Model Nielsen

w is the intermediate dimension of the particle and t is the smallest dimension of the particle [41]. 

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R. V. Nielsen. Model experiments for the determination of airflow in large spaces. In Indoor Air 9.. Proceedings of the 6th International Conference on Indoor Air Quality and Climate. Helsinki, Finland, 1993. 

Feilberg, A., and T. Nielsen, Model Systems to Simulate Photochemistry in the Organic Liquid Phase of Combustion Aerosols, presented at the 6th FECS Conference on Chemistry and the Environment, Atmospheric Chemistry and Air Pollution, University of Copenhagen, Copenhagen, Denmark, August 26-28, 1998. 

Feilberg, A., R. M. Kamens, M. R. Strommen, and T. Nielsen, Modeling the Formation, Decay, and Partitioning of Semivolatile Nitro-Polycyclic Aromatic Hydrocarbons (Nitronaphthalenes) in the Atmosphere, Atmos. Environ., 33, 1231-1243 (1999a). 

The thermal conductivity (Ke) of a filled adhesive may be predicted from the Lewis and Nielsen model. °... 

Figure 2.16. Predicted thermal conductivity using the Nielsen Model compared with actual data. (Copyright Adhesives Age, 1989, reproduced with permission.)...

Fig. 12 Percent elongation at break (yield) for the incompatible PpCIS/PPO blends. ( ), elongation at break ( O elongation at yield. Values within parentheses indicate the fraction of samples failing in the principal mode in the embrittlement region. Error bars indicate 95% confidence intervals. Curve 1 was drawn from values calculated from the Nielsen model for perfect adhesion composites (Eq. 7).

For diffusion of liquid through rubbery polymer composites, Fickian and non-Fickian diffusion theories are frequently used to describe the mechanism of transport, but for gas or vapour, other models have been developed to fit experimental data of diffusion profiles. The models of gas transport include Maxwell s model," free volume increase mechanism," solubility increase mechanism," nanogap hypothesis," Nielsen model, " " Bharadwaj model, ° Cussler model " " and Gusev and Lusti model, " etc. 

The Nielsen model has been a popular theory, originally used to explain polymer lay nanocomposites. This model is used to describe the tortuosity effect of plate-like particulates of filled rubber polymer composite on the gas permeation. An increase in barrier properties of gas permeation of rubber polymer nanocomposites is a result of the impermeable nature of filler particles which creates a long path of penetrant molecule by directing them around the particle. 

Bharadwaj model was modified from Nielsen model by incorporating an orientation parameter, S. The range of relative orientations of the clay sheets with respect to each other is represented by 9, the angle between the direction of preferred orientation and the normal sheet. 

Using the Kerner-Nielsen model for expressing the effect of filler concentration on Young s modulus (85) ... 

FIG. 11 (left). Schematic representation of the effect on G of mixing some polybutadiene (PB) with the polystyrene (PS)-rich phase. For clarity, it is assumed that there is no interphase ( =0). The PB peak is reduced because becomes smaller, and the PS peak becomes correspondingly larger and shifts to a lower T because of infusion of PB (homogeneously distributed) into that phase. The small drop in plateau level is due to reduction of (ss g) in the Nielsen model. 

The Nielsen model (31) describes the elastic shear modulus G of a two-phase composite consisting of inclusions having volume fraction suspended uniformly in a continuous matrix. For the case of rubbery inclusions in a glassy matrix (here, a PS-rich matrix), the model takes the form ... 

FIG. 17 (right). Detailed representation of the included element in the Nielsen model, consisting of the interphase plus PB phase. Thus, and maximum... 

Figure 17.11. Nielsen models for two-phase systems using MFC parameters...

C. T. Stansberg, J. R. Krokstad and F. G. Nielsen, Model testing of the slow drift motion of a moored semi submersible in multidirectional waves, Proc. lAHR Sem. Multidirectional Waves Their Interaction with Structures, 27th lAHR Cong., ed. E. Mansard, San Francisco, USA (1997). 

The Lewis-Nielsen model considers the effect of the shape of the filler and the orientation or type of packing for a two-phase system or single-phase reinforcement composite, resulting in equation (11.8) for effective thermal conductivity (Tavman... 

A modified Nielsen model is another frequently used equation, " " espe-... 

The following input parameters were used for the Kemer-Nielsen model vm = 0.5 for mbbery matrix Vmax 0-b for random packing of spheres modulus of the rabbery epoxy network matrix Gm(=Ge) = 2.2 x 10 Pa modulus of incompletely condensed siloxane-silica domains was taken from literature data (12) on xerogels... 

Figure 10. Relative modulus of the O-I hybrid as a function of the effective volume fraction of the hard phase, Veff. Curves - theoretical models, Gsi = 4 x 10 Pa, Ge = 2.2 X 10 Pa, 1 Kemer-Nielsen model (eq. 1) Vmax = 0.6, vm = 0.5, 2 Davies model (eq. 4) Veff = vsi + VEg. Experimental results A ET-1,0 ET-2, E1-T2, DGEBA-D2000.

FIGURE 2.9 Comparison of theoretical models quantifying the effect of path tortuosity on the permeability of a composite Nielsen model [eq. (2.8)], Friedrickson-Bicraano [eq. (2.10)], modified Nielsen [eq. (2.9)], and Cussla--Aris [eq. (2.11)]. 

Aggregated Microcomposites. Agglomeration of clay platelets leads to tac-toid stractures (micro composites) with reduced aspect ratios and, according to the Nielsen model, reduced barrier efficiencies. 

Fig. 3. The predicted effect of maximum packing fraction on the relative thermal conductivity of composites filled with spherical particles in which kf/k 1000, according to the Nielsen model...

Some additional experimental considerations were introduced in the Lewis and Nielsen model [17] through adjustable parameters A and Om as described in Eq 6. 

For a polymer-filler system, the Nielsen model is described by the following equation ... 

Similar to the Nielsen model, the Bharadwaj model is based strictly on tortuosity arguments. The main difference is the consideration of the orientation and... 

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