Maximum packing fraction effect

The final density of the compact is less than the maximum packing fraction of the particles, PF ax [cf. Eqs. (4.8) and (4.67)], due to frictional forces at particle contacts that retard particle sliding The effectiveness of the compaction process is quantified... 

A large number of empirical modifications to this expression have been proposed which model the viscosity of a liquid containing moderate concentrations of spherical particles [5] These include Mooney [6], Maron-Pierce [7] and Krieger-Dougherty [8] expressions which take into account the maximum packing fraction of the particles, and where interaction effects are absent, and can be represented by the general form ... 

In this way, /3 is related to the particle volume fraction in terms of the maximum packing fraction such that the separation between the particle surfaces approaches zero in the limit effective microstructure of a flowing suspension is a simple cubic (, = 0.52), or body centered cubic = 0.68), or face centered cubic = 0.74). It is therefore assumed that Eq. (9.3.9) is also applicable to other effective suspension microstructures such as the random microstructure. Equation (9.3.8) is appropriate only for high solid volume fractions ( 2 0.25) since it was developed for concentrated suspensions for which the average separation distance between two similar size particles is close to or less than the particle size. 

The micromechanical models used for the comparison was Halpin-Tsai (H-T) [89] and Tandon-Weng (T-W) [90] model and the comparison was performed for 5 wt% CNT/PP. It was noted that the H-T model results to lower modulus compared to FEA because H-T equation does not account for maximum packing fraction and the arrangement of the reinforcement in the composite. A modified H-T model that account for this has been proposed in the literature [91], The effect of maximum packing fraction and the arrangement of the reinforcement within the composite become less significant at higher aspect ratios [92],... 

The effect of particles and matrix properties on the shear viscosity of LDPE/ GTR blend was also studied by developing a theoretical model to predict the viscosity of the composites as a function of the rheological properties of the matrix, solid concentration, particle size distribution, particle shape, and deformability (Bhattacharya and Sbarski 1998). The real viscosity measurements were found in good agreement with the values predicted below the maximum packing fraction. 

How do these effects occur When any suspension of particles is placed next to a smooth wall, the original microstructure is locally disturbed. For a simple suspension at rest where the particles are randomly dispersed in space, the concentration of particles undergoes a damped oscillatory variation as one moves away from the wall, see figpre 16, where the concentration is at the maximum packing fraction, so that the effect is enhanced. The new distribution has two effects, first that the variation in concentration does not die out until about five particle radii away from the wall, and secondly that the average particle concentration is zero at the wall and less than average for a small distance away from the wall. 

Eq. (42) is only valid when < ><1%. Ball [26] assumed that the effect of the panicle in a concentrated suspension is the sum of the effect of the particle added sequentially. The free volume unoccupied by the particle relative to the maximum packing fraction is ... 

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...

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