Volume fraction of cluster

At incipient fluidization, e = 0 and the volume fraction for bubbles (e — eQ) diminishes to zero, and so does the correction factor at the particle terminal velocity, = 1, and the volume fraction of clusters (1 — e) diminishes to zero, and so does the correction factor. 

Fig. 3. Volume fraction of clusters in melts of phenyl benzenes. (From Magill and Ubbelohde.i )...

Within the frameworks of the cluster model the relative volume fraction of clusters... 

This is because the representative volume element for a unidirectional fiber-reinforced composite consists of a cluster of three co-axial cylinders of the same height, taken equal to unity, and therefore the volume fractions of the phases are proportional to the squares of the radii of the respective cylinders. 

Lagues et al. [17] found that the percolation theory for hard spheres could be used to describe dramatic increases in electrical conductivity in reverse microemulsions as the volume fraction of water was increased. They also showed how certain scaling theoretical tools were applicable to the analysis of such percolation phenomena. Cazabat et al. [18] also examined percolation in reverse microemulsions with increasing disperse phase volume fraction. They reasoned the percolation came about as a result of formation of clusters of reverse microemulsion droplets. They envisioned increased transport as arising from a transformation of linear droplet clusters to tubular microstructures, to form wormlike reverse microemulsion tubules. 

An MR hydrogel of a crosslinked PVA network and Fe304 particles dispersed at random was also synthesized [59]. The viscosity of the gel in a magnetic field increased with time. It has been suggested that the dispersed Fe304 particles aggregate and form a cluster. The effect of the volume fraction of the particles on the viscosity has also been discussed. The authors have pointed out that when the volume fraction is about 15%, the ratio of the viscosities with and... 

To illustrate how the effect of the adsorption on the modulus of the filled gel may be modelled we consider the interaction of the same HEUR polymer as described above but in this case filled with poly(ethylmetha-crylate) latex particles. In this case the particle surface is not so hydrophobic but adsorption of the poly (ethylene oxide) backbone is possible. Note that if a terminal hydrophobe of a chain is detached from a micellar cluster and is adsorbed onto the surface, there is no net change in the number of network links and hence the only change in modulus would be due to the volume fraction of the filler. It is only if the backbone is adsorbed that an increase in the number density of network links is produced. As the particles are relatively large compared to the chain dimensions, each adsorption site leads to one additional link. The situation is shown schematically in Figure 2.13. If the number density of additional network links is JVL, we may now write the relative modulus Gr — G/Gf as... 

These hole-rich droplets represent a ferromagnetic second phase having a 7c < 7n the volume fraction of this minority phase grows with increasing x, and in the range 0.1 < x < 0.13 the droplets are condensed into large clusters having 7c > 7n. The crossover from 7c < 7n to 7c > 7n occurs at about x = 0.10 near a point where the 2D orbital order-disorder transition (or onset of orbitally disordered clusters) at T (same T as in fig. 14) crosses Tn. 

Understanding the magnetic properties of a collection of well-isolated clusters is of great interest for exploring FePt clusters as a media for EHDR beyond 1 Tera bit/in. Dilute FePt C cluster films were prepared by the multilayer method as described earlier. Thus Stoner-Wohlfarth-like behavior has been observed in a FePt C cluster film with FePt volume fraction of 5 %, [45], Figure 27 shows the zero-field-cooled (ZFC) and field-cooled (FC) magnetization curves for as-deposited and annealed FePt C cluster film with 5 vol. % FePt. 

The initial porous texture of a catalyst pellet and the change in texture caused by metal deposition in it can be described using the percolation theory. In the percolation approach the pellet is constructed as a binary interdispersion of void space and (deposited) solid material. In this binary interdispersion, the void space can exist as (1) isolated clusters surrounded by solid material or (2) sample overspanning void space that allows mass transport from one side to the other. The total void space c can be split into the sum of the volume fraction of isolated clusters t1 and the volume fraction of accessible void space tA, If is below a critical value, called the percolation threshold all the void space is distributed as isolated clusters and transport is impossible through the pellet. 

---