Suspensions, non-Newtonian behavior

The viscosity of a fluid arises from the internal friction of the fluid, and it manifests itself externally as the resistance of the fluid to flow. With respect to viscosity there are two broad classes of fluids Newtonian and non-Newtonian. Newtonian fluids have a constant viscosity regardless of strain rate. Low-molecular-weight pure liquids are examples of Newtonian fluids. Non-Newtonian fluids do not have a constant viscosity and will either thicken or thin when strain is applied. Polymers, colloidal suspensions, and emulsions are examples of non-Newtonian fluids [1]. To date, researchers have treated ionic liquids as Newtonian fluids, and no data indicating that there are non-Newtonian ionic liquids have so far been published. However, no research effort has yet been specifically directed towards investigation of potential non-Newtonian behavior in these systems. 

With this background of non-Newtonian behavior in hand, let us examine the viscous behavior of suspensions and slurries in ceramic systems. For dilute suspensions on noninteracting spheres in a Newtonian liquid, the viscosity of the suspension, r)s, is greater than the viscosity of the pure liquid medium, rjp. In such cases, a relative viscosity, rjr, is utilized, which is defined as rjs/rjL. For laminar flow, is given by the Einstein equation... 

Figure 5.2. Non-Newtonian behavior of suspensions (a) viscosity as a function of shear rate, 0.4 wt % polyacrylamide in water at room temperature (b) shear stress as a function of shear rate for suspensions of TiOz at the indicated vol % in a 47.1 wt % sucrose solution whose viscosity is 0.017 Pa sec (Denn, Process Fluid Mechanics, Prentice-Hall, Englewood Cliffs, NJ, 1980).

This unit describes a method for measuring the viscosity (r ) of Newtonian fluids. For a Newtonian fluid, viscosity is a constant at a given temperature and pressure, as defined in unit hi. i common liquids under ordinary circumstances behave in this way. Examples include pure fluids and solutions. Liquids which have suspended matter of sufficient size and concentration may deviate from Newtonian behavior. Examples of liquids exhibiting non-Newtonian behavior (unit hi. i) include polymer suspensions, emulsions, and fruit juices. Glass capillary viscometers are useful for the measurement of fluids, with the appropriate choice of capillary dimensions, for Newtonian fluids of viscosity up to 10 Pascals (Newtons m/sec 2) or 100 Poise (dynes cm/sec 2). Traditionally, these viscometers have been used in the oil industry. However, they have been adapted for use in the food industry and are commonly used for molecular weight prediction of food polymers in very dilute solutions (Daubert and Foegeding, 1998). There are three common types of capillary viscometers including Ubelohde, Ostwald, and Cannon-Fenske. These viscometers are often referred to as U-tube viscometers because they resemble the letter U (see Fig. HI.3.1). 

The relationship between shear stress and shear rate is also an indication of the degree of Newtonian behavior that a fluid exhibits. The linearity of the relationship is a direct indication of Newtonian behavior. The 5% corn stover suspension exhibited Newtonian behavior the remaining corn stover suspensions exhibited non-Newtonian behavior. At the other concentrations (>5%), the degree of linearity decreased with increasing mass concentration. Figure 4 illustrates the non-Newtonian characteristics of the remaining corn stover suspensions. 

S. Bhattacharji and P. Savic, Real and Apparent Non Newtonian Behavior in Viscous Pipe flow of Suspensions Driven by a Fluid Piston, Proc. Heat and Mass Transfer Fluid Mechanics Institute, 15, 248 (1965). 

Repulsive interparticle forces cause the suspension to manifest non-Newtonian behavior. Detailed calculations reveal that the primary normal stress coefficient [cf. Eq. (8.7)] decreases like y 1. In contrast, the suspension viscosity displays shear-thickening behavior. This feature is again attributed to the enhanced formation of clusters at higher shear rates. 

Foods can be classified in different manners, including as solids, gels, homogeneous liquids, suspensions of solids in liquids, and emulsions. Fluid foods are those that do not retain their shape but take the shape of their container. Fluid foods that contain significant amounts of dissolved high molecular weight compounds (polymers) and/or suspended solids exhibit non-Newtonian behavior. Many non-Newtonian foods also exhibit both viscous and elastic properties, that is, they exhibit viscoelastic behavior. 

Non-Newtonian behavior occurs in solutions or melts of polymers and in suspensions of solids in liquids. Some t — y plots are shown in Figure 6.2, and the main classes are described following. 

