Rheopectic

The coefficient Tj is termed the modulus of rigidity. The viscosities of thixotropic fluids fall with time when subjected to a constant rate of strain, but recover upon standing. This behavior is associated with the reversible breakdown of stmctures within the fluid which are gradually reestabflshed upon cessation of shear. The smooth sprea ding of paint following the intense shear of a bmsh or spray is an example of thixotropic behavior. When viscosity rises with time at constant rate of strain, the fluid is termed rheopectic. This behavior is much less common but is found in some clay suspensions, gypsum suspensions, and certain sols. 

Thixotropy and Other Time Effects. In addition to the nonideal behavior described, many fluids exhibit time-dependent effects. Some fluids increase in viscosity (rheopexy) or decrease in viscosity (thixotropy) with time when sheared at a constant shear rate. These effects can occur in fluids with or without yield values. Rheopexy is a rare phenomenon, but thixotropic fluids are common. Examples of thixotropic materials are starch pastes, gelatin, mayoimaise, drilling muds, and latex paints. The thixotropic effect is shown in Figure 5, where the curves are for a specimen exposed first to increasing and then to decreasing shear rates. Because of the decrease in viscosity with time as weU as shear rate, the up-and-down flow curves do not superimpose. Instead, they form a hysteresis loop, often called a thixotropic loop. Because flow curves for thixotropic or rheopectic Hquids depend on the shear history of the sample, different curves for the same material can be obtained, depending on the experimental procedure. 

Rheopectic behavior is the opposite of thixotropy. Shear stress increases with time at constant shear rate. Rheopeclic behavior has been obsei ved in bentonite sols, vanadium pentoxide sols, and gypsum suspensions in water (Bauer and Colhns, ibid.) as well as in some... 

The behaviour of a rheopectic fluid is the reverse of that of a thixotropic fluid and is illustrated by the broken lines in Figures 3.33 and 3.34. 

Newtonian flow, and their viscosity is not constant but changes as a function of shear rate and/or time. The rheological properties of such systems cannot be defined simply in terms of one value. These non-Newtonian phenomena are either time-independent or time-dependent. In the first case, the systems can be classified as pseudoplastic, plastic, or dilatant, in the second case as thixotropic or rheopective. 

If, in contrast, the viscosity increases with time while the material is being sheared and recovers its original viscosity when allowed to rest, the material is called rheopective. In this case the down curve is positioned below the up curve. 

Among other characteristics, non-Newtonian fluids exhibit an apparent viscosity that varies with shear rate. Consequently, the determination of the shear stress-shear rate curve must be an initial consideration. Although the apparent viscosity of a thixotropic or a rheopectic fluid changes with the duration of shearing, meaningful measurements may be made if the change is relatively slow. Viscoelastic fluids also exhibit behaviour that is a function of time but their apparent viscosities can be measured provided conditions of steady shearing are obtained. 

Rheopexy, a reversible time-dependent effect like thixotropy, is a rare phenomenon in pigmented systems. Rheopectic fluids increase in viscosity t with time when sheared at a constant shear rate D or a constant shear stress t until they approach a viscosity maximum (Fig. 53). 

The 3 1 LDAO/SDS mixture becomes viscoelastic and rheo-pectic when a small amount of NaCl Is added. Its viscosity shows a reversible Increase with time of shearing at constant shear rate. The rheopectic behavior Is probably due to long thread-like micelles that are aligned parallel to the flow In weakly bound clusters, as In the case of cetyltrlmethyl ammonium bromide and monosubstituted phenol mixed solutions (21). 

Further non-Newtonian types of behavior appear when time is introduced as a variable. Fluids whose viscosity decreases with time when sheared at a constant rate are called thixotropic, whereas fluids whose viscosity increases with time when sheared at a constant rate are termed rheopectic. Thixotropic behavior is represented schematically in Figure 4.6. Note that the two viscosities (slope of shear stress vs. shear rate) rip and r P2 are different, depending upon the time they were sheared at a given rate. 

These time-of-shear-dependent non-Newtonians may be divided into two groups, depending on whether the shear stress increases or decreases with time of shear at a constant shearing rate. The former are termed rheopectic the latter thixotropic Quids (P3). 

The causes for thixotropic and rheopectic behavior are possibly very similar to those for pseudoplasticity and dilatancy, respectively. The proposed causes of pseudoplasticity, i.e., the alignment of asymmetrical molecules and particles or the breakdown of solvated masses, could not always be expected to be instantaneous with respect to time. Therefore it seems that pseudoplastic behavior may simply be that form of thixotropy which has too small a time element to be measurable on most instruments in current use. Exactly the same argument may be applied... 

It is true, therefore, for Newtonian, Bingham-plastic, pseudoplastic and dilatant fluids. The same relationship can possibly be extended to thixotropic and rheopectic fluids by evaluating the shear stress at the wall over a differential length of tube, i.e., by replacing D P/4L with DdP/idL. This term will vary with distance along the pipe, however, and as no evident means of developing this relationship has been... 

Exclusive of thixotropic and rheopectic fluids, and of the few materials (see Section VI) which may slip at the wall. 

All pipe-line work to date has dealt with fluids which are not thixotropic and rheopectic. To an extent this may be justified because the limiting conditions (at startup—for thixotropic materials, and after long times of shear for rheopectic fluids) in pipe flow and some mixing problems are of primary importance. Design for these conditions would be similar to the techniques discussed herein for other fluids. This is not true of problems in heat transfer, however, and inception of work on the laminar flow of thixotropic fluids in round pipes would appear to be in order as a prerequisite to an understanding of such more complex nonisothermal problems. 

In rotational viscometers thixotropy shows up as a progressive decrease in torque as time increases (until the infinite-time properties are reached) at constant rotational speed. Care must be taken, however, not to confuse the initial oscillation of a viscometer cup or bob, which is due to inertial forces, with thixotropy. Conversely, rheopectic behavior shows progressively increasing torques at constant rotational speeds. 

Figure 6.2. Relations between shear stress, deformation rate, and viscosity of several classes of fluids, (a) Distribution of velocities of a fluid between two layers of areas A which are moving relatively to each other at a distance x wider influence of a force F. In the simplest case, F/A = fi(du/dx) with ju constant, (b) Linear plot of shear stress against deformation, (c) Logarithmic plot of shear stress against deformation rate, (d) Viscosity as a function of shear stress, (e) Time-dependent viscosity behavior of a rheopectic fluid (thixotropic behavior is shown by the dashed line). (1) Hysteresis loops of time-dependent fluids (arrows show the chronology of imposed shear stress).

Figure 6.3. Time-dependent rheological behavior of a rheopectic fluid, a 2000 molecular weight polyester [after Steg and Katz, J. Appl. Polym. Sci. 9, 3177 (7965)].

Rheopectic fluids have apparent viscosities that increase with time, particularly at high rates of shear as shown on Figure 6.3. Figure 6.2(f) indicates typical hysteresis effects for such materials. Some examples are suspensions of gypsum in water, bentonite sols, vanadium pentoxide sols, and the polyester of Figure 6.3. 

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