Values of yield stress

The values of apparent yield stresses measured for different sorts of liquidlike foods range over the following values. 

Within the limited time-scale of eating a meal, it is obvious what the concept of a yield stress means to the non-expert, in terms of, for instance, the confined spreading out of a liquid-like food when poured out, which seems to come to a constant thickness, e.g. thick sauces and ketchup. 

In food processing, given the limited time-scales of many processing operations, the thickness of layers of liquid-like foodstuffs left on vertical walls after drainage has taken place can be calculated from the yield stress a for CTo= pgh, where p is the fluid density, g is the acceleration due to gravity, and h is the layer 

Sherman [2] listed the following values of yield stress (in pascals) and their every-day significance for soft-solid, food-like, spreadable materials (such as margarine and butter) - 

The yield stress of such materials can be easily calculated as Oo = WAia for a right-angled cone of radius a at the plane of penetration, where W is the loading of the cone in newtons. 

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A comparison of values of yield stress for filled polymers of the same nature but of different molecular weights is of fundamental interest. An example of experimental results very clearly answering the question about the role of molecular weight is given in Fig. 9, where the concentration dependences of yield stress are presented for two filled poly(isobutilene)s with the viscosity differing by more than 103 times. As is seen, a difference between molecular weights and, as a result, a vast difference in the viscosity of a polymer, do not affect the values of yield stress. 

According to the concepts, given in the paper [7], a significant difference between the values of yield stress of equiconcentrated dispersions of mono- and polydisperse polymers and the effect of molecular weight of monodisperse polymers on the value of yield stress is connected with the specific adsorption on the surface of filler particles of shorter molecules, so that for polydisperse polymers (irrespective of their average molecular weight) this is the layer of the same molecules. At the same time, upon a transition to a number of monodisperse polymers, properties of the adsorption layer become different. 

The role of interaction between a polymer and a filler in the net-formation is clearly manifested in the influence of a specific surface of a filler on the value of yield stress. As follows from qualitative considerations, with an increase in the surface of a filler the values grow, moreover, the variation may be 10-fold [7]. 

The situation becomes most complicated in multicomponent systems, for example, if we speak about filling of plasticized polymers and solutions. The viscosity of a dispersion medium may vary here due to different reasons, namely a change in the nature of the solvent, concentration of the solution, molecular weight of the polymer. Naturally, here the interaction between the liquid and the filler changes, for one, a distinct adsorption layer, which modifies the surface and hence the activity (net-formation ability) of the filler, arises. Therefore in such multicomponent systems in the general case we can hardly expect universal values of yield stress, depending only on the concentration of the filler. Experimental data also confirm this conclusion [13],... 

Generally speaking, to obtain, reliable rheological characteristics of disperse systems with fibre-like filler turned out to be a difficult methodological problem. Therefore, the question on the effect of the shape of a filler particles on the value of yield stress is left open at present. In the papers published we can encounter only individual examples and qualitative considerations concerning this question, which do not enable us to formulate general conclusions. 

Using the cathetometer the force at initiation was measured on notched bars of % inch thick extruded Lexan polycarbonate sheet over the widest temperature range possible at one rate of deformation. These initiation forces and the forces at failure are shown in Figure 7a. Brittle failure parallels craze initiation in its temperature dependence. Yield force has a greater temperature dependence—one that approximately parallels the measured values of yield stress in linear tensile tests (data... 

If the yield stress of a sample is known from an independent experiment, ATh and can be determined from linear regression of log a — ctoh versus log()>) as the intercept and slope, respectively. Alternatively, nonlinear regression technique was used to estimate ctoh> and h (Rao and Cooley, 1983). However, estimated values of yield stress and other rheological parameters should be used only when experimentally determined values are not available. In addition, unless values of the parameters are constrained a priori, nonlinear regression provides values that are the best in a least squares sense and may not reflect the true nature of the test sample. 

Figure 4-27 Texture Map Based on Static (-S) and Dynamic (-D) Values of Yield Stress of Cross-Linked Waxy Maize (CWM), Tapioca, and Amioca 5% (w/w) Starch Dispersions at 20°C.

Figure 4-42 Values of Yield Stress of Starch-Xanthan Dispersions Relative to those of the Starch-Water Dispersions (YSA SO) and Relative Mean Granule Diameters (D/DO) Plotted against Values of c[j) of Xanthan Gum waxy maize (WXM), cross-linked waxy maize (CWM), and cold water swelling (CWS).

