Rosen model

A study of the effect of the mesophase layer on the thermomechanical behaviour and the transfer mechanism of loads between phases of composites will be presented in this study. Suitable theoretical models shall be presented, where the mesophase is taken into consideration as an additional intermediate phase. To a first approximation the mesophase material is considered as a homogeneous isotropic one, while, in further approximations, more sophisticated models have been developed, in which the mesophase material is considered as an inhomogeneous material with progressively varying properties between inclusions and matrix. Thus, improvements of the basic Hashin-Rosen models have been incorporated, making the new models more flexible and suitable to describe the real behaviour of composites. 

The novel element in these models is the introduction of a third phase in the Hashin-Rosen model, which lies between the two main phases (inclusions and matrix) and contributes to the progressive unfolding of the properties of the inclusions to those of the matrix, without discontinuities. Then, these models incoporate all transition properties of a thin boundary-layer of the matrix near the inclusions. Thus, this pseudo-phase characterizes the effectiveness of the bonding between phases and defines a adhesion factor of the composite. 

Note that up to now it has been assumed that the diffusion in the micropores of microporous adsorbents is not rate controlling. This assumption is also a prerequisite for the Rosen model (Rosen 1954). 

Again, the coefficients of the models are not directly comparable, as each model uses a different scaling for impact speed. Note, that the Rosen model used kph, whereas impact speed for the GIDAS model was scaled using standard deviation and mean and for PCDS using only the mean, see Sect. 5.2.3. 

Theoretical breakthrough curves for nonlinear systems may be calculated by numerical solution of the model equations using standard finite difference or collocation methods. Such solutions have been obtained by many authors and a brief summary is given in Table 8.4. In all cases plug flow was assumed and the equilibrium relationship was taken to be of cither Langmuir or Freundlich form. As linearity is approached ( ->1.0) the linearized rate models approach the Anzelius model (Table 8.1, model la) while the diffusion models approach the Rosen model (Table 8.1, model la). The conformity of the numerical solution to the exact analytic solution in the linear limit was confirmed by Garg and Ruthven. ... 

Vargo-Gogola, T, and J. M. Rosen. Modeling Breast Cancer One Size Does Not Fit All. Nature Reviews Cancer 7 (2007) 659-72. 

A variation on the exact soiutions is the so-caiied seif-consistent modei that is explained in simpiest engineering terms by Whitney and Riiey [3-12]. Their modei has a singie hollow fiber embedded in a concentric cylinder of matrix material as in Figure 3-26. That is, only one inclusion is considered. The volume fraction of the inclusion in the composite cylinder is the same as that of the entire body of fibers in the composite material. Such an assumption is not entirely valid because the matrix material might tend to coat the fibers imperfectiy and hence ieave voids. Note that there is no association of this model with any particular array of fibers. Also recognize the similarity between this model and the concentric-cylinder model of Hashin and Rosen [3-8]. Other more complex self-consistent models include those by Hill [3-13] and Hermans [3-14] which are discussed by Chamis and Sendeckyj [3-5]. Whitney extended his model to transversely isotropic fibers [3-15] and to twisted fibers [3-16]. 

Figure 3-49 Rosen s Tensile Failure Model (After Rosen [3-27])...

The solutions obtained by Rosen show that at low pressures, the burning rate becomes linear in pressure and the surface pyrolysis characteristics are not important. At high pressures, however, the burning rate becomes independent of pressure and is determined almost entirely by the decomposition reactions at the solid surface. Rosen points out that this simple model can... 

A better approach for the Rosen-Hashin models is to adopt models, whose representative volume element consists of three phases, which are either concentric spheres for the particulates, or co-axial cylinders for the fiber-composites, with each phase maintaining its constant volume fraction 4). 

Dijkhuizen RM, Asahi M, Wu O, Rosen BR, Lo EH. Delayed rt-PA treatment in a rat embolic stroke model Diagnosis and prognosis of ischemic injury and hemorrhagic transformation with magnetic resonance imaging. J Cereb Blood Flow Metab. 2001 21 964-971. 

In order to evaluate different approximations in the context of modeling electrochemical systems [Haftel and Rosen, 2003 Kitchin et al., 2004 Gunnarsson et al., 2004 Feng et al., 2005 Rossmeisl et al., 2006 Taylor et al., 2006 Jacob, 2007a, b], in the following, we shall discuss each term of (5.15) separately ... 

Haftel Ml, Rosen M. 2001. Surface embedded atom model of the electrolyte-metal interface. Phys Rev B 64 195405. 

The reaction is carried out in a non-cooled, continuous stirred-tank reactor (Fig. 5.58), and it is required to find the effect of changes in the reactor inlet conditions on the degree of polymerisation obtained. The model is that of Kenat, Kermode and Rosen (1967). 

The use of material balances in the modelling of complex unsteady-state processes is discussed in the books by Myers and Seider (1976) and Henley and Rosen (1969). 

Saxena, S. C., Rosen, M., Smith, D. N., and Ruether, J. A., Mathematical Modeling of Fischer-Tropsch Slurry Bubble Column Reactors, Chem. Eng. Comm., 40 97 (1986)... 

Sverdrup, H., Warfvinge, P., Rosen, K. (1995). A model for the impact of soil solution Ca Al ratio, soil moisture and temperature on tree base cation uptake. Water, Air and Soil Pollution, 61, 365-383. 

R. Rosen, Two factor models, neural nets, and biochemical automata, /. Theor. Biol, 15, 282-297 (1967). 

A major problem with these approaches, however, lies in the complexity and nonuniqueness involved with identification of parameterizations for processes of particle straining, deposition, and detachment. An alternative to CFT-based theories is given by Amitay-Rosen et al. (2005), who suggest a simple phenomenological model of particle deposition and porosity reduction that avoids these difficulties. 

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