Bimodal model, applications

Figure 9.4.1 Relative viscosity of a bidisperse coal slurry made up of a colloidal fine fraction of mean diameter 2.3 /j,m and a noncolloidal coarse fraction of 200—300 m particles of mean diameter about 250 fim as a function of shear rate. The volume fraction of the colloidal particles = 0.30 and of the coarse particles , = 0.52. The solid line is a mean curve through the measured viscosities of the colloidal fraction. The triangles are the experimental points for the measured viscosity for the fine plus coarse mixture. The dashed line is the fine relative viscosity experimental curve redrawn through the data points to illustrate the parallelism. The upward shift of this curve corresponds to a coarse relative viscosity log 77, = 2.13. [After Sengun, M.Z. Probstein, R.F. 1989. Bimodal model of slurry viscosity with application to coal-slurries. Part 2. High shear limit behavior. Rheol. Acta 28, 394-401. Steinkopff Darmstadt. With permission.]...

SENGUN, M.Z. PROBSTEIN, R.F. 1989b. Bimodal model of slurry viscosity with application to coal-slurries. Part 1. Theory and experiment. Rheol. Acta 28, 382-393. 

Probably this requires timescales of <10 yr (Podosek and Cassen, 1994). In contrast, the most widely accepted dynamic models advocated for the formation of the terrestrial planets (Wetherill, 1986), involve protracted timescales —10 -10 yr. Application of these same models to the outer planets would mean even longer timescales. In fact, some of the outermost planets would not have yet formed. Therefore, the bimodal distribution of planetary density and its striking spatial distribution appear to require different accretion mechanisms in these two portions of the solar system. However, one simply cannot divide the accretion dynamics into two zones. A range of rate-limiting processes probably controlled accretion of both the terrestrial and Jovian planets and the debates about which of these processes may have been common to both is far from resolved. There almost certainly was some level of commonality. 

This chapter has presented a number of adsorption models for homogeneous particles where parallel diffusion mechanism is operating. This type of mechanism is applicable to solids such as activated carbon. We will present in the next chapter a number of models for zeolite type solids where a bimodal diffusion mechanism is operating. 

The successful application and generalization of the SFM model triggers our attempts to establish a structure-dependent mass transfer model which may unify our past efforts on mass transfer modehng. Similar to what has been presented in Section 5.1, we introduce the nonequffibrium, bimodal distribution into the modeling of mass transfer and reactions in a similar way, as detailed in the following. 

Here, we examine the flow behavior of composite paste materials containing bimodal and trimodal (near or spherical) powders, mixtures of short fibers, or platelets with near-spherical powders. Ceramic materials are used as model systems though the results are universally applicable for nonreactive products. 

To put it simply the ontology of Safety-1 cannot be sustained. Or rather, Safety-1 thinking is no longer universally applicable. We must keep in mind that even if we limit the focus to traditional safety concerns, this way of thinking was developed almost a century ago. The Domino model was described in a book published in 1931, but the experiences that led to the ideas and theories described in the book were from the preceding decades. The thinking that was relevant for the work environments at the beginning of the twentieth century is unlikely to be relevant today when socio-technical systems are not decomposable, bimodal, or predictable. 

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