In both the studies on basalts, the breaks in the slope of the log Pq vs. (1/T,K) curves occur at 20 to 30 volume percent of suspended crystals. The non-Newtonian behavior of these molten silicate suspensions appears to arise from the increasing concentration of suspended crystals in the melt. This suggests that in modeling fluid flow in silicate systems, power law behavior should be considered when the suspended crystal concentration exceeds 20 volume percent. 

Most common fluids of simple structure are Newtonian (i.e., water, air, glycerine, oils, etc.). However, fluids with complex structures (i.e., high polymer melts or solutions, suspensions, emulsions, foams, etc.) are generally non-Newtonian. Examples of non-Newtonian behavior include mud, paint, ink, mayonnaise, shaving cream, polymer melts and solutions, toothpaste, etc. Many two-phase systems (e.g., suspensions, emulsions, foams, etc.) are purely viscous fluids and do not exhibit significant elastic or memory properties. However, many high polymer fluids (e.g., melts and solutions) are viscoelastic and exhibit both elastic (memory) as well as nonlinear viscous (flow) properties. A classification of material behavior is summarized in Table 5.1 (in which the subscripts have been omitted for simplicity). Only purely viscous Newtonian and non-Newtonian fluids are considered here. The properties and flow behavior of viscoelastic fluids are the subject of numerous books and papers (e.g., Darby, 1976 Bird et al., 1987). 

The polymer solutions or base gels and suspensions exhibited pseudoplastic non-Newtonian behavior, and they were characterized by the following Ostwald-de Waele or power law fluid model. 

The Newtonian behavior of suspensions in Newtonian liquids is limited to low concentrations. An exception seems to be the exten-sional flow of anisometric particles (irrotational flow field) where the rate of strain independent region extends to concentrations where strong non-Newtonian behavior would be expected in shear. These rate of deformation dependent phenomena will be summarized below. 

In the absence of interlayer slip, addition of a second phase leads to an increase of viscosity. The simplest way to treat the system is to consider that the relative viscosity as a function of the solids volume fraction, particle aspect ratio and orientation. There is no difference between the flow of suspensions in Newtonian liquids and that of polymeric composites, when the focus is on the Newtonian behavior. The non-Newtonian behavior of suspensions originates either from the non-Newtonian behavior of the medium or from the presence of filler particles. The problems associated with this behavior can originate in inter-particle interactions (viz. yield stress), and orientation in flow [Leonov, 1990 Mutel and Kamal, 1991 Vincent and Agassant, 1991 Shi-kata and Pearson, 1994]. 

The quantity /i, is the viscosity coefficient of a Newtonian fluid—that is, a fluid that follows the Newtonian viscosity law. It is an intensive property and is generally a function of temperature and pressure, although under most conditions for simple fluids it is a function of temperature alone. All gases and most simple liquids closely approximate Newtonian fluids. Polymeric fluids and suspensions may not follow the Newtonian law, and when they do not they are termed non-Newtonian fluids. Non-Newtonian behavior falls under the science of rheology which will be discussed in Chapter 9. 

The values of the constants were measured to be Tq = 10 Pa, n = 0.630, and m = 0.167 Pa s . This relation is seen to be a combination of the Bingham plastic and power law behavior and is found to fit the measurements to within an accuracy of 1—2%. In Fig. 9.1.3 we have drawn in the velocity distribution for a Bingham plastic fluid using the measured value of the yield stress and a measured value of rja = 0.57 from which we calculate G = 1.4x10 Pam", Mp = 2.28 X 10 Pa s, and 3, = 1.84 m s The agreement between the theory and measurement, although not as excellent as for the yield-power law behavior, is nevertheless seen to be quite good and shows clearly the nature of the non-Newtonian behavior associated with the flow of a colloidal suspension. 

To numerically illustrate the effect of particle size on the dimensionless groups, we note that in water at standard temperature for a = 100 (im, a potential of 10 mV, and A = 10 °J, we have Pe = 10 y, N5R = 10 y, and = 10 y. Clearly for 100 /um particles, all of the dimensionless groups are very large compared to unity even at a shear rate of 1 s In the high shear limit, non-Newtonian behavior should vanish and the viscosity should attain a stationary value independent of the shear rate. We note here the analogue between the high shear limit for suspensions and the infinite-shear-rate-viscosity limit for polymers discussed above. 

Owing primarily to the organic character of the cell and the rich content in water, the suspension, once concentrated, tends to exhibit the non-Newtonian behavior. Transportation, heat transfer and mass transfer (i.e. drying and so on), all of which are the subjects adjunct to the separation, abound with problems still remaining to be dissolved in regard to the non-Newtonian characteristics. 

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