Void Models

The model framework for describing the void problem is schematically shown in Figure 6.3. It is, of course, a part of the complete description of the entire processing sequence and, as such, depends on the same material properties and process parameters. It is therefore intimately tied to both kinetics and viscosity models, of which there are many [3]. It is convenient to consider three phases of the void model void formation and stability at equilibrium, void growth or dissolution via diffusion, and void transport. 

This model can also provide resin pressure gradients, resin flow rates, consolidation profiles, and, when combined with the void model, void profiles at any point in the laminate. 

Fig. 3. Details of the model analysis of Fig. 2. The upper diagram shows, in addition to the overall Tx fit for 5CB, the three T zm contributions M = OF, Rot and SD) according to equations (la) and (lb) and indicates that, with a maximum Tiz. Tip ratio of 3, the contribution by equation (4a) cannot describe the angular dependent results in the kHz regime. The lower diagram illustrates the differences between the Nordio small-step and the Void third-rate rotational model and the preference of the second concept, which becomes visible mainly by the A = 90° data in the MHz regime. In the first case (Nordic model), the experimental error limits of 7% are smaller than the standard deviation of 17% between the calculated and the observed relaxation times. In the second case (Void model), both limits are of comparable magnitude.

The suspension model of Einstein and Guth is extended into 4-th order function of v, and the parallel voids model is extended into the 3-rd order function of v. The fraction of reinforcing material in the filler space Cr is considered as a measure of the efficiency of the reinforcing material for a given two-component polymer system, indicating also the state of adhesion at the phase boundary. 

We have therefore attempted to compare the obtained results with the parallel voids model (cf. Table 1), for which the reinforcement function e can be written as... 

According to the parallel voids model (Table 1) we have... 

Figure 5.9 Percentage reduction in the through-thickness elastic modulus (Ezz) induced by voids. Modelling prediction [11] compared with test data from [12].

The voids model along with the variable and direction descriptions is illustrated in Fig. 2.21. 

Since the final objective of this tqtproach is coiK aiied with the cured composite characteristics, void formation shotud also be included in the modelling effort. The void model should ideally be able to predict die amditions needed to avoid the formation of voids. In addition, it is also of interest the prediction of the volume fraction and of the size distribution of voids in the cured composite, for qiecified processing conditions. 

Systems involving granular metal particles and polymers have been modeled in terms of mixtures of random voids and conductive particles. There is also an inverted random void model [15]. For CB in polymers, percolation is the process by which charge is transported through a system of interpenetrating phases. 

Note DFT/PaSD with void model, self-consistent model of a mixture of voids, cylindrical and slit-shaped pores, self-consistent regularization with respect to both PoSD (fy(i p)) and PaSD ((l)( z)) with the model of voids, (5 ), Aw=Sgg j-/(5 ) - 1, f)pHH e fractal dimension with Frenkel-Halsey-Hill equation accounting for adsorbate surface tension effects (Quantachrome Instruments software), Ag j is the gelatin adsorption in mg per gram of silica. 

Chigada PI. Characterisation of flow and heat transfer patterns in low aspect ratio packed beds by a 3D network-of-voids model. Chemical Engineering Research and Design 2011 89 230-238. 

Kinetics models of gas-solid non-catalytic reaction include uniform conversion model (UCN), multiple fine particle model (GPM), crack core model (CCM), phase-change model (PCM), change void model (CVM), thermal decomposition model (TDM), shrinking core model with multi-step reactions, and multi-step reaction model of formation porous structure in reaction etc. Among these models, the shrinking core model (SCM) is the most important and most widely used. For conversion of solid it is also the most simple and practical model. Commonly it is suitable for experimental data. However, it can only be used in some reactions of many solid reactions. A more complex model must be used in other cases. 

The subcooled void model used is the Levy s one (Jackson Todreas 1981), which calculates the true quality in terms of the equilibrium quality and the quality started by bubble departure. It is also necessary to choose a turbulent crossflow model. The model used is shown in Eq. 3. The slip ratio between liquid and vapor was considered equal to 1.0. 

Following the Babinet principle, we cannot exclude the possibility that Rg is a size of void (polymer-poor region) instead of cluster (polymer-rich region), since the scattering intensity is proportional to the square of tte Ap whether Ap is positive or negative cannot be judged by the present scattering experiments. A similar calculation with the void model is also possible, and will be described elsewhere. 

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