Solid volume fraction

Probably Fl is a function of particle Reynolds number and concentration, but Fig. 6-33 gives Durand s empirical correlation for Fl as a function of particle diameter and the input, feed volume fraction solids, Cs = QsKQs + Ql)- The form of Eq. (6-145) may be derived from turbulence theory, as shown by Davies (Chem. Eng. Sci., 42, 1667-1670 [1987]). 

V,s = settling velocity for hindered uniform spherical particle, ft/s or m/s (terminal) c = volume fraction solids K = constant given by equation above Nrc = Reynolds number, Dp V,pf/ j. 

For 0.1 volume fraction solids for hindered settling velocity ... 

Al = Cross-secdonal area allocated to lighL phase, sq ft Ap = Area of particle projected on plane normal to direction of flow or motion, sq ft A, = Cross-sectional area at top of vessel occupied by continuous hydrocarbon phase, sq ft ACFS = Actual flow al conditions, cu ft/sec bi = Constant given in table c = Volume fraction solids C = Overall drag coefficient, dimensionless D = Diameter of vessel, ft Db = See Dp, min Dc = Cyclone diameter, ft Dc = Cyclone gas exit duct diameter, ft Dh = Hydraulic diameter, ft = 4 (flow area for phase in question/wetted perimeter) also, DH in decanter design represents diameter for heavy phase, ft... 

Voorhees s experimental study of low-volume-fraction-solid liquid+solid Pb-Sn mixtures carried out under microgravity conditions during a space shuttle flight enabled a wider range of solid-phase volume fractions to be studied without significant influence of buoyancy (flotation and sedimentation) effects [13]. The rate of approach to the steady-state particle-size distribution in 0.1-0.2 volume-fraction... 

Recalculation in terms of the volume fraction solid, d>, gives... 

Uto = terminal velocity of a single sphere (infinite dilution) c = volume fraction solid in the suspension n = function of Reynolds number Re = d.pUfQp/ x as given... 

The dry thickness is directly related to the wet thickness and always depends on suspension properties such as volume fraction solids and colloidal stability. In this respect self-metered and pre-metered coating flows do not differ. The self-metered process is much more complex, because the wet thickness also depends on the suspension properties. 

Fig. 21. a Local d75 volume fraction (1—4>) as a function of depth z ( points and the thick solid line), determined for the h86/d75 blend monolayer with 30%h86 following 46 h of annealing at 86 °C [145]. The thin solid line corresponds to the non-annealed sample with identical bulk composition. The hatched area marks the h86 surface excess z. The inset marks the h86 bulk compositions <)> for which z was determined. Solid curve in the inset denotes binodal, determined previously [91] and described by %=(0.547/T-8X10"5)(l-0.217c])). b Segregation isotherm data (corresponding to T=72 °C (O) and T=86 °C ( )) plotted as normalized surface excess z w - )] vs normalized bulk volume fraction Solid lines are generated by Eq. 44 to fit the data. Dashed horizontal lines are normalized surface excess values for the bulk phase enriched at the surface to the compositions < >s such that (c))2-())s)/(<[)2—c])1)= 10%, 5%, and 1%, respectively... 

Fig. 8 Fracture strengths, in terms of in-plane macrostress (triangles) and maximum "equivalent noni stress" in PSZ phase (circles), plotted against PSZ volume fraction. Solid and open markings refer to the cases with and without taking account of residual stresses.

FIGURE 17.22 Properties of fats consisting of hydrogenated palm oil in sunflower oil, crystallized at various initial supersaturation In /i0 (indicated near the curves) as functions of the volume fraction solid q>. (a) Permeability B. (b) Storage shear modulus G. Heavy solid lines give experimental results. (From results by W. Kloek. Ph.D. thesis, Wageningen University, 1998.)... 

Tests were conducted with a rotational viscometer with 30, 40, and 60 lb HPG/1000 gal fluids containing neutrally buoyant 60-100 mesh styrene divinylbenzene beads at concentrations up to 12 lb/gal and temperatures up to 65.5 °C. Data were gathered only at three shear rates 5, 170, and 1000 s-1. Their modified Eiler s equation was based on correlating relative viscosity as a function of clean fluid n values, solids concentration, and fracture shear rate. The gel concentration and temperature effects were incorporated into n. Figure 1 depicts the effect of polymer concentration on the relative viscosity of suspension at a shear rate of 170 s-1 and 23.9 °C. It can be seen that the lower polymer concentration has the greater viscosity ratio than the higher concentrations and that the difference between these increases with volume fraction solids. 

The ns and Ks values are plotted as a function of volume fraction solids in Figure 3 for fluids tested at 60 °C. It can be seen in this figure for these fluids, as the volume fraction solids increases, the ns values decrease whereas the Ks values increase. This means the degree of the non-Newtonian character of the base gels increases by adding sand. The assumption that the ns values of sand-laden fluids remain the same as the carrier fluid n by previous investigators does not seem to be valid. 

It should be remembered that unlike Nolte s proposed equation, Shah s results show definite shear rate-dependent relative viscosities. Also, power law exponent, ns, of slurry is not the same as the carrier fluid n as assumed by Nolte. Prud homme (26) has also reported decreasing n values with increasing volume fraction solids. 

Figure 14.14 A plot of vs Vf during the diying of a latex dispersion. The values are taken from experiments similar to that shown in Figure 14.S, and Vf refers to the volume fraction solids in the wet portion of the dispersion monitored in the experiment. The open symbols refer to experimental data. (Taken from ref. [12c].)...

At this point the integral viscosity has to be expressed as a function of the volume fraction solid. A number of relationships have been proposed to describe the increase in viscosity with volume fraction solid. Good reviews are incorporated in the two-volume book on polymer blends by Paul and Newman [263] some other references are 264 through 267. A useful expression is the Maron-Pierce relationship, which for a power law fluid results in the following expression for the consistency index ... 

Figure 1.8 Self-diffusion coefficients of p-xylene as a function of the micellar volume fraction. Solid curve is the prediction for spherical micelles (Eqs. 1.14 and 1.16) dashed curves are the prediction for prolate spheroids with axial ratio=3 or 5 for all the simulations, the parameters...

S = ratio of density of solids to density of liquid Qb = volume fraction solids in the bed... 

Isk volume fraction solids in slurry below Z dimensionless... 

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