Model solids mixing

A stirred-tank model has been proposed, (Daly, 1980), to model the mixing behavior of an air-solid, spouted, fluidised-bed reactor. The central spout is modelled as two tanks in series, the top fountain as a further tank and the down flowing annular region of the bed as 6 equal tanks in series. It is assumed that a constant fraction of the total solids returns from each stage of the annular region into the central two tank region, as depicted below. 

Figure 38. Experimental solids mixing data and model predictions—0.254 m jet, Set Point 3, Sampling Port A.

Figure 11. Ultimate activities of OHA and FA at the spinodal compositions in the model of mixed-type regular and subregular solid solutions.

Titration results for the mixed erne s of the SDS/CgE4 and C12E2S/C8E4 systems as a function of their relative mole fraction in solution are shown in Figures 2 and 3, respectively. Here, the experimentally determined points are compared with calculated results from the nonideal mixed micelle model (solid line) and the ideal mixed micelle model (dashed line). Good agreement with the nonideal model is seen in each case. 

The dispersion model of solids mixing (Kunii and Levenspiel, 1991) is based on Tick s equafion which describes unsfeady-sfafe mass transfer in one dimension. Thus... 

Vazquez and Calvelo (1983b) presented a model for the prediction of the minimum residence time in a fluidized bed freezer which can then be equated to the required freezing time. The model is defined in terms of a longitudinal dispersion coefficient D, which is a measure of the degree of solids mixing within the bed in the direction of flow (and has the dimensions of a diffusivity, and hence units of m s ), a dimensionless time T... 

Rottenbacher, L., Schofiler, M. and Bauer, W., Mathematical modelling of alcoholic fermentation in a gas/solid bioreactor - combined effects of solids mixing and non-steady-state kinetics. Proceedings of the First IFAC Symposium on Modelling and Control of Biotechnological Processes, Noordwijkerhout, 1985b, 151-157. 

Results for the various binary mixed surfactant systems are shown in figures 1-7. Here, experimental results for the surface tension at the cmc (points) for the mixtures are compared with calculated results from the nonideal mixed monolayer model (solid line) and results for the ideal model (dashed line). Calculations of the surface tension are based on equation 17 with unit activity coefficients for the ideal case and activity coefficients determined using the net interaction 3 (from the mixed micelle model) and (equations 12 and 13) in the nonideal case. In these calculations the area per mole at the surface for each pure component, tOj, is obtained directly from the slope of the linear region in experimental surface tension data below the cmc (via equation 5) and the maximum surface pressure, from the linear best fit of... 

Cluster models of mixed oxide catalysts and of relationships between solid and solution catalysts... 

In this review, we introduce another approach to study the multiscale structures of polymer materials based on a lattice model. We first show the development of a Helmholtz energy model of mixing for polymers based on close-packed lattice model by combining molecular simulation with statistical mechanics. Then, holes are introduced to account for the effect of pressure. Combined with WDA, this model of Helmholtz energy is further applied to develop a new lattice DFT to calculate the adsorption of polymers at solid-liquid interface. Finally, we develop a framework based on the strong segregation limit (SSL) theory to predict the morphologies of micro-phase separation of diblock copolymers confined in curved surfaces. 

What follows is a survey of the fluid-mechanical principles of fluidization technology, gas and solid mixing, gas-solid contact in the fluidized bed, typical industrial applications, and approaches to modeling fluidized-bed reactors. Further information is given in... 

Figure 9. (a) Fits of Z(r) data (solid circles from TEM and open circles from SAXS) of uncapped ZnO nanorods to the Ostwald ripening (I3) model (solid curve), (b) Fits of Z(r) data (3olid circles from TEM and open circles from SAXS) of PVP-capped ZnO nanorods to the Ostwaid ripening (Z3) model (broken curve) and mixed diffusion-surface control growth (Z3 + Z2) model (solid curve). 

For the calculation of solid-solution mineral behavior, two conceptual models may be used the end-member model (arbitrary mixing of two or more phases) and the site-mixing model (substituting elements can replace certain elements only at certain sites within the crystal structure). 

Bader et al. (1988) used common salt as a solid tracer, which was injected into a flowing catalyst bed. Solids samples, withdrawn downstream of tracer injection, were leached with water and the salt concentration determined by electrical conductivity of the solution. Their results indicated substantial solids backmixing. Li et al. (1991) observed solids mixing in a fast fluidized bed combustor by using raw coal as a tracer, which was injected into the ash bed. Their results also showed that near-perfect mixing prevailed. Similar experiments was also conducted by Chesonis et al. (1991) in a cold model. 

For gas velocities ranging 4.1 to 6.3 m/s, the measured axial solids dispersion coefficients Ds varied from 0.39 to 0.91 m2/s for dilute solid suspension, while for the whole fast bed, in the same gas velocity range, Ds was 0.22 to 1.67 m2/s. Axial solid dispersion coefficient generally increases with both gas velocity and solids circulation rate. Milne and Berruti (1991) have also given their own model for solids mixing. 

Milne, B. J., and Berruti, F. Modelling the mixing of solids in circulating fluidized beds, in Circulating Fluidized Bed Technology III (P. Basu, M. Horio and M. Hasatani, eds.), pp. 575-580. Pergamon Press, 1991. 

Diffraction Methods in Inorgaitic Chemistry Electronic Structure of Solids Mixed Valence Compounds Oxides Solid-state Chemistry Solids Computer Modeling. 

The chemistry component of the model is, in most aspects, identical to the chemistry of the classical models of fluidized bed gasification. A major difference between the classical reactor models and the present fluidized bed coal gasifier computer model is that the classical models require specification of the bed hydrodynamics, such as bubble size. The present model can predict bubble size and the associated solids mixing. Again it is expected that the two types of models are complimentary. The present model can be used to define the hydrodynamics in the hot reactive environment and these hydrodynamics (e.g., bubble size) can then be used as... 

It should be noted that deriving the bulk composition of the Earth in general by simple models of mixing between meteoritic components has generally always found difficulties, especially with elements of greater volatility. However, the possibility remains that solid materials that contributed to the Earth, with unique major-volatile characteristics, are no longer represented in the solar system. 

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