Effects of Volume Fraction

Tool is shorter, hence coalescence will be faster and d will be larger, unless k remains small. 

In turbulent flow, increase in 0 will induce turbulence depression in principle, this will lead to a larger d. It is often assumed that for small 0 the root-mean-square eddy velocity u x) (see eqn. 2.14) will be smaller by a factor (1 -l- bcp), where b values reported vary widely, from 0.8 to 8 see e.g. refs. 2, 28 and 55. In the authors view this may be an oversimplification. As mentioned in Section 2.3, turbulence depression 1 added high polymers tends to remove the smallest eddies from the spectrum, thereby causing the average d to be larger and the size distribution to be more narrow. 

If the mass ratio of surfactant to continuous phase is constant, an increase in 4 gives a decrease in surfactant concentration, hence an increase in y, hence an increase in d and also an increase in k, hence an increase in coalescence rate, hence an increase in d. These conclusions would not apply if at all stages 

If the mass ratio of surfactant to disperse phase is constant, the changes as mentioned under 5 are reversed again, unless k C 1. 

It may be clear that general conclusions cannot easily be drawn, since several of the mechanisms mentioned may come into play. Some experimental results will briefly be mentioned. Goulden and Phipps and Walstra used a high-pressure homogenizer and compared various j (up to 0.4) at constant initial me, regime TI, 

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Figure 14 Effect of volume fraction of maleic modified PE and phenolic modified PE on the particle size reduction of 70 30 HDPE-NBR blend. Source Ref. 75.

Fig. 7. Effect of volume fraction of dispersed particles in a gel on the shear modulus of the gel under electric fields. The sample used was a silicone gel containing PMACo particles. The particles were dispersed at random in the gel...

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

Effect of volume fraction of SiC whiskers in composite with code 1723 matrix on critical aspect ratio, according to (O) Dow s analysis and( ) Rosen s analysis (reproduced by permission of Am. Ceram. Soc. Bull.) . 

Effect of volume fraction of Ni particles on the fracture strength of Ni-Al203 nanocomposites, produced by the reduction of NiO particles ( ), and the reduction of Ni-nitrate ( ). Reproduced from Sekino ef a/.,12 with permission from the Journal of the American Ceramic Society. 

Fig. 4.8 Effect of volume fraction rigid spheres on the relative viscosity of the suspension. In these studies, the particle diameter ranged from 0.1 to 440 /xm. Data from Ref. 66.

Figure 13.15. Effects of volume fraction O and aspect ratio Af on the zero-shear viscosity rio(relative) for dispersions of infinitely rigid anisotropic filler particles. The curve labels denote Af. At any given d> and Af, T)o increases more with fibers than it does with platelets.

Figure 6 depicts the effect of volume fraction of solids on the relative viscosity for 40 lb HPG/1000 gal fluid at 100 s-1 and at test temperatures of 26.7, 43.3, and 60 °C (23). A Newtonian relative viscosity-concentration curve based on Thomas (24) and Maron and Pierce (25) correlations are shown for comparison. 

Following the descriptions of Probstein and Sengun (1987) and Sengun and Probstein (1989b), we shall examine the forces in concentrated suspensions. We reserve our discussion of the effect of volume fraction for the sections that follow. 

FIGURE 35.7 Effect of volume fraction of HA on E and strain to failure of HA-reinforced PE composites, in comparison to cortical bone. 

In order to clarify the effect of volume fraction of fiber on the viscoelastic properties of surface treated GFL/PP composites in this section, the relationship between the storage... 

Davies CKL, Nash P, Stevens RN (1980) Effect of volume fraction of precipitate on Ostwald ripening. Acta Metall 28 179-189... 

Ardell AJ (1972) Effect of volume fraction on paiticle coarsening—theoretical considereations. Acta Metall 20 61-71... 

Figure 12.9. Effect of volume fraction of glass beads on yield strength of poly(phenylene oxide). (O) Untreated ( ) A-llOO treated. The term A-1100 refers to the silane coupling agent used to enhance adhesion (Wambach et al., 1968). Note that the upper curve corresponds to ultimate strength, for fracture occurred prior to yielding.

Figure 12.19. Effect of volume fraction of glass beads and bead surface treatment on the gamma-fracture toughness of epoxy composites at 25° C (DiBenedetto and Wambach, 1972). Code numbers refer to various silane surface treatments, with degree of adhesion conferred ranging from strong and positive for A-1100 to negative for A-156.

Ardell, A. J., The effect of volume fraction on particle coarsening theoretical considerations, Acta MetalL, 20, 61-71, 1972. 

The effect of volume fraction of the dispersed phase on plug length at constant mixture velocity and at constant velocity of the carrier phase is shown in Fig. 4.13. In all channel sizes the length of the plug was found to increase as e[Pg.81]

Figure 16.5 Effect of volume fraction of glassy phase on thermal conductivity of 3-Si3N4 for R (aspert ratio) = 1 in 3-grain and 6= 1 and 10 nm.

When the effect of volume fraction is also taken into account the result is shown in Table 1.3. 

Bray DJ, Dittanet P, Guild FJ, Kinloch AJ, Masania K, Pearson RA, Taylor AC (2013) The modelling of the toughening of epoxy polymers via silica nanoparticles the effects of volume fraction and particle size. Polymer 54(26) 7022-7032... 

FIGURE 3.1 B Effect of volume fraction on SAN-PMMA blend miscibility predicted by... 

FIGURE 17.4 Multiplicity during isothermal CSTR polymerization effect of volume fraction. With permission from Reference 19, Kwalik KM. Bifurcation characteristics in closed-loop polymerization reactors [PhD thesis]. Atlanta School of Chemical Engineering, Georgia Institute of Technology 1988. 

Hine, P.J., Lusti, H.R. and Gusev, A.A. (2002) Numerical simulation of the effects of volume fraction, aspect ratio and fibre length distribution on the elastic and thermoelastic properties of short fibre composites. Comp. Sci. Tech., 62, 1445. 

The effects of volume fraction of the dispersed phase and of temperature on the conductivity behavior are intimately related. An increase of temperature can induce a conductivity percolation in a situation where O is not high enough for percolation to occur. This is clearly demonstrated in a study of AOT/decane/aqueous 0.5% NaCl system. The... 

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