Viscosity time-dependent behavior

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. 

Discussions in Chapter 2 may be referred to for explanations of the various symbols. It is straightforward to apply such conservation equations to single-phase flows. In the case of multiphase flows also, in principle, it is possible to use these equations with appropriate boundary conditions at the interface between different phases. In such cases, however, density, viscosity and all the other relevant properties will have to change abruptly at the location of the interface. These methods, which describe and track the time-dependent behavior of the interface itself, are called front tracking methods. Numerical solution of such a set of equations is extremely difficult and enormously computation intensive. The main difficulty arises from the interaction between the moving interface and the Eulerian grid employed to solve the flow field (more discussion about numerical solutions is given in Chapters 6 and 7). 

Relaxation Time - Maxwell proposed a model in the 19 century to describe the time-dependent behavior of viscous materials such as pitch or tar. This model has also been applied to plastics and polymers. A parameter has been defined in this model called relaxation time that is a characteristic of the plastic material. Relaxation time is the ratio of viscosity to the Young s modulus of elasticity. 

Time-Dependent Rheology. The rheological properties of suspensions are often time-dependent. If the apparent viscosity continuously decreases with time under shear with a subsequent recovery of the viscosity when the flow is ceased, the system is called thixotropic. The opposite behavior is called antithixopy or rheopexy. Figure 2 shows the time-dependent behaviors of suspensions. Curve 1 in Figure 2 illustrates a hysteresis produced by a thixotropic suspension, where con-... 

An important distinction between polymeric liquids and suspensions arises from their different microstructures and is evidenced by the elastic recoil phenomena that polymers exhibit but suspensions do not. The polymeric or macromolecular system when deformed under stress will recover from very large strains because like an elastic material the restoring force increases with the deformation. With a suspension, however, the forces between the particles decrease with increasing separation so that there is limited mechanism for recovery. There are, however, a variety of rheological properties common to polymeric liquids that suspensions will exhibit including shear rate dependent viscosity and time-dependent behavior. We shall discuss these differences in more detail in the following section. 

Thixotropic A rheological behavior characterized by a reversible viscosity increase over time. Application of a high shear force will return the fluid to its "original viscosity and restart the time-dependent behavior. 

In fluids with time-dependent behavior, the effects of time can be either reversible or irreversible. If the time effects are reversible, the fluids are either thixotropic or rheopectic. Thixotropy is the continuous decrease of apparent viscosity with time under shear and the subsequent recovery of viscosity when the flow is discontinued. Rheopexy is the continuous increase of apparent viscosity with time under shear it is also described by the term anti-thixotropy. A good review on thixotropy was given by Mewis [45]. Polymer melts do exhibit some thixotropic effects however, thixotropy can also occur in inelastic fluids. The time scale of thixotropy is not necessarily associated with the time scale for viscoelastic relaxation. 

Rheomalaxic Time-dependent behavior in which shear-rate changes cause irreversible changes in viscosity. An emulsion that when sheared inverts to a higher (or lower) viscosity emulsion, and does not reinvert when the shear is removed. 

There are several terms that apply to time-dependent behavior. Thixotropic fluids possess a structure that breaks down as a function of time and shear rate. Tlius the viscosity is lowered. A famous example of this reversible phenomenon is the ubiquitous catsup bottle, yielding its contents only after sharp blows. The opposite effect, although rarely observed, is called antithixotropic, or rheopectic behavior, where materials set up as a function of time and shear rate that is, the viscosity increases or the material gels. 

The shear-viscosity and viscoelastic properties of paper coatings and their time-dependent behavior are important attributes that need to be measured for better understanding and optimization of the process. 

Steady values of F decrease from = 1 at rest to F = 0 as I>1 becomes unbounded. Consequently, this model exhibits yield and the time-dependent behavior characteristic of thixotropic materials. Harris [18] proposes a continuum theory for time-dependent behavior that has some similarities with the Slibar and Paslay model. This theory is based on an integral expression for the difference between viscosity and its rest value following a long time period. This approach can be formulated in terms of the equations... 

Amorphous polymers deform viscously above their glass transition temperature. Polymers generally exhibit non-Newtonian behavior (viscosity is not constant) and their time-dependent behavior can be modeled mechanically by a combination of springs and dashpots. 

Generally speaking, any material that exhibits behavior not predicted by Equation 11.7 is non-Newtonian. Three well-known reasons for non-Newtonian behavior are shear rate-dependent viscosity, viscoelasticity, and nonelastic time-dependent behavior. In order to establish a background on non-Newtonian fluid mechanics, it is important to understand standard flows that are frequently used to investigate them and specify which material functions are relevant. 

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). 

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. 

All these features were observed experimentally for solutions of 3-amino-/V-methylphthalimide, 4-amino-/V-methylphthalimide, and for nonsubstituted rhoda-mine. The results were observed for cooled, polar solutions of phthalimides, in which the orientational relaxation is delayed. Exactly the same spectral behavior was observed [50] by picosecond spectroscopy for low viscosity liquid solutions at room temperature, in which the orientational relaxation rate is much higher. All experimental data indicate that correlation functions of spectral shifts Av-l(t), which are used frequently for describing the Time Dependent Stokes Shift, are essentially the functions of excitation frequency. 

The dynamic behavior of fluid interfaces is usually described in terms of surface rheology. Monolayer-covered interfaces may display dramatically different rheological behavior from that of the clean liquid interface. These time-dependent properties vary with the extent of intermolecular association within the monolayer at a given thermodynamic state, which in turn may be related directly to molecular size, shape, and charge (Manheimer and Schechter, 1970). Two of these time-dependent rheological properties are discussed here surface shear viscosity and dynamic surface tension. 

The poly[a(carboxymethyl)alkyl isocyanides] are also soluble polyisocyanides, but exhibit a time dependent-viscosity behavior. The description of this phenomenon is given after the following sections in which viscometry in di-and trichloroacetic acid is described. 

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