Viscosity time independent

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). 

All fluids for which the viscosity varies with shear rate are non-Newtonian fluids. For uou-Newtouiau fluids the viscosity, defined as the ratio of shear stress to shear rate, is often called the apparent viscosity to emphasize the distiuc tiou from Newtonian behavior. Purely viscous, time-independent fluids, for which the apparent viscosity may be expressed as a function of shear rate, are called generalized Newtonian fluids. 

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. 

For a Newtonian fluid, the shear stress is proportional to the shear rate, the constant of proportionality being the coefficient of viscosity. The viscosity is a property of the material and, at a given temperature and pressure, is constant. Non-Newtonian fluids exhibit departures from this type of behaviour. The relationship between the shear stress and the shear rate can be determined using a viscometer as described in Chapter 3. There are three main categories of departure from Newtonian behaviour behaviour that is independent of time but the fluid exhibits an apparent viscosity that varies as the shear rate is changed behaviour in which the apparent viscosity changes with time even if the shear rate is kept constant and a type of behaviour that is intermediate between purely liquid-like and purely solid-like. These are known as time-independent, time-dependent, and viscoelastic behaviour respectively. Many materials display a combination of these types of behaviour. 

A general time-independent non-Newtonian liquid of density 961 kg/m3 flows steadily with an average velocity of 2.0 m/s through a tube 3.048 m long with an inside diameter of 0.0762 m. For these conditions, the pipe flow consistency coefficient K has a value of 1.48 Pa s0,3 and n a value of 0.3. Calculate the values of the apparent viscosity for pipe flow p.ap, the generalized Reynolds number Re and the pressure drop across the tube, neglecting end effects. 

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. 

Figure H1.1.4 A complete flow curve for a time-independent non-Newtonian fluid. r 0 and i , are the viscosities associated with the first and second Newtonian plateaus, respectively. Regions (1) and (2) correspond to viscosities relative to low shear rates induced by sedimentation and leveling, respectively. Regions (3) and (4) correspond to viscosities relative to the medium shear rates induced by pouring and pumping, respectively. Regions (5) and (6) correspond to viscosities relative to high shear rates by rubbing and spraying, respectively.

Shear-thinning, as the term suggests, is characterised by a gradual (time-independent) decrease in apparent viscosity with increasing rate of shear, and can arise from a number of causes. 

In Kramers theory that is based on the Langevin equation with a constant time-independent friction constant, it is found that the rate constant may be written as a product of the result from conventional transition-state theory and a transmission factor. This factor depends on the ratio of the solvent friction (proportional to the solvent viscosity) and the curvature of the potential surface at the transition state. In the high friction limit the transmission factor goes toward zero, and in the low friction limit the transmission factor goes toward one. 

By assuming only that the polymer melt is viscous and time independent, and that the viscosity is a function of the shear rate, //( >), without the need to specify any specific viscosity function, we can state that for capillary flow at the wall,... 

The basic models contain a modulus E and a viscosity p that are assumed to be time-independent. Many attempts have been made to describe real time-dependent phenomena by combinations of these basic models. 

To conclude this subsection, we expose an interesting paradox arising from the time dependence of the particle configuration. As discussed in Section III, Frankel and Acrivos (1967) developed a time-independent lubrication model for treating concentrated suspensions. Their result, given by Eq. (3.7), predicts singular behavior of the shear viscosity in the maximum concentration limit where the spheres touch. Within the spatially periodic framework, the instantaneous macroscopic stress tensor may be calculated for the lubrication limit, e - 0. The symmetric portion of its deviatoric component takes the form (Zuzovsky et al, 1983)... 

If)/ is independent of shear history, the material is said to be time independent. Such liquids can exhibit different behavior patterns, however, if, as is frequently the case with polymers, )/ varies with shear rate. A material whose viscosity is independent of shear rate, e.g., water, is a Newtonian fluid. Figure 11-26 illustrates shear-thickening, Newtonian and shear-thinning rj-y relations. Most polymer melts and solutions are shear-thinning. (Low-molecular-weight polymers and dilute solutions often exhibit Newtonian characteristics.) Wet sand is a familiar example of a shear-thickening substance. It feels hard if you run on it, but you can sink down while standing still. 

The instantaneous extensional stress W(e, t) is the force F(e, t) along the cylinder axis required to pull the cylinder ends apart, divided by the instantaneous cross-sectional area A s, t) of the cylinder thus a(e, r) = F e, t)/A(e, t). The time-dependent extensional viscosity, rj(e, t), is then ct( , t)/e. If this viscosity reaches a time-independent value within the duration of the experiment, that value is called the steady-state extensional viscosity, r ( ). 

For Newtonian fluids the viscosity is independent of time. However, for most non-Newtonian fluids the viscosity at a shear rate high enough to place the fluid in the non-Newtonian region evolves with time as schematically indicated by the lower curve of Figure 13.39. The viscosity decreases with time until steady-state conditions are reached. This phenomenon is called thixotropy. The cause of this behavior lies in the fact... 

To be more precise, the general tensor equation of Newton s law of viscosity should be obeyed by a Newtonian fluid (2) however, for onedimensional flow, the applicability of eq 1 is sufficient. For a Newtonian fluid, a linear plot of t versus 7 gives a straight line whose slope gives the fluid viscosity. Also, a log-log plot of t versus 7 is linear with a slope of unity. Both types of plots are useful in characterizing a Newtonian fluid. For a Newtonian fluid, the viscosity is independent of both t and 7, and it may be a function of temperature, pressure, and composition. Moreover, the viscosity of a Newtonian fluid is not a function of the duration of shear nor of the time lapse between consecutive applications of shear stress (3). 

Fluids that do not obey Newton s law of viscosity can be broadly grouped into time-independent and time-dependent non-Newtonian fluids. Subclassifications for each group are convenient (3). 

Time-Independent Non-Newtonian Fluids. Time-independent non-Newtonian fluids are characterized by having the fluid viscosity as a function of the shear rate (or shear stress). However, the fluid viscosity is independent of the shear history of the fluid. Such fluids are also referred to as non-Newtonian viscous fluids". Figure 1 shows a typical shear diagram for the various time-independent non-Newtonian fluids. 

To proceed formulating the momentum equation we need a relation defining the total stress tensor in terms of the known dependent variables, a constitutive relationship. In contrast to solids, a fluid tends to deform when subjected to a shear stress. Proper constitutive laws have therefore traditionally been obtained by establishing the stress-strain relationships (e.g., [11] [12] [13] [89] [184] [104]), relating the total stress tensor T to the rate of deformation (sometimes called rate of strain, i.e., giving the name of this relation) of a fluid element. However, the resistance to deformation is a property of the fluid. For some fluids, Newtonian fluids, the viscosity is independent both of time and the rate of deformation. For non-Newtonian fluids, on the other hand the viscosity may be a function of the prehistory of the flow (i.e., a function both of time and the rate of deformation). 

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