Yield stress value

The same is indicated by yield stress values (as the position of the whole flow curve) when we compare the properties of different polymer matrices with the same filler [11],... 

Figure 9 Casson plot, slope of line reflects yield stress value. Interior coating formulation including d.HPMC O, SMAT 0,HEUR.

A third technical application is to control the thickness of solutions by means of vesicles A solution of tightly-packed vesicles behaves like a viscoelastic fluid. Frequently, such solutions have a yield stress value, which means that a certain amount of force is necessary to make these solutions flow. Air bubbles in such fluids do not rise to the top (cf. Figure 7). Such a behavior is obtainable with an addition of only 1-2% of surfactant. 

Fig. 7 Shower gel with a yield stress value. The air bubbles suspended in the solution do not rise to the top [8]...

Hoffmann H, Rauscher A (1993) Aggregating systems with a yield stress value. Colloid Polym Sci 271 390-395... 

Yield stress values can depend strongly on filler concentration, the size and shape of the particles and the nature of the polymer medium. However, in filled polymer melts yield stress is generally considered to be independent of temperature and polymer molecular mass [1]. The method of determining yield stress from flow curves, for example from dynamic characterization undertaken at low frequency, or extrapolation of shear viscosity measurements to zero shear rate, may lead to differences in the magnitude of yield stress determined [35]. 

In the (T - Ta) range from - 160 to - 90 °C, the larger increase in toughness observed for MT0.5I0.5 than for MI does not agree with the difference in ve (it would go in the opposite direction). Furthermore, it cannot be explained from the yield stress values since they are identical in this temperature range, as shown in Fig. 111. The effect of the intramolecular cooperativity of the n-flip motions of the fere-phthalic rings, already invoked for the results in the low temperature range, appears to be the most likely reason these cooperative... 

For many years, several authors have tried to explain and predict the yield stress of polymers (crosslinked or not), as a function of the experimental test parameters (T, e) and/or structural parameters (chain stiffness, crosslinking density). These models would be very useful to extrapolate yield stress values in different test conditions and to determine the ductile-brittle transition. 

Yield Stress Values for Corn Stover Suspensions Determined with Shear Stress vs Shear Rate Data Extrapolation... 

The yield stress values given in Table 3 demonstrate that the yield stresses determined with the Herschel-Bulkley model were lower than the yield stresses determined with all the other methods at equal concentrations. The yield stress predicted by direct data extrapolation and by the Herschel-Bulkley model was similar for each concentration of corn stover. 

Experimental rheologic data were fit to the power law, Herschel-Bulkley, and Casson models. The power law model does not predict yield stress. Yield stress for 21% grain slurries predicted by the Herschel-Bulkley model was a negative value, as shown in Table 6. Yield stress values predicted by the Herschel Bulkley model for 23 and 25% solids were 8.31 and 56.3 dyn/cm2, respectively. Predicted yield stress values from the Casson model were 9.47 dyn/cm2 for 21% solids, 28.5 dyn/cm2 for 23% solids, and 44.0 dyn/cm2 for 25% solids. 

Figure 3.3 illustrates the special cases of Eq. 3.6 used to describe Herschel-Bulkley fluids and, depending on the flow exponent and yield stress values, Newtonian fluids, shear thinning, shear thickening, and Bingham fluids. The values for Eq. 3.6 are given in Table 3.1. 

If a sample shows elastic, solid-like deformation below a certain shear stress ay and starts flowing above this value, ay is called a yield stress value. This phenomenon can occur even in solutions with quite low viscosity. A practical indication for the existence of a yield stress value is the trapping of bubbles in the liquid Small air bubbles that are shaken into the sample do not rise for a long time whereas they climb up to the surface sooner or later in a liquid without yield stress even if their viscosity is much higher. A simple model for the description of a liquid with a yield stress is called Bingham s solid ... 

It is easy to understand that these solutions must exhibit viscoelastic properties. Under shear flow the vesicles have to pass each other and, hence, they have to be deformed. On deformation, the distance of the lamellae is changed against the electrostatic forces between them and the lamellae leave their natural curvature. The macroscopic consequence is an elastic restoring force. If a small shear stress below the yield stress ery is applied, the vesicles cannot pass each other at all. The solution is only deformed elastically and behaves like Bingham s solid. This rheological behaviour is shown in Figure 3.35. which clearly reveals the yield stress value, beyond which the sample shows a quite low viscosity. 

