Solid volume fraction concentration

The solids concentration can be expressed in terms of either the solids volume fraction (mass ratio of solids to fluid (R). If volume fraction of solids in the feed stream (flow rate gf) and (pu is the volume fraction of solids in the underflow (flow rate gu), then the solids ratio in the feed, Rf = [(mass of solids)/(mass of fluid)]feed, and in the underflow, Ru = [(mass of solids)/(mass of liquid)]u, are given by... 

You must determine the maximum feed rate that a thickener can handle to concentrate a waste suspension from 5% solids by volume to 40% solids by volume. The thickener has a diameter of 40 ft. A batch flux test in the laboratory for the settled height versus time was analyzed to give the data below for the solids flux versus solids volume fraction. Determine ... 

With the viscosity of a liquid we mean the resistance to flow of that particular liquid. This resistance is caused by internal friction and other interactions between the particles. Among other things, viscosity is dependent on temperature, the solid volume fraction and the properties of the particles. The viscosity of normal liquids, solutions and lyophobic colloids which are not too concentrated and contain symmetrical particles is measured by allowing a certain volume to flow through a capillary and measuring the time required by the liquid to flow through it. In figure 5.10 you can see the instrument which is used for this measurement the Ostwald viscometer. 

Effects of Solids Size. The effect of solids size on the viscosity of the emulsion-solids mixtures is shown in Figure 19 for synthetic OAV emulsions. The oil concentration (solids-free basis) is 60% by volume, and the solids used are silica sand. The comparison is made at shear stresses of 6 and 14 Pa. The viscosity is expressed as the relative viscosity (t7ows/ 7ow)t lhat is, the viscosity of the emulsion-solids mixture divided by the viscosity of the solids-free emulsion. At low solids volume fraction (<0.1), solids size has little effect. 

As the size ratio of the sand particle to the oil droplets d d increases to about 2, there is less dependence on the oil concentration, as shown in Figure 21b. When the size ratio increases to about 3, as shown in Figure 21c, the relative viscosity becomes independent of the oil concentration this result indicates that the emulsions act as a continuous phase toward the solids. Under this condition, the solids and the droplets behave independently, and no interparticle interaction occurs between the solids and the droplets. Yan et al. (64) showed that when the emulsions behave as a continuous phase toward the solids, the viscosity of the mixtures can be predicted quite accurately from the viscosity data of the pure emulsions and the pure solids suspensions. The viscosity of an emulsion-solids mixture having an oil concentration of Pq (solids-free basis) and a solids volume fraction of 0s (based on the total volume) can be calculated from the following equation ... 

We now turn to the prediction of the suspension mechanism of the ballotini versus the speed ratio in the coaxial mixer. The average volume concentration is 1%, and the solids are initially at rest in the tank bottom. The first case investigated corresponds to the motion of the sole anchor arm at a speed of 40 rpm. Simulations are carried out in the Lagrangian frame of reference (fixed anchor, rotating vessel). Fig. 12 shows the predicted and experimental solid volume fraction at equilibrium. The computation of the solid-liquid interface at the bottom is fairly well... 

Figure 19 shows the steady shear relative viscosity variation with the relative volume fraction of the large particles, eL, for various large to small particle size ratios, dh/ds, and different total solid volume fraction, 0, for bimodal concentrated dispersions of submicron resin particles at a shear stress level of 0.0155 Pa. The experimental data are taken from Hoffman (129). We can observe that the relative viscosity exhibits a minimum near eL = 0.8. The minimum viscosity behavior is more-pronounced at large particle diameter ratios, djds. The bimodal system viscosity can be several order of magnitudes lower than the corresponding monodispersed systems when the larger particles composed of about... 

Figure 39 shows the shear moduli variation with solid volume fraction for the electrostatically stabilized suspension of 1.4 pm polystyrene latices in aqueous solutions of NaCl. At the lower NaCl concentration (10 5 M), the double-layer thickness, l/ c, is 100 nm, and therefore the suspension show soft type interaction due to the extended double... 

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. 

D is the diffusion coefficient 5 is the thickness of the concentration boundary layer is the solids volume fraction on the wall (f), is the solids volume fraction in the bulk solution k is the mass transfer coefficient = D/5... 

In three phase systerns kL a is changed by the solid particles. With solid volume fractions >15 % and particle diameter dp< 200 jm kL a does not change significantly (smaller than 10-20%) but higher solid concentrations and larger particle size drastically decrease kL a, mainly because a decreases [28]. But porous solids having a absorption capacity for the gas can also increase kL a by a factor of two and even more [29]. 

The principal objective of an expression test is to determine the compression deliquoring characteristics of a cake. However, the nature of the test allows both filtration and compression characteristics to be determined when the starting mixture is a suspension (i.e. where the solids are not networked or they are interacting to a significant extent). Cake formation rate, specific resistance and solids volume fraction data can be determined for the filtration phase while analysis of a subsequent consolidation phase allows the calculation of parameters such as consolidation coefficient, consolidation index and ultimate solids concentration in the cake. Repeated use of the expression test over a range of constant pressures allows the evaluation of scale-up coefficients for filter sizing and simulation as described in Section 4.7. 

Rensner and Werther (1993) determined the effective measuring volume of a single fiber optical probe (d = 0.6 mm) for FCC and quartz sand as a function of particle concentration. In both cases (i.e., quartz and FCC), the 50% transmission length was less than 1 mm for the solids volume fraction p = 0.002 and less than 0.1 mm for = 0.2. Concerning the calibration of particle concentration probes Amos et al. (1996) did detailed analysis and experiments. 

Increasing photocatalyst particle concentration is predicted to cause progressively sharper radial diminution of photon flux the competing trade-off between increased catalyst surface and decreased photon distribution gives rise to a predicted and experimentally observed maximum in the product yield versus catalyst solid fraction. The maximum predicted at 25x10" volume fraction or approximately 1.08x10" g/cm corresponds reasonably to the smallest solid volume fraction (0.1 wt%) [108] found to give complete absorbance in a reactor of comparable radial dimensions. This study is the... 

Here we develop a constitutive model for a mixture of solid and fluid constituents based on the Twiss-Eringen approach. The model is then applied to a Poiseuille flow setting. For a single neutrally buoyant solid constituent, it is seen that the flow is governed by five nonlinear coupled ordinary differential equations. These equations describe profiles of the fluid and solid velocities, gyrations, and the solid volume fraction or suspended load concentration. Some example profiles are developed from numerical integrations of these equations. 

The constant k is known as the Einstein coefficient and has the value of 2.5. However, this relation is applicable to only correlate loading of less than 15%. A number of expressions have since been developed to relate relative viscosity to solid volume fraction for concentrated suspensions. A typical characteristic of such equations incorporates the function of (c-< )) in the denominator. Therefore flie relative viscosity can be correlated to the extra volume of binder over and above the immobile binder, (l-[Pg.240]

From Figure 14, it can be observed that yield stress increases with an increase in EVA concentration in the binder. One possible explanation for such a phenomenon is by assuming the formation of an immobile absorbed layer of binder molecular chains on the iron particles surface. The formation of such an interface or mesophase layer [53] would effectively increase the apparent size of the particles and in mm increase the effective solid volume fraction of the feedstock [54]. The increase in effective solid volume fraction would in mrn lead to higher suspension yield stress by the same reasoning described in the previous section [51, 52]. The thickness of this absorbed layer corresponds to the random coil dimension for the molecular chains. The chain end-to-end distance, /i, of a polymer molecular chain ranges from 20 to 100 nm and is given by the following expression [55]. 

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