Pseudoplastic suspensions

Figure 7.33 A plot of shear stress x against shear rate D for plastic and pseudoplastic suspensions. As )/ = r/D, the slope of the line represents the viscosity at each rate of shear in both the plastic and pseudoplastic systems the viscosity at level A is greater than that at level B.

Colloidal dispersions often display non-Newtonian behaviour, where the proportionality in equation (02.6.2) does not hold. This is particularly important for concentrated dispersions, which tend to be used in practice. Equation (02.6.2) can be used to define an apparent viscosity, happ, at a given shear rate. If q pp decreases witli increasing shear rate, tire dispersion is called shear tliinning (pseudoplastic) if it increases, tliis is known as shear tliickening (dilatant). The latter behaviour is typical of concentrated suspensions. If a finite shear stress has to be applied before tire suspension begins to flow, tliis is known as tire yield stress. The apparent viscosity may also change as a function of time, upon application of a fixed shear rate, related to tire fonnation or breakup of particle networks. Thixotropic dispersions show a decrease in q, pp with time, whereas an increase witli time is called rheopexy. 

Pseudoplastic fluids are the most commonly encountered non-Newtonian fluids. Examples are polymeric solutions, some polymer melts, and suspensions of paper pulps. In simple shear flow, the constitutive relation for such fluids is... 

The apparent viscosity, defined as du/dj) drops with increased rate of strain. Dilatant fluids foUow a constitutive relation similar to that for pseudoplastics except that the viscosities increase with increased rate of strain, ie, n > 1 in equation 22. Dilatancy is observed in highly concentrated suspensions of very small particles such as titanium oxide in a sucrose solution. Bingham fluids display a linear stress—strain curve similar to Newtonian fluids, but have a nonzero intercept termed the yield stress (eq. 23) ... 

Suspensions of fine sohds may have pseudoplastic or plastic-flow properties. When they are in laminar flow in a stirred vessel, motion in remote parts of the vessel where shear rates are low may become negligible or cease completely. To compensate for this behavior of slurries, large-diameter impellers or paddles are used, with (D /Df) > 0.6, where Df is the tank diameter. In some cases, for example, with some anchors, > 0.95 Df. Two or more paddles may be used in deep tanks to avoid stagnant regions in slurries. 

For suspension of free-settling particles, circulation of pseudoplastic slurries, and heat transfer or mixing of miscible liqiiids to obtain uniformity, a speed of 3.50 or 420 r/min should be stipulated. For dispersion of dry particles in hquids or for rapid initial mixing of hquid reactants in a vessel, an 11.50- or 1750- r/min propeller should be used at a distance Df/4 above the vessel bottom. A second propeller can be added to the shaft at a depth below the hquid surface if the submergence of floating hquids or particiilate solids is other wise inadequate. Such propeller mixers are readily available up to 2.2 kW (3 hp) for off-center sloped-shaft mounting. 

For suspension of rapidly setthng particles, the impeller turbine diameter should be Df/3 to Dfl2. A clearance of less than one-seventh of the fluid depth in the vessel should be used between the lower edge of the turbine blade tips and the vessel bottom. As the viscosity of a suspension increases, the impeller diameter should be increased. This diameter may be increased to 0.6 Df and a second impeller added to avoid stagnant regions in pseudoplastic slurries. Moving the baffles halfway between the impeller periphery and the vessel wall will also help avoid stagnant fluid near the baffles. 

This equation is based on the assumption that pseudoplastic (shear-thinning) behaviour is associated with the formation and rupture of structural linkages. It is based on an experimental study of a wide range of fluids-including aqueous suspensions of flocculated inorganic particles, aqueous polymer solutions and non-aqueous suspensions and solutions-over a wide range of shear rates (y) ( 10 to 104 s 1). 

