Shear rate time dependent

Designation Effect of increasing shear rate Time dependent ... 

Rheological properties of mayonnaise have been studied using different rheological techniques steady shear rate-shear stress, time dependent shear rate-shear stress, stress growth and decay at a constant shear rate, dynamic viscoelastic behavior, and creep-compliance viscoelastic behavior. More studies have been devoted to the study of rheological properties of mayonnaise than of salad dressings, probably because the former is a more stable emulsion and exhibits complex viscous and viscoelastic rheological behavior. 

The rheology of a paint material can be described by its viscosity and the dependence of this viscosity on parameters such as shear rate, time, etc. 

In general, each of these parameters depends on the shear rate. This dependence is associated with the fact that the macromolecule rotates around the vorticity axis in the shear flow, and if flexible, at sufficiently high shear rate becomes distorted and oriented in the direction of flow [Hsieh and Larson, 2004 Texeira et al., 2005]. However, at sufficiently low shear rates, there is a regime where any distortion and orientation of the macromolecular structure by the flow field is erased by Brownian motion on a time scale much faster than the flow rate. Here we focus on this Newtonian regime, where t]iy), I (y), and [Pg.19]

It is not possible to put forward simple mathematical equations of general validity to describe time-dependent fluid behavioin, and it is usually necessary to make measurements over the range of conditions of interest. The conventional shear stress-shear rate curves are of limited utility imless they relate to the particular history of interest in the application. For example when the material enters a pipe slowly and with a minimum of shearing, as from a storage tank directly into the pipe, the shear stress-shear rate-time curve should be based on tests performed on samples which have been stored imder... 

Consider the application of a constant shear stress ao to a viscoelastie solid at t = 0 in simple shear (or alternatively in tension as pure shear). The time-dependent response is ideally an instantaneous elastic flexure followed by time-dependent creep as depicted schematically in Fig. 5.1(a), which at a monotonically decreasing rate asymptotieally approaches a constant shear strain proportional to the applied shear stress. Removal of the shear stress at any time t results in an instantaneous elastic recovery followed by a reverse creep response that asymptotically returns the solid to its initial state, as also depicted in Fig. 5.1(a). 

In more generalised flows, both the stress and the rate of deformation (strain rate) are tensor quantities, and the constitutive relationship between these may be very complex (Schowalter, 1978 Bird et a/., 1987a). The relationship between stress and shear rate frequently depends on the shear rate (flow rate), as is the case in a simple shear thinning fluid. However, for some fluids the stress may depend on the strain itself as well as on the rate of strain, and such fluids show some elasticity or memory behaviour, in that their stress at a given time depends on the recent strain history such fluids are... 

Dynamic rheological properties are dynamic viscosity and dynamic modulus. They depend on frequency, shear rate, time, and temperature. The parameters generally used are complex dynamic viscosity (r ) and its viscous (11 ) and elastic (ri"") components, and shear relaxation modulus (G ) and its storage modulus (G ) and loss modulus (G ) components (Figures 5.8). G for LDPE has the highest value, and G for LLDPE and mPE are very similar. The study of tan 6 = ti /ti" is of great interest for processing. 

That is, the apparent viscosity of a non-Newtonian liquid can be expressed as the ratio of shear stress to shear rate at a specific point within the fluid, and perhaps even at a specific point in time, or within a specific shear-rate range, depending on the nature of the liquid. 

The transport properties of polymeric materials which distinguish them most from other materials are their flow properties or rheological behavior. There are many differences between the flow properties of a polymeric fluid and typical low molecular weight fluids such as water, benzene, sulfuric acid, and other fluids, which we classify as Newtonian. Newtonian fluids can be characterized by a single flow property called viscosity (/r) and their density (p). Polymeric fluids, on the other hand, exhibit a viscosity function that depends on shear rate or shear stress, time-dependent rheological properties, viscoelastic behavior such as elastic recoil (memory), additional normal stresses in shear flow, and an extensional viscosity that is not simply related to the shear viscosity, to name a few differences. 

In amoriDhous poiymers, tiiis reiation is vaiid for processes tiiat extend over very different iengtii scaies. Modes which invoived a few monomer units as weii as tenninai reiaxation processes, in which tire chains move as a whoie, obey tire superjDosition reiaxation. On tire basis of tiiis finding an empiricai expression for tire temperature dependence of viscosity at a zero shear rate and tiiat of tire mean reiaxation time of a. modes were derived ... 

Viscous Hquids are classified based on their rheological behavior characterized by the relationship of shear stress with shear rate. Eor Newtonian Hquids, the viscosity represented by the ratio of shear stress to shear rate is independent of shear rate, whereas non-Newtonian Hquid viscosity changes with shear rate. Non-Newtonian Hquids are further divided into three categories time-independent, time-dependent, and viscoelastic. A detailed discussion of these rheologically complex Hquids is given elsewhere (see Rheological measurements). 

