Shear thinning colloidal suspensions

In the last section we introduced the concept of two asymptotic viscosity limits for shear thinning colloidal suspensions as a function of shear rate. One is the high shear limit which corresponds to high values of the Peclet number where viscous forces dominate over Brownian and interparticle surface forces. Generally this limit is attained with non-colloidal size particles since to achieve large Peclet numbers by increase in shear rate alone requires very large values for colloidal size particles. In this limit, non-Newtonian effects are negligible for colloidal as well as non-colloidal particles. 

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. 

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... 

As discussed in Sect. 4, in the fluid, MCT-ITT flnds a linear or Newtonian regime in the limit y 0, where it recovers the standard MCT approximation for Newtonian viscosity rio of a viscoelastic fluid [2, 38]. Hence a yrio holds for Pe 1, as shown in Fig. 13, where Pe calculated with the structural relaxation time T is included. As discussed, the growth of T (asymptotically) dominates all transport coefficients of the colloidal suspension and causes a proportional increase in the viscosity j]. For Pe > 1, the non-linear viscosity shear thins, and a increases sublin-early with y. The stress vs strain rate plot in Fig. 13 clearly exhibits a broad crossover between the linear Newtonian and a much weaker (asymptotically) y-independent variation of the stress. In the fluid, the flow curve takes a S-shape in double logarithmic representation, while in the glass it is bent upward only. 

Colloidal dispersions often display non-Newtonian behaviour, where the proportionality in equation (C2.6.2) does not hold. This is particularly important for concentrated dispersions, which tend to be used in practice. Equation ( 2.6.21 ean be used to define an apparent viseosity, rj at a given shear rate. If r pp deereases with increasing shear rate, the dispersion is ealled shear thinning (pseudoplastic) if it increases, this is known as shear thiekening (dilatant). The latter behaviour is typieal of eoneentrated suspensions. If a finite shear stress has to be applied before the suspension begins to flow, this is known as the yield stress. The apparent viscosity may also change as a funetion of time, upon applieation of a fixed shear rate, related to the formation or breakup of partiele networks. Thixotropie dispersions show a deerease in r pp with time, whereas an increase with time is called rheopexy. 

Truly bimodal suspensions of colloidal and noncolloidal particles are of considerable practical interest. For such suspensions at low shear rates, the viscosity is high so that, for example, during storage, settling is reduced. On the other hand, because the mixture is shear thinning, at higher shear rates when the suspension is pumped the viscosity decreases, thereby enabling the mixture to be pumped at a lower pressure drop. 

The bimodal model has also been applied to polydisperse suspensions (Probstein et al. 1994), which in practice generally have particle sizes ranging from the submicrometer to hundreds of micrometers. In order to apply the bimodal model to a suspension with a continuous size distribution, a rational procedure is required for the separation of the distribution into fine and coarse fractions. Such a procedure has not been developed so that an inverse method had to be used wherein the separating size was selected which resulted in the best agreement with the measured viscosity. Again, however, the relatively small fraction of colloidal size particles was identified as the principal agent that acts independently of the rest of the system and characterizes the shear thinning nature of the suspension viscosity. 

In concentrated suspensions, the settling velocity of a sphere is less than the terminal falling velocity of a single particle. For coarse (non-colloidal) particles in mildly shear-thinning liquids (1 > n > 0.8) [Chhabra et al., 1992], the expression proposed by Richardson and Zaki [1954] for Newtonian fluids applies at values of Re(= up to about 2 ... 

Figure 9.5. Degree of shear thinning of silicon nitride suspensions at different solids content. (From L. Bergstrom, Colloids Suif., A, 133, 151-155 (1998) with permission from Elsevier Science)...

Figure 4.35 Typical rheological behavior of colloidal suspensions (i) Newtonian, (ii) shear thickening or dilatant, (iii) shear thinning or pseudoplastic, (iv) Bingham plastic, (v) pseudoplastic with a yield stress.

Figure 5.14 The transition from Brownian dominated random structures to preferred flow structures as shear rate is increased is the mechanism for the shear thinning behaviour of concentrated suspensions of hard sphere colloids... 

Similar to conventional colloidal suspensions, ER suspensions also show the shear tliickening and shear thinning behaviors. Figure 23 shows the viscosity of the 3-(methacryloxy propyl)-trimethoxysilane coated... 

Figure 19-11. Reduced viscosities as a function of the reduced shear stress of colloidal silica suspensions (diameter of 100 nm) in the presence of addedpolymer (polystyrene). The solvent used is decalin which is a near theta solvent for polystyrene. The size ratio of the polymer radius of gyration to the colloid radius (Rg/R) is 0.02S. The colloid volume fraction ((f>) is kept fixed at 0.4. In the absence of added polymer (Cp/c = 0), the particles behave as hard spheres and as more polymer is added to the system, the particles begin to feel an attraction. The colloid-polymer suspensions at (p of 0.4 shear thin between a zero rate viscosity of r o and a high shear rate plateau viscosity r]x,. The shear thinning behavior (in the absence and presence of polymer) is well captured by equation (19-10) with n = 1.4. Note rjo, rjao and cTc are functions of volume fraction and strengths of attraction but weakly dependent on range of attraction (Shah, 2003c Rueb, 1997).

After Couette described his apparatus, several researchers used the design to study a wide variety of fluids. They soon found that many colloidal suspensions and polymer solutions did not obey this simple linear relation. Nearly all these materials give a viscosity that decreases with increasing velocity gradient in shear. Figure 2.1.2 shows that shear thinning occurs in a wide range of materials... 

Figure 13.7 Plot of viscosity versus shear stress showing shear thinning and shear thickening for colloidal suspensions of various volume fractions. (Redrawn from Larson 1999.)...

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