Plastic fluids are Newtonian or pseudoplastic liquids that exhibit a yield value (Fig. 3a and b, curves C). At rest they behave like a solid due to their interparticle association. The external force has to overcome these attractive forces between the particles and disrupt the structure. Beyond this point, the material changes its behavior from that of a solid to that of a liquid. The viscosity can then either be a constant (ideal Bingham liquid) or a function of the shear rate. In the latter case, the viscosity can initially decrease and then become a constant (real Bingham liquid) or continuously decrease, as in the case of a pseudoplastic liquid (Casson liquid). Plastic flow is often observed in flocculated suspensions. 

The typical viscous behavior for many non-Newtonian fluids (e.g., polymeric fluids, flocculated suspensions, colloids, foams, gels) is illustrated by the curves labeled structural in Figs. 3-5 and 3-6. These fluids exhibit Newtonian behavior at very low and very high shear rates, with shear thinning or pseudoplastic behavior at intermediate shear rates. In some materials this can be attributed to a reversible structure or network that forms in the rest or equilibrium state. When the material is sheared, the structure breaks down, resulting in a shear-dependent (shear thinning) behavior. Some real examples of this type of behavior are shown in Fig. 3-7. These show that structural viscosity behavior is exhibited by fluids as diverse as polymer solutions, blood, latex emulsions, and mud (sediment). Equations (i.e., models) that represent this type of behavior are described below. 

Newtonian fluids containing a high concentration of rigid particles can show non-Newtonian flow behaviour with increasing shear rate, due to a break up of agglomerates in the shear field [4]. For many pseudoplastic fluid suspensions the... 

Since n is less than unity, the apparent viscosity decreases with the deformation rate. Examples of such materials are some polymeric solutions or melts such as rubbers, cellulose acetate and napalm suspensions such as paints, mayonnaise, paper pulp, or detergent slurries and dilute suspensions of inert solids. Pseudoplastic properties of wallpaper paste account for good spreading and adhesion, and those of printing inks prevent their running at low speeds yet allow them to spread easily in high speed machines. 

The results of the latest research into helical flow of viscoplastic fluids (media characterized by ultimate stress or yield point ) have been systematized and reported most comprehensively in a recent preprint by Z. P. Schulman, V. N. Zad-vornyh, A. I. Litvinov 15). The authors have obtained a closed system of equations independent of a specific type of rheological model of the viscoplastic medium. The equations are represented in a criterion form and permit the calculation of the required characteristics of the helical flow of a specific fluid. For example, calculations have been performed with respect to generalized Schulman s model16) which represents adequately the behavior of various paint compoditions, drilling fluids, pulps, food masses, cement and clay suspensions and a number of other non-Newtonian media characterized by both pseudoplastic and dilatant properties. 

Steady State Measurements Fig. 1 shows the shear rate-shear stress curves at various bentonite concentrations (calculated on the basis of the continuous phase) Hysteresis in the shear rate-shear stress curves was insignificant and the correlation between the ascending and descending curves was within experimental error. The results shown in Fig. 1 were therefore, the mean value of the ascending and descending curves. In the absence of any bentonite the suspension was Newtonian, whereas all suspensions containing bentonite at concentrations > 30 g dm were all pseudoplastic. This is illustrated from a plot of viscosity versus shear rate (Figure 2) which shows an exponential reduction of h with increase in shear rate. 

Yield-dilatant (n > 1) materials are rare but several cases of yield-pseudoplastics exist. For instance, data from the literature of a 20% clay in water suspension are represented by the numbers To = 7.3dyn/cm, K = 1.296dyn(sec)"/cm and n = 0.483 (Govier and Aziz, 1972, p. 40). Solutions of 0.5-5.0% carboxypolymethy-lene also exhibit this kind of behavior, but at lower concentrations the yield stress is zero. 

Dilatant Fluids. Dilatant fluids or shear-thickening fluids are less commonly encountered than pseudoplastic (shear-thinning) fluids. Rheological dilatancy refers to an increase in the apparent viscosity with increasing shear rate (3). In many cases, viscometric data for a shear-thickening fluid can be fit by using the power law model with n > 1. Examples of fluids that are shear-thickening are concentrated solids suspensions. 

---