Flow behavior curve

In the steady state shear flow test, two main relationships of double logarithmic scales illustrate the rheological fingerprints of the sample under study. These are the flow behavior curve (Figure 5.9a), showing the relationship... 

Figure 5.9 (a) Flow behavior curve (b) Viscosity behavior curve. 

Fig. 2. Flow curves (shear stress vs shear rate) for different types of flow behavior.

One characteristic of shear banded flow is the presence of fluctuations in the flow field. Such fluctuations also occur in some glassy colloidal materials at colloid volume fractions close to the glass transition. One such system is the soft gel formed by crowded monodisperse multiarm (122) star 1,4-polybutadienes in decane. Using NMR velocimetry Holmes et al. [23] found evidence for fluctuations in the flow behavior across the gap of a wide gap concentric cylindrical Couette device, in association with a degree of apparent slip at the inner wall. The timescale of these fluctuations appeared to be rapid (with respect to the measurement time per shear rate in the flow curve), in the order of tens to hundreds of milliseconds. As a result, the velocity distributions, measured at different points across the cell, exhibited bimodal behavior, as apparent in Figure 2.8.13. These workers interpreted their data... 

In the case of polymer samples, it is expected that, at the temperatures and frequencies at which the rheological measurements were carried out, the polymer chains should be fully relaxed and exhibit characteristic homo-polymer-like terminal flow behavior (i.e., the curves can be expressed by a power-law of G oc co2 and G" oc co). 

The second group exhibits the phenomenon of drawability. This manifests itself in the stress-strain behavior (curve II in Fig. 2.21) as follows At first these materials behave in a similar way to those of curve I. The proportionality limit lies at low values, and the deformation with increasing load is also quite small. Then, suddenly, a large extension occurs, even though the load remains constant or becomes smaller. The material begins to flow and the stress-strain curve sometimes runs nearly parallel to the abscissa. The point at which the... 

In the case of non-Newtonian liquids, p depends on y as well. These liquids can be classified in various categories of materials depending on their flow behavior in y) —flow curve and p(t) —viscosity curve. 

Another often used representation of the viscoelastic flow behavior utilizes normal stress coefficients P/ = Ni/y. Figure 10 depicts flow curves of a family of PAA/water solutions differing in concentrations and therefore in their viscosities. Normalized by the zero-shear viscosity fiQ and by a constant shear rate /q shear stress value of to= 1 N/m they produce master curves for viscosity and the normal stress coefficient. The preparation... 

Accordingly pragmatic individuals have long been interested in the evolution of a universal explanation for fluid behavior of all kinds and the establishment of quantitative relationships with which to correlate and extrapolate the flow curves of all fluids, Newtonian and non-Newtonian alike. Progress toward the former of these two objectives appears to be too limited to warrant presentation at this stage, but recently a method has been proposed (F2, Mil, W4) by means of which the flow behavior of all fluids which are not time dependent may be compared. Two indexes are necessary to accomplish this ... 

With these instruments the relationship between DAP/4L and 8 V/D is obtained directly. On a logarithmic plot of DAP/4L versus 8 V/D the slope of the curve at any point is equal to the flow-behavior index n extension of the tangent to the curve at this point to a value of 8V/D of unity gives the corresponding value of the consistency index K. ... 

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. 

Ob and Eg are determined from force-deformation curves for materials which exhibit squeezing flow behavior (e.g., peanut butter, processed cheese). 

Monodisperse melts appear to exhibit a plateau region in the stress vs shear rate flow curve [51,62,65]. The capillary flow behavior actually closely resembles the oscillatory shear behavior in the sense that the flow curve essentially overlaps on the absolute value of complex modulus G vs the oscillation frequency (0 [62]. Thus.it appears that the transition-like capillary flow behavior of highly entangled monodisperse melts reflects constitutive bulk properties of the melts and is not interfacial in origin. It remains to be explored whether this plateau indeed manifests a real constitutive instability, i.e., whether it is double-valued. 

There is a different flow behavior of plastic when compared to water. The volume of a so-called Newtonian fluid, such as water, when pushed through an opening is directly proportional to the pressure applied following a straight line (flow vs. pressure). The flow rate of a non-Newtonian fluid such as plastics when pushed through an opening increases more rapidly than the applied pressure resulting in a curved line. Different plastics have their own flow rates so that their non-Newtonian curves are different. 

Materials that exhibit a direct proportionality between shearing stress and rate of shear are called Newtonian materials. These include water and aqueous solutions, simple organic liquids, and dilute suspensions and emulsions. Most foods are non-Newtonian in character, and their shearing stress-rate-of-shear curves are either not straight or do not go through the origin, or both. This introduces a considerable difficulty, because their flow behavior cannot be expressed by a single value, as is the case for Newtonian liquids. 

In this equation, viscosity is independent of the degree of dispersion. As soon as the ratio of disperse and continuous phases increases to the point where particles start to interact, the flow behavior becomes more complex. The effect of increasing the concentration of the disperse phase on the flow behavior of a disperse system is shown in Figure 8-41. The disperse phase, as well as the low solids dispersion (curves 1 and 2), shows Newtonian flow behavior. As the solids content increases, the flow behavior becomes non-Newtonian (curves 3 and 4). Especially with anisotropic particles, interaction between them will result in the formation of three-dimensional network structures. These network structures usually show non-Newtonian flow behavior and viscoelastic properties and often have a yield value. Network structure formation may occur in emulsions (Figure 8-42) as well as in particulate systems. The forces between particles that result in the formation of networks may be... 

---