Colloid shear rate

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. 

Colloidal State. The principal outcome of many of the composition studies has been the delineation of the asphalt system as a colloidal system at ambient or normal service conditions. This particular concept was proposed in 1924 and described the system as an oil medium in which the asphaltene fraction was dispersed. The transition from a coUoid to a Newtonian Hquid is dependent on temperature, hardness, shear rate, chemical nature, etc. At normal service temperatures asphalt is viscoelastic, and viscous at higher temperatures. The disperse phase is a micelle composed of the molecular species that make up the asphaltenes and the higher molecular weight aromatic components of the petrolenes or the maltenes (ie, the nonasphaltene components). Complete peptization of the micelle seems probable if the system contains sufficient aromatic constituents, in relation to the concentration of asphaltenes, to allow the asphaltenes to remain in the dispersed phase. 

One characteristic of shear banded flow is the presence of fluctuations in the flow field. Such fluctuations also occur in some glassy colloidal materials at colloid volume fractions close to the glass transition. One such system is the soft gel formed by crowded monodisperse multiarm (122) star 1,4-polybutadienes in decane. Using NMR velocimetry Holmes et al. [23] found evidence for fluctuations in the flow behavior across the gap of a wide gap concentric cylindrical Couette device, in association with a degree of apparent slip at the inner wall. The timescale of these fluctuations appeared to be rapid (with respect to the measurement time per shear rate in the flow curve), in the order of tens to hundreds of milliseconds. As a result, the velocity distributions, measured at different points across the cell, exhibited bimodal behavior, as apparent in Figure 2.8.13. These workers interpreted their data... 

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. 

If colloids are sufficiently large or the fluid shear rate high, the relative motion from velocity gradients exceeds that caused by Brownian (thermal) effects (orthokinetic agglomeration). 

This latter case is the same result as Einstein calculated for the situation where slip occurred at the rigid particle-liquid interface. Cox15 has extended the analysis of drop shape and orientation to a wider range of conditions, but for typical colloidal systems the deformation remains small at shear rates normally accessible in the rheometer. The data shown in Figure 3.11 was calculated from Cox s analysis. His results have been confirmed by Torza et al.16 with optical measurements. The ratio of the viscous to interfacial tension forces, Rf, was given as ... 

Fig. 8.22 Fraction of naphthalene concentration due to colloidal entrainment at (a) G = 5 and (b) = 20 s , for naphthalene and naphthalene compounds containing 1,2, or 3 C as side chains, where is the mean shear rate. Reprinted with permission from Sterhng Jr MC, Bonner JS, Page CA, Ernest ANS, Auteniieth RL (2003) Partitioning of crude oil polycyclic aromatic hydrocarbons in aquatic systems. Environ Sci Technol 37 4429 434. Copyright 2003 American Chemical Society...

The top-down approach involves size reduction by the application of three main types of force — compression, impact and shear. In the case of colloids, the small entities produced are subsequently kinetically stabilized against coalescence with the assistance of ingredients such as emulsifiers and stabilizers (Dickinson, 2003a). In this approach the ultimate particle size is dependent on factors such as the number of passes through the device (microfluidization), the time of emulsification (ultrasonics), the energy dissipation rate (homogenization pressure or shear-rate), the type and pore size of any membranes, the concentrations of emulsifiers and stabilizers, the dispersed phase volume fraction, the charge on the particles, and so on. To date, the top-down approach is the one that has been mainly involved in commercial scale production of nanomaterials. For example, the approach has been used to produce submicron liposomes for the delivery of ferrous sulfate, ascorbic acid, and other poorly absorbed hydrophilic compounds (Vuillemard, 1991 ... 

It turns out that the Krieger-Dougherty equation can also be used for intermediate shear rates with suitable modifications. Experimental data also suggest that [77] and 7 are independent of particle size, although they are stress dependent. Therefore viscosities of monodis-persed colloids of different particle sizes can be represented by a single equation by suitably defining the variables. A discussion of these and other extensions may be found in Barnes et al. (1989). 

Fig. 8.7. Shear rate dependence of viscosity for undiluted polystyrenes of different molecular weights. Weight-average molecular weights are 48500 117000 G 179000 G 217000 242000. All data are reduced to 183° C the dashed line has a slope of -0.82 (324). (Reproduced from Journal of colloid and interfache science, Vol. 22, Fig. 1, p. 520. New York ...

I. The achievement of high viscosities at low shear rates without high molecular weights. 2. Minimization of the elastic behavior of the fluid at high deformation rates that are present when high molecular weight water-soluble polymers are used. 3. Providing colloidal stability to disperse phases in aqueous media, not achievable with traditional water-soluble polymers. 

If particle aggregation occurs in a colloidal system, then an increase in the shear rate will tend to break down the aggregates, which will result, among other things, in a reduction of the amount of solvent immobilised by the particles, thus lowering the apparent viscosity of the system. 

In some colloidal dispersions, the shear rate (flow) remains at zero until a threshold shear stress is reached, termed the yield stress (rY), and then Newtonian or pseudoplastic flow begins. A common cause of such behaviour is the existence of an interparticle or intermolecular network which initially acts like a solid and offers resistance to any positional changes of the volume elements. In this case flow only occurs when the applied stress exceeds the strength of the network and what was a solid becomes instead a fluid. 

Attempts to describe the unlimited increase of the viscosity of dispersions and emulsions observed when their concentrations approach the maximum values (tPmax) meet great theoretical difficulties. Various approaches were developed to overcome these difficulties. Thus, for example, Russel et al. [58] suggested that account should be taken of the Brownian motion of particles in colloidal dispersions in the form of a hydrodynamic contribution. They showed that this contribution which is to be taken into account in considering a slow flow (with slow shear rates y), increases considerably with increasing dispersion concentration. For a description of the dependence of viscosity on concentration the above authors obtained an exact equation only in the integral form. At low shear rates it gives the following power series ... 

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... 

Pe should control the onset of shear thickening in colloidal suspensions. This being the case, the shear rate at which shear thickening occurs is (approximately) given by... 

FIGURE 12.9 Viscosity (at low shear rate) of AI2O3 suspensions at different pH values adjusted by the addition of various amounts of 0.2 M AICI3. Near the isoelectric point the suspension is not colloidally stable, giving a high viscosity. Data taken from Reed [23]. 

This section draws heavily from two good books Colloidal Dispersions by Russel, Seville, and Schowalter [31] and Colloidal Hydrodynamics by Van de Ven [32] and a review paper by Jeffiey and Acrivos [33]. Concentrated suspensions exhibit rheological behavior which are time dependent. Time dependent rheological behavior is called thixotropy. This is because a particular shear rate creates a dynamic structure that is different than the structure of a suspension at rest. If a particular shear rate is imposed for a long period of time, a steady state stress can be measured, as shown in Figure 12.10 [34]. The time constant for structure reorganization is several times the shear rate, y, in flow reversal experiments [34] and depends on the volume fraction of solids. The viscosities discussed in Sections 12.42.2 to 12.42.9 are always the steady shear viscosity and not the transient ones. 

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