The other models can be appHed to non-Newtonian materials where time-dependent effects are absent. This situation encompasses many technically important materials from polymer solutions to latices, pigment slurries, and polymer melts. At high shear rates most of these materials tend to a Newtonian viscosity limit. At low shear rates they tend either to a yield point or to a low shear Newtonian limiting viscosity. At intermediate shear rates, the power law or the Casson model is a useful approximation. 

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. 

Time-dependent effects ate measured by determining the decay of shear stress as a function of time at one or more constant shear rates (Fig. 7)... 

A rotational viscometer connected to a recorder is used. After the sample is loaded and allowed to come to mechanical and thermal equiUbtium, the viscometer is turned on and the rotational speed is increased in steps, starting from the lowest speed. The resultant shear stress is recorded with time. On each speed change the shear stress reaches a maximum value and then decreases exponentially toward an equiUbrium level. The peak shear stress, which is obtained by extrapolating the curve to zero time, and the equiUbrium shear stress are indicative of the viscosity—shear behavior of unsheared and sheared material, respectively. The stress-decay curves are indicative of the time-dependent behavior. A rate constant for the relaxation process can be deterrnined at each shear rate. In addition, zero-time and equiUbrium shear stress values can be used to constmct a hysteresis loop that is similar to that shown in Figure 5, but unlike that plot, is independent of acceleration and time of shear. 

Results from measurements of time-dependent effects depend on the sample history and experimental conditions and should be considered approximate. For example, the state of an unsheared or undisturbed sample is a function of its previous shear history and the length of time since it underwent shear. The area of a thixotropic loop depends on the shear range covered, the rate of shear acceleration, and the length of time at the highest shear rate. However, measurements of time-dependent behavior can be usehil in evaluating and comparing a number of industrial products and in solving flow problems. 

Effect of Temperature. In addition to being often dependent on parameters such as shear stress, shear rate, and time, viscosity is highly sensitive to changes in temperature. Most materials decrease in viscosity as temperature increases. The dependence is logarithmic and can be substantial, up to 10% change/°C. This has important implications for processing and handling of materials and for viscosity measurement. 

When the overflow clarity is independent of overflow rate and depends only on detention time, as in the case for high soHds removal from a flocculating suspension, the required time is deterrnined by simple laboratory testing of residual soHd concentrations in the supernatant versus detention time under the conditions of mild shear. This deterrnination is sometimes called the second-order test procedure because the flocculation process foUows a second-order reaction rate. 

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.). 

Emulsions Almost eveiy shear rate parameter affects liquid-liquid emulsion formation. Some of the efrecds are dependent upon whether the emulsion is both dispersing and coalescing in the tank, or whether there are sufficient stabilizers present to maintain the smallest droplet size produced for long periods of time. Blend time and the standard deviation of circulation times affect the length of time it takes for a particle to be exposed to the various levels of shear work and thus the time it takes to achieve the ultimate small paiTicle size desired. 

In order to complete the discussion of methodical problems, we should mention two more methods of determining yield stress. Figure 6 shows that for plastic disperse systems with low-molecular dispersion medium, when a constant rate of deformation, Y = const., is given, the dependence x on time t passes through a maximum rm before a stationary value of shear stress ts is reached. We may assume that the value of the maximal shear stress xm is the maximum strength of the structure which must be destroyed so that the flow can occur. Here xm as well as ts do not depend or depend weakly on y, like Y. The difference between tm and xs takes into account the difference between maximum stress and yield stress. For filled polymer melts at low shear rates Tm Ts> i,e- fhese quantities can be identified with Y. 

When water (a Newtonian liquid) is in an open-ended pipe, pressure can be applied to move it. Doubling the water pressure doubles the flow rate of the water. Water does not have a shear-thinning action. However, in a similar situation but using a plastic melt (a non-Newtonian liquid), if the pressure is doubled the melt flow may increase from 2 to 15 times, depending on the plastic used. As an example, linear low-density polyethylene (LLDPE), with a low shear-thinning action, experiences a low rate increase, which explains why it can cause more processing problems than other PEs. The higher-flow melts include polyvinyl chloride (PVC) and polystyrene (PS). 

Many fluids, including some that are encountered very widely both industrially and domestically, exhibit non-Newtonian behaviour and their apparent viscosities may depend on the rate at which they are sheared and on their previous shear history. At any position and time in the fluid, the apparent viscosity pa which is defined as the ratio of the shear stress to the shear rate at that point is given by ... 

When the apparent viscosity is a function of the shear rate, the behaviour is said to he shear-dependenf, when it is a function of the duration of shearing at a particular rate, it is referred to as time-dependent. Any shear-dependent fluid must to some extent be time-dependent because, if the shear rate is suddenly changed, the apparent viscosity does not alter instantaneously, but gradually moves towards its new value. In many eases, however, the time-scale for the flow process may be sufficiently long for the effects of time-dependence to be negligible. 

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