Achayuthakan et al. (2006) studied vane yield stress of Xanthan gum-stareh dispersions. The intrinsic viscosity of Xanthan gum was determined to be 112.3 dl/g in distilled water at 25°C. In addition, the size of the granules in the dispersions of the studied starches waxy maize (WXM), cross-linked waxy maize (CWM), and cold water swelling (CWS) were determined. The values of yield stress of the starch-xanthan dispersions relative to those of the starch-water dispersions (YSA"S0) and relative mean granule diameters (D/DO) plotted against values of c[ ] of xanthan gum are shown in Figure 4-42. With the values of YS/YSO being less than 1.0, there was no synergism between CLWM starch and xanthan gum. 

Note determination of two values of yield stress for each gel, low one after low shear rate applied, high one after gel sheared at shear rate of 80 seer1, prior to measurement... 

It has been observed that for many systems the value of yield stress depends on the time scale of the measurements. Setting all controversies aside, pragmatically it is advantageous to consider that in these systems, there are aggregates of different size, characterized by the dynamic interparticle interactions. For a given sysjtem, these interactions have specific strength, CT, and the... 

Figure 11.4 shows the variation of yield stress with strain rate for the a-PP and 3-PP specimens. Compared to a-PP, the incorporation of (3-nucleator brings about distinct softening as evidenced by lower values of yield stress at various strain rates. The strain rate dependence of yield stress can be described by Frying equation given by... 

This derivation relies on the fact that the condition of differentiability is not that one limit of the integral be zero (as is the case in the infinite cup solution) but that one limit be constant. Thus, for systems which may be described in terms of a constant value of yield stress, equation (2.12) may be differentiated, giving ... 

Measurements are made of the yield stress of two carbopol solutions (density 1000 kg/m ) and of a 52.9% (by weight) silica-in-water suspension (density 1491 kg/m ) by observing their behaviour in an inclined tray which can be tilted to the horizontal. The values of the angle of inclination to the horizontal, 0, at which flow commences for a range of liquid depths, H, are given below. Determine the value of yield stress for each of these liquids. 

Yield stress measurements were made at 20 C on three pofypro-pylene materials, each containing different volume fractions of rubber particles. Table 5.1 gives values of yield stress as a function of e and <. Calculate V for each pofymer, and suggest why V varies with 4>. 

When a/W < 0.05, Y = 1.12. A toughened rigid PVC water pipe has / = 147.5 mm and R2 = 167.5 mm. Tests show Kiq = 3.1 MPa m and a.. - 40 MPa. The largest defects are equivalent to 100 >m cracks in the outer surface. (1) Determine whether the pipe will fail by yield or fracture in a pressurization test, and find the pressure to cause failure. (2) Find the maximum value of yield stress ductile failure in the pipe as strain rate increases, assuming that Ky( remains constant. (3) Calculate cTy(max) for poorly processed PVC pipe, for which = 1.5 MPa m -, assuming that a remains unchanged at 100 pm.. 

Recently, Kotomin [S. Kotomin, Moscow, personal communication, Sept. 1998] has suggested a simple means of measuring yield stress using two open-topped capillaries immersed in a yield-stress liquid. The value of yield stress Go is given by the simple equation... 

Yield stress refers to the minimum stress (force) that is required to initiate flow. Below this stress, the system behaves like an elastic solid. Relatively higher value of yield stress for the emulsion with 0% soft-tallow amidoamine is... 

Measuring yield stress of concentrated suspensions can be carried out using various rheological techniques that can be broadly classified under two categories the controlled rate rheometry and the controlled stress rheometry. A controlled rate rheometer deforms a specimen at a constant shear rate and measures the shear stress. On the other hand, a controlled stress rheometer imposes a constant shear stress on a specimen and then measures the corresponding strain. The latter approach involves a more sophisticated control system and is only introduced in the last ten years. These techniques can be further classified as direct (or static) or indirect methods (or dynamic). The indirect determination of yield stress involves the extrapolation of experimental shear stress - shear rate data to obtain a yield stress, which is the shear stress at zero shear rate. This is illustrated in Figure 9. It is evident that the choice of the model or methods yield differing values of yield stress. 

Even at the approximate peak melting temperature of the linear samples, they all exhibit a small, but measurable, yield stress. At each temperature there is an approximate correlation between the values of yield stress for the linear samples and their degree of crystallinity this further correlates with their relative molecular weights. The relationship of elastic modulus to drawing temperature follows a pattern similar to that of the yield stress, with the notable exception that the moduli of branched samples are significantly greater than those of the linear materials at 100°C. 

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