Quemada

The approach developed within the scope of the energy dissipation principle led Quemada [71] to a simpler expression for determination of the viscosity of maximum concentrated dispersions which is based on the relationship cp/[Pg.121]

In diluted solutions Quemada s theory leads to the following equation ... 

To illustrate, solution of problems of this kind in the percolation theory, Quemada [71] cites the analysis of the dependence of electrical conductivity on concentration for a mixture of conducting and nonconducting spherical particles carried out by Fitzpatrick [80] or Clerk [81]. According to Clerk, this dependence is described by an equation similar to Eq. (66) or other similar formulas ... 

Quemada et al. (1985) proposed a viscosity equation for dispersed systems based on zero-shear, tjq, and infinite-shear, i oo> viscosities, and a structural parameter, k, dependent on the shear rate, that may be written as ... 

Figure 2-8 The Relative Viscosity (ijr) Values of Tapioca Starch Dispersions Strongly Depended on their Volume Fraction. The Line in the Figure Represents Values Predicted by the Model of Quemada et al. (1985) with the Structural Parameter = 1.8 (Rao and Tattiyakul, 1998).

Quemada, D., Fland, P., and Jezequel, P. H. 1985. Rheological properties and flow of concentrated diperse media. Chem. Eng. Comm. 32 61-83. 

Quemada et al. (1985) reported values of k in the range 2.50-3.82 for dispersions of rigid solids, and 1.70-1.85 for red blood suspensions. Because heated starch granules... 

Quemada et al. (1985) model (Equation 2.11) was used to analyze data on cocoa dispersions (Fang et al., 1996) and the role of cocoa butter replacers (Fang et al., 1997). Selected values of rheological properties of chocolate are given in Table 5-G. In addition, the data of Fang et al. (1996) (Table 5-H) before and after degasification as a function of temperature are note worthy. 

D Quemada. In J Casas-Vazquez, D Jou, eds. Rheological Modelling Thermodynamical and Statistical Approaches. New York Springer-Verlag, 1991, p 158. 

Electrically charged particles in aqueous media are surroimded by ions of opposite charge (counterions) and electrolyte ions, namely, the electrical double layer. The quantity He represents the energy of repulsion caused by the interaction of the electrical double layers. The expression for He depends on the ratio between the particle radius and the thickness of the electrical double layer, k, called the Debye length. For K.a > 5 (Quemada and Berli, 2002) ... 

Quemada, D. and Berli, C. Energy of interaction in colloids and its implications in rheological modeling, Adv. Colloid Interface Sci., 98, 51, 2002. 

Lepez et al. (1990) examined the rheology of glass-bead-filled HOPE and PS. They found that a Cross model describes the viscosity-shear-rate relationship, a Quemada model describes the concentration dependence of the viscosity, and a compensation model applies for the tempemture dependence of the viscosity. This model is expressed as... 

Quemada (1978a, 1978b) examined the rheology and modelling of concentrated dispersions and described simple viscosity models that incorporate the effects of shear rate and concentration of filler and separate effects of Brownian motion (or aggregation at low shear) and particle orientation and deformation (at high shear). The ratio of structure-build-up and -breakdown rates is an important parameter that is influenced by the ratio of the shear rate to the particle diffusion. A simple form of viscosity relation is given here ... 

For concentrated systems, equation 31 loses its appeal because of the difficulties involved in evaluating the higher order coefficients. Instead, semiempirical models are more suitable. Such models are given by the Mooney equation (77), the Krieger-Dougherty equation (67), and the Quemada equation. In particular, the Quemada equation is the most used equation because of its simplicity and utility. The Mooney equation is given by... 

Heuristic derivations of equations 32 and 33 have been presented by Mooney (77), Krieger (67), Ball and Richmond (78), and Stein (79). The Quemada expression is given by... 

The same line of arguments can be made for the Quemada expression, for example, letting e = 1 and making appropriate assumptions when equation 39 is considered. However, one can notice that the Quemada expression is not very accurate for dilute systems where equation 31 may be useful. It is also possible to match equations 31 and 33 asymptotically to give a better equation that is suitable for the entire range of volume fraction,... 

In deriving equation 32 or equation 33, it is assumed that 0max is the solid volume fraction at which the suspended particles cease moving. Thus, the forces, such as shearing, that can disturb the suspension structure and hence improve the mobility of particles will have an effect on the value of max. This is confirmed by the fact that a value of kH = 6.0 is observed at low shear limit, that is, y 0 and at high shear limit, y - oo, kH = 7.1 is found. Typical values of max have been found with the use of Quemada s equation as 0max = 0.63 0.02 in the low shear limit and high shear limit for submicrometersized sterically stabilized silica spheres in cyclohexane (72, 85, 88). 

Jones and co-workers (72, 88) found that the suspension viscosity variation with shear rate can be fitted fairly well by the Cross equation, equation 12, with m = 0.5 — 0.84. Both the low and high shear limit relative viscosities, Mro, Mroo> can be expressed by the Quemada s equation with 0max = 0.63 and 0.71, respectively. 

Equation 50 does not agree with the experimentally observed Quemada equation. However, by comparing equations 48 and 49 with 50, we may expect that the longitudinal viscosity of the cylindrical fiber suspension is smaller than the viscosity of spherical particle suspensions at a concentrated state, whereas the transverse viscosity is higher than the viscosity of spherical suspensions. 

Kitano et al. (82) found that the relative viscosity of a suspension of cylindrical rods can be estimated by the Quemada equation with the maximum packing fraction given by... 

By an asymptotic matching of the dilute limit homogeneous viscosity with the Quemada equation, Phan-Thien and Graham (118) obtained the following equation valid for a wide range of solid concentration ... 

Equations 66 and 68 indicate that the droplet behaves like a solid particle only when the viscosity ratio of the dispersed phase to the continuous phase is large. For liquid-in-liquid dispersions, the modified Quemada equation, Krieger-Dougherty equation, and Mooney equation are still applicable provided that the maximum packing limit and the Einstein constant are left as adjustable parameters for a given system. 

D. Quemada, Rheology of concentrated disperse systems. III. General features of the proposed non-Newtonian model. Comparison with experimental data, Rheol. Acta 17 (1978) 643-653. 

A similar equation but with the exponent of —2 was advanced by Quemada [31]. For instance, this type of equation was shown to describe well the experimental data obtained on relatively monodisperse dispersions of hydrophobically modified silica particles suspended in cyclohexane [32], i.e., systems that can well be regarded as good model systems for a hard-sphere fluid. Typical values for O , are 0.6-0.7 [32], i.e., values that correspond to the packing fraction of a cubic array of spheres. 

D. E. Quemada, in Lecture Notes in Physics Stability of Thermodynamic Systems (J. Cases-Vasquez and J. Lebon, eds.). Springer, Berlin, 1982, pp. 210-247. 

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