Viscosity of suspension

At least, in absolute majority of cases, where the concentration dependence of viscosity is discussed, the case at hand is a shear flow. At the same time, it is by no means obvious (to be more exact the reverse is valid) that the values of the viscosity of dispersions determined during shear, will correlate with the values of the viscosity measured at other types of stressed state, for example at extension. Then a concept on the viscosity of suspensions (except ultimately diluted) loses its unambiguousness, and correspondingly the coefficients cn cease to be characteristics of the system, because they become dependent on the type of flow. 

Chemical compatibility/Stability considerations White granules or grayish white powder. Aqueous solutions are neutral to litmus. Combustible Uses (routes) Orally, as a 0.1 to 5% mixture with water. Acts to increase viscosity of suspension, thereby reducing settling rate and improving homogeneity... 

Integrating this equation to any volume fraction, q>, with the boundary conditions that the elasticity is equal to the network value when there are no particles present, and that when the volume fraction reaches packed filler bed), then gives us Equation (2.64). There is an analogous equation describing the viscosity of suspensions of particles and this will be introduced in Chapter 3. When a value of 0.64 is used for the maximum filler concentration, Equation (2.64) becomes... 

Figure 11.19(b) plots the steady state ratio of the viscosities of suspensions of spherical particles in Newtonian liquids, /iv, to the viscosity of the Newtonian fluid, /y. It was constructed by Thomas (79) using the data of a number of investigators. A variety of uniform-sized particles having diameters of 1 —4(X) pm were used. They included PS and... 

Fig. 11.19 Viscosity of suspensions of spherical particles in Newtonian fluids, (a) Curve constructed by Bigg. [Reprinted by permission from D. M. Bigg, Rheological Behavior of Highly Filled Polymer Melts, Polym. Eng. Sci, 23, 206 (1983).] (b) Curves presented by Thomas (79).

Only at very low concentrations can the coils be considered as separate spheres. In that case Einstein s relation for the viscosity of suspensions can be applied ... 

Einstein Equation for Viscosity of Suspensions—Einstein derived a general equation for computation of the viscosity of a suspensoid in terms of viscosity of the medium, and the ratio of aggregate volume of solid particles to total volume of suspensoid. Einstein s equation is... 

In electrochemistry several equations are used that bear Einsteins name [viii-ix]. The relationship between electric mobility and diffusion coefficient is called Einstein relation. The relation between conductivity and diffusion coefficient is called - Nernst-Einstein equation. The expression concerns the relation between the diffusion coefficient and the viscosity and is known as the - Stokes-Einstein equation. The expression that shows the proportionality of the mean square distance of the random movements of a species to the diffusion coefficient and the duration of time is called - Einstein-Smoluchowski equation. A relationship between the relative viscosity of suspension and the volume fraction occupied by the suspended particles - which was derived by Einstein - is also called Einstein equation [ix]. 

Brownian motion must be taken into account for suspensions of small (submicron-sized) particles. By their very nature, such stochastic Brownian forces favor the ergodicity of any configurational state. Although no completely general framework for the inclusion of Brownian motion will be presented here, its effects will be incorporated within specific contexts. Especially relevant, in the present rheological context, is the recent review by Felderhof (1988) of the contribution of Brownian motion to the viscosity of suspensions of spherical particles. 

Patzold (1980) compared the viscosities of suspensions of spheres in simple shear and extensional flows and obtained significant differences, which were qualitatively explained by invoking various flow-dependent sphere arrangements. Goto and Kuno (1982) measured the apparent relative viscosities of carefully controlled bidisperse particle mixtures. The larger particles, however, possessed a diameter nearly one-fourth that of the tube through which they flowed, suggesting the inadvertant intrusion of unwanted wall effects. 

Analysing the rate of energy dissipation in concentrated suspensions of solid spheres, Frankel and Aerivos [69] also arrived at the conclusion that the relative viscosity of suspensions is a function of the relation a/h ... 

At very low shear rates (i.e., flow velocities), particles in a chemically stable suspension approximately follow the layers of constant velocities, as indicated in Fig. 2. But at higher shear rates hydro-dynamic forces drive particles out of layers of constant velocity. The competition between hydrodynamic forces that distort the microstructure of the suspension and drive particles together, and the Brownian motion and repulsive interparticle forces keeping particles apart, leads to a shear dependency of the viscosity of suspensions. These effects depend on the effective volume fraction of... 

The qualitative behavior of the viscosity of suspensions over a large range of shear rates is depicted in Fig. 7. This type of shear dependency is found, for example, for concentrated colloidal suspensions. These results cannot be immediately carried over to ceramic inks since the experiments are done with much higher concentrations of solids and at much lower shear rates than are applicable for the inkjet process. The suspended particles in these experiments are usually spherical at sizes of about 1 fim or smaller. But the shear dependency of the viscosity found for concentrated... 

The hydrodynamic behavior of complex particles in solution is similar to that of suspensions of solid spheres. Applying to the solutions of the PMAA-poly(ethylene glycol) complex, Einstein s equation for the viscosity of suspension of spherical particles, t]Sp/c = 2.54 q> (where tp is the volume fraction of dissolved substance) the solvent content in complex coils has been estimated33. It is about 75 vol%, i.e. the complex particles contain comparatively small quantities of the solvent in comparison with a usual random coil in solution which contains about 97-99 vol% of solvent34. ... 

Wildemuth, C. R. and Williams, M. C. 1984. Viscosity of suspensions modeled with a shear-dependent maximum packing fraction. Rheol. Acta 23 627-635. 

Figure 6.2 Reduced viscosity of suspensions of sterically stabilized polysty-rene hard spheres of diameter d = 420 and 870 nm, as a function of volume fraction (p, replotted from data of Saunders (1961), compared to the prediction of Eq. (6-2). (From Macosko, Rheology Principles, Measurements, and Applications, Copyright 1994. Reprinted by permission from John Wiley Sons.)...

Theoretical expressions similar to those presented in this section have recently been successfully used to predict the modulus and viscosity of suspensions of charged rod-like particles (Solomon and Boger 1998). 

The effect of particle size distribution on the viscosities of suspensions and emulsions has been investigated (28, 32-35). Most of these studies indicate that the effect of particle size distribution is of enormous magnitude... 

As the suppository base is heated before moulding, certain effects can be noted which are unique to this type of medication. Testosterone dissolves when hot in the semisynthetic excipient Witepsol H, to give, on cooling, crystals of about 2-3 /rm in diameter. After dissolution in theobroma oil, the dmg does not crystallise on cooling but remains dissolved as a solid solution. In the former case, high absorption rates are obtained, while in the latter poor absorption is achieved. Because of the effect of particle size on the viscosity of suspensions (see section 7.4.4) it is preferable to avoid the incorporation of ultra-fine crystals as the resultant melt of suspension has a higher viscosity than those produced from coarser crystals. 

With increasing shear, Pe — the relative viscosity of suspensions — usually decreases (see Fig. 6.19). This shear thinning effect is quite moderate in colloidally stable suspensions, which actually can behave as nearly Newtonian up to... 

Einstein derived the following equation for the viscosity of suspensions of rigid, uncharged, spherical particles which do not interact with the suspension medium ... 

Important process parameters to consider are the viscosity of suspensions as a function of solid particle loading as well as deposition rates that can be achieved. 

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