Time-dependent fluid

The rheopectic fluid also is called an anti-thixotropic fluid. In a rheopectic fluid, the increase in viscosity with time often is caused by the formation of 

Polymer melts and solutions may present thixotropic or rheopectic behavior if they degrade or crosshnk during shear, especially at elevated temperatures. Polymers that do not experience reactions during shear traditionally are considered as time-independent fluids. However, recent research shows the disentanglement of polymer chains during shear may cause time-dependent effects. Compared with most traditional thixotropic and rheopectic fluids, the time-de-pendent effects caused by polymer chain disentanglement are relatively small. Hence, in this book, all polymer melts and solutions are treated as time-independent shear-thinning fluids. 

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Purely viscous fluids are further classified into time-independent and time-dependent fluids. For time-independent fluids, the shear stress depends only on the instantaneous shear rate. The shear stress for time-dependent fluids depends on the past history of the rate of deformation, as a result of structure or orientation buildup or breakdown during deformation. 

Time-dependent fluids are those for which structural rearrangements occur during deformation at a rate too slow to maintain equilibrium configurations. As a result, shear stress changes with duration of shear. Thixotropic fluids, such as mayonnaise, clay suspensions used as drilling muds, and some paints and inks, show decreasing shear stress with time at constant shear rate. A detailed description of thixotropic behavior and a list of thixotropic systems is found in Bauer and Colhns (ibid.). 

Steady state, fuUy developed laminar flows of viscoelastic fluids in straight, constant-diameter pipes show no effects of viscoelasticity. The viscous component of the constitutive equation may be used to develop the flow rate-pressure drop relations, which apply downstream of the entrance region after viscoelastic effects have disappeared. A similar situation exists for time-dependent fluids. 

Figure 3.34. Effect of sudden change of shear rate on apparent viscosity of time-dependent fluid...

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).

Chapter HI relates to measurement of flow properties of foods that are primarily fluid in nature, unithi.i surveys the nature of viscosity and its relationship to foods. An overview of the various flow behaviors found in different fluid foods is presented. The concept of non-Newtonian foods is developed, along with methods for measurement of the complete flow curve. The quantitative or fundamental measurement of apparent shear viscosity of fluid foods with rotational viscometers or rheometers is described, unithi.2 describes two protocols for the measurement of non-Newtonian fluids. The first is for time-independent fluids, and the second is for time-dependent fluids. Both protocols use rotational rheometers, unit hi.3 describes a protocol for simple Newtonian fluids, which include aqueous solutions or oils. As rotational rheometers are new and expensive, many evaluations of fluid foods have been made with empirical methods. Such methods yield data that are not fundamental but are useful in comparing variations in consistency or texture of a food product, unit hi.4 describes a popular empirical method, the Bostwick Consistometer, which has been used to measure the consistency of tomato paste. It is a well-known method in the food industry and has also been used to evaluate other fruit pastes and juices as well. 

Limited computational domain In the case of complex three-dimensional, time-dependent fluid processes we cannot calculate the flow throughout the entire extruder because today s computers do not (yet) have the required computing power. 

Time-dependent fluids Fluids in which the viscous properties vary with time. These can be further classified. 

Figure 3.79 shows the viscosity profiles for time-dependent fluids. From Figure 3.79 one may define the following systems. Time-independent fluids obviously undergo no change in viscosity with respect to time. Rheopectic fluids show an increase in viscosity with respect to time. Thixotropic fluids show a decrease in viscosity with respect to time. 

The method of domain perturbations was used for many years before its formal rationalization by D. D. Joseph D. D. Joseph, Parameter and domain dependence of eigenvalues of elliptic partial differential equations, Arch. Ration. Mech. Anal. 24, 325-351 (1967). See also Ref. 3f. The method has been used for analysis of a number of different problems in fluid mechanics A. Beris, R. C. Armstrong and R. A. Brown, Perturbation theory for viscoelastic fluids between eccentric rotating cylinders, J. Non-Newtonian Fluid Mech. 13, 109-48 (1983) R. G. Cox, The deformation of a drop in a general time-dependent fluid flow, J. Fluid Mech. 37, 601-623 (1969) ... 

Time-dependent fluids are those for which the components of the stress tensor are a function of both the magnitude and the duration of the rate of deformation at constant temperature and pressure [4]. These fluids are usually classified into two groups—thixotropic fluids and rheopectic fluids—depending on whether the shear stress decreases or increases with time at a given shear rate. Thixotropic and rheopectic behavior are common to slurries and suspensions of solids or colloidal aggregates in liquids. Figure 10.2 shows the general behavior of these fluids. 

Time-dependent fluids in which the shear stress is not a single-valued function of the strain rate but depends on the shear stress history of the fluid. 

For time-dependent fluids (thixotropic or rheopectic) there are no simple relations now available for showing the stress-strain-rate-time. dependence. Figure 15.2 is, a typical stress-time curve for a thixotropic fluid, showing lines of... 

In a time-dependent fluid, the shear rate depends upon the time for which it has been subjected to a given shear stress. Conversely, if the shear rate is kept constant, the shear stress will change with time. However, with all time-dependent fluids an equilibrium conditipn is reached if the imposed condition (e.g. shear rate or shear stress) is maintained constant. Some fluids respond so quickly to changes that the effect of time dependence can be neglected. Others may have a much longer constant, and in changing flow situations will never be in the equilibrium state. 

Time-dependent fluid behaviour may be further sub-divided into two categories thixotropy and rheopexy or negative thixotropy. 

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