coarse fraction is rich in agglomerates of small brown belite and agglomerates of minute alite crystals combined with dark interstitial phase. 

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