Thixotropic flow yield stress

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. 

Flow and self-leveling characteristics of these products are governed by the rheological behavior of the slurrylike materials. At the low water-cement ratios required to ensure proper suspension of the solids, most selfleveling compositions are characterized by a yield stress and thixotropic behavior [75]. To obtain self-leveling properties, the yield stress has to be reduced and this is achieved by the selection and combination of suitable mix ingredients at... 

Example. A colloidal system can exhibit several of these characteristics at once. For example, paint must be plastic and thixotropic so that it will flow when brushed on and (only) immediately after brushing (for a smooth finish) a further benefit is that vigorous mixing readily disperses the pigments which then stay dispersed for some time when standing (high yield stress). 

Thixotropy is a rheological property that results in yield stress on standing. Thixotropic flow is defined as a reversible, time-dependent, isothermal gel-sol transition. Thixotropic systems exhibit easy flow at relatively high shear rates. However, when the shear stress is removed, the system is slowly reformed into a structured vehicle. The usual property of thixotropy results from the breakdown and buildup of floccules under stress. A small amount of particle settling takes place until the system develops a sufficiently high yield value. The primary advantage of thixotropic flow is that it confers pourability under shear stress and viscosity and sufficiently high yield stress when the shear stress is removed at rest. 

For some substances their viscosities may show time dependent changes. It may decrease with time under shear but return to its original value when the shear stress is removed. Such material is termed thixotropic. Negative thixotropic refers to substances that display the opposite behavior. Other fluids are solid-like and will not flow till some critical yield stress is exceeded. Such fluids are known as viscoplastic. ... 

For the most part, PFDs exhibit shear-thinning (pseudoplastic) rheological behavior that is either time-independent or time-dependent (thixotropic). In addition, many PFDs also exhibit yield stresses. The time-independent flow curves are illustrated in Figure 1. The shear-thinning behavior appears to be the result of breakdown of relatively weak structures and it may have important relationship to mouthfeel of the dispersions. Because the viscosity of non-Newtonian foods is not constant but depends on the shear rate, one must deal with apparent viscosity defined as ... 

Gels are.essentially dispersions in which the attractive interactions between the elements of the disperse phase are so strong that the whole system develops a rigid network structure and, under small stresses, behaves elastically. In some instances the gel may flow plastically above a limiting yield stress [Chapter 8, Figure 8.3(e)] the gel then often exhibits thixotropic behaviour, the rigid gel state being re-formed when the stress is removed. 

Time dependency also enters into the consideration of the rheological response of any viscoelastic system. In the steady-state testing of such materials as molten polymers, the selected time scale should be sufficiently long for the system to reach equilibrium. Frequently, the required period, t > 10" sec, is comparable to that in thixotropic experiments. More direct distinctions between these two types of flow are the usual lack of elastic effects and larger strain values at equilibrium observed for the thixotropic materials (see Table 7.4). There is a correlation between these two phenomena, and theories of viscoelasticity based on thixotropic models have been formulated by Leonov [1972, 1994]. Inherent to the concept of thixotropy is the yield stress. 

Equation 7.42 well describes the flow behavior of polymeric systems, and it was found useful for polymer blends. It should be stressed that Equations 7.41-7.43 described the flow behavior of fluids without yield stress or thixotropicity. 

One further feature must be mentioned about pharmaceutical suspensions, namely, their desirable rheolt ical properties (7). In practice, a Bingham plastic" behavior is most used a minimum shear stress yield stress) is needed for the suspension to begin to flow. For tower stresses—and, of course, when the system is left undisturbed—the viscosity is so high that the particles will likely remain homogeneously dispersed. According to Falkiewicz (7). thixotropy is another flow characteristic that can be useful, since in thixotropic fluids a finite lime is needed to rebuild the structure after, for instance, shaking it for administration. For this reason, most formulations contain thixotropic flow regulators intended to confer optima viscous flow propertie.s to the suspensions. The reader is referred to Chapter 5 of this book for details. 

Figure 9 Schematic flow curves for complex thixotropic fluids having a yield stress.

If a stress above the yield stress is applied, the gelled structure is broken into smaller units (floes), which can then move past each other. If floe attrition is affected by the strength of the hydrodynamic and attractive forces, pseudoplastic behaviour is observed and the viscosity decreases with shear rate. The strong shear forces at high shear cause flow units to be smaller and flow is facilitated. The destruction of floes releases constrained solvent, which results in a decrease in the effective volume-fraction of the floes. This phenomenon may create thixotropic behaviour in the system if the breakup and formation of floes is reversible. 

A summary of the various rheological classifications can be found in Refs. [27,28]. Emulsions are frequently pseudoplastic, as shear rate increases viscosity decreases, this is also termed as shearthinning. An emulsion may also exhibit a yield stress, that is, the shear rate (flow) remains zero until a threshold shear stress is reached — the yield stress (ry) — then pseudoplastic or Newtonian flow begins. The pseudoplastic flow may also be time dependent, or thixotropic, in which case viscosity decreases under constant applied shear rate. 

Like plastic systems, a thixotropic system is transferred from a gel to a flowing system by exerting a stress o > o, the yield stress. This may be achieved by simply shaking or stirring. In contrast to plastic behavior, after releasing the stress, thixotropic systems need a finite time to recover the gel state. 

At higher shear rates, three types of deviations are observable when compared to ideal Newtonian flow (see Fig. 2.1).The first kind of deviation relates to the existence of a flow threshold (yield point). In the case of a Bingham fluid, flow occurs only when the yield stress is exceeded. The second type of deviation is shear thickening, observed where the viscosity increases with shear rate. This is the case for a dilating fluid, behaviour which is seldom apparent in polymers. Last, where viscosity decreases with increase in shear rate, fluxing is observed and such fluids are usually referred to as pseudoplastic fluids. This last phenomenon is a general characteristic of thermoplastic polymers. Flow effects may also be time dependent. Where viscosity does not depend only on the shear rate, but also on the duration of the applied stress, fluids are thixotropic. Polymers in a molten state thus behave as pseudoplastic fluids having thixotropic characteristics. 

The c of CMC has been established at around 1 % w/v. Below the c value CMC dispersions exhibit pseudoplastic flow without yield stress. However, at high concentrations, CMC dispersions exhibit thixotropic and viscoelastic behavior. 

Some shear-thinning materials deform like elastic solids until a certain stress, known as the yield stress, is reached, after which they deform as normal shear-thinning liquids. These materials are described as shear thinning with yield value, and have a consistency curve like curve 2 of Fig. 6.3. Flow ceases when the stress falls below the yield stress. Materials which show this behaviour include toothpaste and muds. These substances also tend to be thixotropic. 

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