Hoffmann, H., Thunig, C., Schmiedel, R and Munkert, U. (1994) The rheological behavior of different viscoelastic surfactant solutions systems with and without a yield stress value. Tenside Surf. Det., 31(6), 389MD0. 

Spreadability is another important parameter of butter texture. A spreadability index (S) can be calculated from the yield stress value obtained for butter before and after working using a constant-weight penetrometer, as shown in Equation (5), where fu and /w are the yield stress values before and after working respectively (Haighton, 1965). 

Figure 7.11. Milk fat hardness (kg/m) versus solid fat content (%) (A) and butter spread-ability versus yield stress value (B) (adapted from Mortensen and Danmark, 1982).

The simplest model assumes ideal elastic behavior (Figure 7.12A). At a stress below the yield stress (Fy), the sample behaves perfectly elastically. In this region, a modulus of elasticity can be determined. At the yield stress, the sample flows. It continues to flow until the stress is lowered again to below the yield stress value. Therefore, both the elastic modulus and yield stress describe the behavior of a plastic material. They can be determined easily by compression testing. The continuous network of fat crystals in a fat bears the stress below the yield stress and therefore contributes solid or elastic properties to the material (Narine and Marangoni, 1999a). 

Figure 7.16. Relationship between yield stress value (g force) and compressive storage modulus ( ) for milk fat.

Figure 4-26 Static (-S) and Dynamic (-D) Yield Stress Values of Cross-Linked Waxy Maize (CWM), Tapioca, and Amioca 5% (w/w) Starch Dispersions at Different Shear Rates. Filled symbols are values of static yield stress (aps) open symbols are values of dynamic yield stress (oqj).

Vehicles that exhibit the unusual property of Bingham-type plastic rheological flow are characterized by the need to overcome a finite yield stress before flow is initiated. Permanent suspension of most pharmaceutical systems requires yield-stress values of at least 2-5 Pa (20-50 dyn/cm ). Bingham plastic flow is rarely produced by pharmaceutical gums and hydrophilic colloids. National Formulary (NF) carbomers exhibit a sufficiently high yield value at low solution concentration and low viscosity to produce permanent suspensions. The carbomers, however, require a pH value between 6 and 8 for maximum suspension performance. The polymer is essentially incompatible... 

Tensile yield stress gives additional infonnation on filler-matrix interactions and consequently it is one of the preferred methods of composite testing. Figure 8.3 shows that the particle size affects yield stress of PP composites. Only when filler particles become very small does the yield stress value increase as the concentration increases. The smaller the particle size the higher the value of tensile yield stress. The three largest particles are CaCOs and the smallest one is silica. Thus, yield stress behavior not only depends on particle size but also on the interaction with the matrix. If the matrix is deficient in the smallest particles of CaCOs the yield stress decreases. The stress which initiates yielding can be expressed by the equation ... 

The apparent yield stress. Ihe complex viscosity n vs. oi for PP blends with LLDPE-B and LLDPE-C Is shown In Fig. 26. The plot clearly Indicates possible yield stress behavior especially for blends containing 50% PP. Ihe apparent yield stress In dynamic flow data was calculated using Equation 23, with F G or F G". The yield stress values as well as the assumed matrix material for calculating F are listed In Table V. For both systems the maximum value of the apparent yield stress occurred at 50% PP. In fact, there Is a direct correlation - In a given system the yielding Is primarily observed In blends having a co-contlnuous structure. As before (53 ) Gy > Gy... 

The concentration dependence of rig conqjuted from Equation 20 Is shown In Fig. 30, where the solid points represent the experimental data and the open points their values corrected for the effects of PP degradation. For System-1 there Is strong negative deviation (NDB) from the log additivity rule, viz. Equation 1, but for System-2 NDB Is visible at low PP content, converting to positive deviation (PDB) at high. It Is worth recalling that ng was computed from corrected for the yield stress values of n. The NDB behavior. Indicative of Interlayer slip, reflects poor miscibility In System-1 and that at low concentration of PP In System-2. The emulslon-llke behavior of Syetem-2 at high PP content reflects a better Interphase Interaction. 

For example, the cohesion of dairy powders has been studied with an unconfined yield test by preparing cylindrical plugs of powder at different particle sizes and moistures. Unconfined yield stress values were obtained as an index of cohesion for whole milk powder and skim milk powder. Dry... 

Figure 1 shows shear stress curves as a function of shear rate at different time during initial enzymatic hydrolysis and fermentation processes. The yield stress values are shown... 

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