Volume fraction, of particles

Creep Resistsince. Studies on creep resistance of particulate reinforced composites seem to indicate that such composites are less creep resistant than are monolithic matrices. Silicon nitride reinforced with 40 vol % TiN has been found to have a higher creep rate and a reduced creep strength compared to that of unreinforced silicon nitride. Further reduction in properties have been observed with an increase in the volume fraction of particles and a decrease in the particle size (20). Similar results have been found for SiC particulate reinforced silicon nitride (64). Poor creep behavior has been attributed to the presence of glassy phases in the composite, and removal of these from the microstmcture may improve the high temperature mechanical properties (64). 

In all cases where the two phases are moving with different velocities, it is important to differentiate between the concentration of particles in the pipe (their holdup 5) and the volume fraction of particles (C) in the discharge. The implications of this will now be considered, together with possible means of experimentally determining the holdup... 

Fig. 12. Effect of volume fraction of particles on AG and AG" induced by a magnetic field...

The crucial question is at what value of <)> is the attraction high enough to induce phase separation De Hek and Vrij (6) assume that the critical flocculation concentration is equivalent to the phase separation condition defined by the spinodal point. From the pair potential between two hard spheres in a polymer solution they calculate the second virial coefficient B2 for the particles, and derive from the spinodal condition that if B2 = 1/2 (where is the volume fraction of particles in the dispersion) phase separation occurs. For a system in thermodynamic equilibrium, two phases coexist if the chemical potential of the hard spheres is the same in the dispersion and in the floe phase (i.e., the binodal condition). 

For a mixture of particles of several sizes, one evaluation of a mean diameter is the volume surface mean, or Sauter mean. When ws is the weight or volume fraction of particles of diameter ds the mean is... 

Figure 3.21 The variation of the Debye length with volume fraction of particles...

Figure 15.6 Particle distributions observed in coarsening experiments on semisolid Pb-Sn alloys. The volume fraction of particles is 0.64. The upper row shows a steady increase in mean particle size with aging time. The lower row is scaled so that the apparent mean particle size is invariant—demonstrating that the particle distribution remains essentially constant during coarsening. From Hardy and Voorhees [7).

Figure 15.8 Rate constant Kd (4>) f°r particle coarsening vs. volume fraction of particles, expressed as a ratio of the rate constant Kd 4>) at volume fraction to that at 0 = 0.6. From Hardy and Voorhees [7].

Eq - volume fraction of gas, i.e. bubbles, eL = volume fraction of liquid, and eP = volume fraction of particles. 

The performance of a three-phase fluidised-bed is to be assessed in relation to a model reaction, the hydrogenation of a-methyl styrene at 50°C. The same catalyst will be used as in Example 4.6, excepting that the diameter of the spherical particles will be 2.0 mm. The liquid and gas flowrates will be such that the volume fraction of particles in the bed will be 0.50 and the volume fraction of gas 0.20 i.e. the relationship shown in Fig. 4.21 will apply, from which the estimated bubble size is 5.0 mm. 

Studies have also shown that, since the amount of reinforcement added affects all mechanical and thermal properties, there is an optimum volume fraction of particle or whisker reinforcement that should be added to the matrix material to ensure superior resistance to thermal shock (Becher, 1981 Jia etal., 1996 Sbaizero and Pezzotti, 2003 Pettersson and Johnson, 2003). The shape of the reinforcement also plays an important role in determining behaviour under thermal shock. Sbaizero and Pezzotti (2003) showed that the use of coarse and elongated particles resulted in better CMC performance compared with the use of fine-grained particles. 

Dependence of the fracture strength of the composites on the volume fraction of particles (6 pm SiC). 

The computed volume fraction of particles, a , for a given control volume in general includes the volumes of fully and partially enclosed solid spheres inside the enclosure, as indicated by the shaded area in Fig. 5.3. With increasing control volumes, the volume fractions of solids obtained from different centered control volumes are close to the same... 

Denote ap as the volume fraction of particles in a gas-solid mixture. The volume-averaged densities of both gas and particle phases are then given by... 

For dilute suspensions, particle-particle interactions can be neglected. The extent of transfer of particles by the gradient in the particle phase density or volume fraction of particles is proportional to the diffusivity of particles Dp. Here Dp accounts for the random motion of particles in the flow field induced by various factors, including the diffusivity of the fluid whether laminar or turbulent, the wake of the particles in their relative motion to the fluid, the Brownian motion of particles, the particle-wall interaction, and the perturbation of the flow field by the particles. 

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