Suspensibility correlation experimental data

Much attention should be given to correlations for liquid-solid suspensions or fluidizing systems derived experimentally. If the experimental data have been correlated to particle density, this kind of density and not the hydraulic density should be used. For instance, this is the case of the Liu-Kwauk-Li criterion for determining the fluidization pattern (Section 3.8.2). However, for correlations that have been derived using nonporous particles, the hydraulic density should be used. This is because the correlation accounts for the whole mass included in the volume of the particle, which is the sum of the solid mass and liquid mass in the pores for porous particles. 

Corn stover, a well-known example of lignocellulosic biomass, is a potential renewable feed for bioethanol production. Dilute sulfuric acid pretreatment removes hemicellulose and makes the cellulose more susceptible to bacterial digestion. The rheologic properties of corn stover pretreated in such a manner were studied. The Power Law parameters were sensitive to corn stover suspension concentration becoming more non-Newtonian with slope n, ranging from 0.92 to 0.05 between 5 and 30% solids. The Casson and the Power Law models described the experimental data with correlation coefficients ranging from 0.90 to 0.99 and 0.85 to 0.99, respectively. The yield stress predicted by direct data extrapolation and by the Herschel-Bulkley model was similar for each concentration of corn stover tested. 

Equation 2 represents a type of additive equation — sometimes described as a special-cubic equation — that has been widely used to correlate properties of mixtures. In Equation 2, Y represents the value of the response variable XI, X2, and X3 the concentrations of the variable components and k is a constant term. In this study, fitting the experimental data by regression analysis to a modification of Equation 2 provides an empirical equation that satisfactorily correlates suspensibility with concentrations of clay, dispersant, and surfactant. The reason for modifying Equation 2, by reducing the number terms in the polynomial, is discussed in the next section. 

Whereas Mersmann and Einenkel [112] correlated their experimental data on the basis of energy equations and Liepe and Joschek [334] set the power needed for particle suspension proportional to the stirrer power, Zehner [603] made use of the laws of momentum transfer. This appeared more reasonable to him, because in this case the efficiency of mechanical energy transfer did not have to be introduced. In his first fundamental investigations he utilized the jet loop, which due to the directional flow in the draught tube and in the annular space enabled easier balancing. 

Thiele et al.8°) modeled the initial polymerization of styrene. A comparison with the experiment showed that there is a satisfactory correlation of W and P up to q < 0.4. On the basis of the literature and experimental data, it has been concluded that kt in isothermal suspension polymerization becomes diffusion-controlled at q > 0.25 initiation efficiency if) becomes diffusion-controlled at q > 0.4 and kp and km become diffusion-controlled at q > 0.75. 

It is evident from the examples described above that a 4-th order equation for the suspension model fits the experimental data for PP-PC blends best. In the case of PC-PMMA blends, however, several equations of different order can be consistent with the experimental data, and the choice of the best one is more difficult. Coefficients of multiple correlation seem to be a rather inadequate criterion here. 

Equally good correlations are obtained for the experimental data for two-phase flow of air and nitrogen with aqueous and non-aqueous suspensions of coal [Farooqi et al., 1980] and china clay particles and aqueous solutions of a wide variety of chemically different polymers [Chhabra et aL, 1984]. A wide range has been covered (0.14 < n < 1 0.1 < Xmod S 200) but most data have been obtained in relatively small diameter (3 mm to 50 mm) pipes [Chhabra and Richardson, 1986]. 

In conclusion, it should be emphasised that most of the cmrently available information on heat transfer to non-Newtonian fluids in stirred vessels relates to specific geometrical arrangements. Few experimental data are available for the independent verification of the individual correlations presented here which, therefore, must be regarded somewhat tentative. Reference should also be made to the extensive compilations [Edwards and Wilkinson, 1972 Poggermann et al., 1980 Dream, 1999] of other correlations available in the literature. Although the methods used for the estimation of the apparent viscosity vary from one correlation to another, especially in terms of the value of ks, this appears to exert only a moderate influence on the value of h, at least for shear-thinning fluids. For instance, for n = 0.3 (typical of suspensions and polymer solutions), a two-fold variation in the value of ks will give rise to a 40% reduction in viscosity, and the effects on the heat transfer coefficient will be further diminished because Nu [Pg.371]

In this work are obtained generalized Reynolds and Hedstrom numbers connected with a three parameter rheological model to correlate the friction coefficient for the laminar, transitional and turbulent regime in annular flow. The use at experimental data covering a considerable range of dimensionless numbers for the flow of bentonite suspensions leads to a calculation technique for the transition velocity and pressure drop of these suspensions in annular geometries. 

The semi-empirical analysis of many experimental data collected in two different pilot plants led to satisfactory correlations for the turbulent friction coefficient and to the prediction of laminar-turbulent transition velocity for the flow of viscoplastic suspensions in annuli. 

The viscosities of suspensions of large non-interactive spheres have been made by various investigators [56 to 60]. The agreement of experimental data with the hydrodynamic theory seems not clear in either dilute or concentrated systems. The best correlation of data with a model over wide range concentrations is with Mooney s [36] Eq. 2.13. 

In order to understand and correlate the heat transfer data, the relevant physical properties of the suspensions must be carefully evaluated. The experimental determination of heat capacity and density pose no particular problem. In many instances it is possible to estimate these values accurately by assuming them to be weight averages of those of the two components. In contrast, great difficulty is associated with the accurate determination of thermal conductivity and viscosity, largely owing to the fact that the solids tend to settle readily in any device where convection currents are eliminated, as they must be for these... 

Miller s recommended equation actually had a higher constant (0.029) substituted for the value of 0.023 shown in Eq. (37). This was found necessary to enable correlation of his data on both water and aqueous suspensions, i.e., he was able to conclude that the same correlating equation is applicable to pure liquids and suspensions alike, although the coefficients were high for both. For the former, Eq. (37) is usually suitable hence it may be concluded that the consistently high coefficients reported by Miller were probably due to unusual experimental factors and are not of general interest. 

Casson models were used to compare their yield stress results to those calculated with the direct methods, the stress growth and impeller methods. Table 2 shows the parameters obtained when the experimental shear stress-shear rate data for the fermentation suspensions were fitted with all models at initial process. The correlation coefficients (/P) between the shear rate and shear stress are from 0.994 to 0.995 for the Herschel-Bulkley model, 0.988 to 0.994 for the Bingham, 0.982 to 0.990 for the Casson model, and 0.948 to 0.972 for the power law model for enzymatic hydrolysis at 10% solids concentration (Table 1). The rheological parameters for Solka Floe suspensions were employed to determine if there was any relationship between the shear rate constant, k, and the power law index flow, n. The relationship between the shear rate constant and the index flow for fermentation broth at concentrations ranging from 10 to 20% is shown on Table 2. The yield stress obtained by the FL 100/6W impeller technique decreased significantly as the fimetion of time and concentration during enzyme reaction and fermentation. 

In Figure 4.7, the experimentally determined values of average liquid holdup, ai, are plotted against the modified parameter Xmod for suspensions of kaolin in aqueous glycerol (same data as shown in Figure 4.5) and it will be seen that they are now well correlated by equation (4.9). 

Roes and van Swaaij [35] (Pall rings) and Verver and van Swaaij [6,37] (double-channel baffle column) experimentally obtained values of the mass transfer rate constant, which were much lower than values calculated from experimental solids holdup data and the well-know Ranz-Marshall correlation [38,39]. The low experimental values are to be attributed to particle-shielding phenomena due to the formation of less diluted suspensions or trickles. 

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