Stressing viscosities

According to the structure of this equation the quantity cp indicates the influence of the filler on yield stress, and t r on Newtonian (more exactly, quasi-Newtonian due to yield stress) viscosity. Both these dependences Y(cp) andr r(cp) were discussed above. Non-Newtonian behavior of the dispersion medium in (10) is reflected through characteristic time of relaxation X, i.e. in the absence of a filler the flow curve of a melt is described by the formula ... 

Viscosity is usually understood to mean Newtonian viscosity in which case the ratio of shearing stress to the shearing strain is constant. In non-Newtonian behavior, which is the usual case for plastics, the ratio varies with the shearing stress (Fig. 8-5). Such ratios are often called the apparent viscosities at the corresponding shearing stresses. Viscosity is measured in terms of flow in Pa s, with water as the base standard (value of 1.0). The higher the number, the less flow. 

Most characterisation of non-linear responses of materials with De < 1 have concerned the application of a shear rate and the shear stress has been monitored. The ratio at any particular rate has defined the apparent viscosity. When these values are plotted against one another we produce flow curves. The reason for the popularity of this approach is partly historic and is related to the type of characterisation tool that was available when rheology was developing as a subject. As a consequence there are many expressions relating shear stress, viscosity and shear rate. There is also a plethora of interpretations for meaning behind the parameters in the modelling equations. There are a number that are commonly used as phenomenological descriptions of the flow behaviour. 

When the shear-stress viscosity relation of the fluid does not obey the simple newtonian expression of Eq. (5-1), the above equations for free-convection heat transfer do not apply. Extremely viscous polymers and lubricants are examples of fluids with nonnewtonian behavior. Successful analytical and experimental studies have been carried out with such fluids, but the results are very complicated. The interested reader should consult Refs. 48 to 50 for detailed information on this subject. 

Molecular Weight Dependence of Constant-Stress Viscosity... 

The molecular weight dependence of the extrapolation length b originates from the same molecular weight dependence of the constant stress viscosity q0. A recent experimental study shows... 

During food engineering operations, many fluids deviate from laminar flow when subjected to high shear rates. The resulting turbulent flow gives rise to an apparent increase in viscosity as the shear rate increases in laminar flow, i.e., shear stress = viscosity x shear rate. In turbulent flow, it would appear that total shear stress = (laminar stress + turbulent stress) x shear rate. The most important part of turbulent stress is related to the eddies diffusivity of momentum. This can be recognized as the atomic-scale mechanism of energy conversion and its redistribution to the dynamics of mass transport processes, responsible for the spatial and temporal evolution of the food system. 

FIGURE 8.15 Relationship among shear stress, viscosity, and shear rate as flow behavior of molten chocolate for 1 the temperature is 35°C, and for 2 it is 45°C (arbitrary scale). 

Blends of HOPE with LDPE were studied by Dobrescu (12) by means of a capillary viscometer. The constant stress viscosity, log Tl(ai2 const) vs. W2 plot indicated a strong positive deviation, PDB, from the log-addltlvlty rule ... 

The concentration dependence of the constant-stress viscosity, provides information on the inherent flow mechanism. The experimental data should be evaluated considering the log-addi-tivity rule, Inrj = Z(t)jlnrij. There are hve possible types of behavior, described as 1. positively... 

Entropy production is caused by nonequilibrium stress (viscosity) and heat flux... 

Most fluids exhibit non-Newtonian behavior—blood, household products like toothpaste, mayonnaise, ketchup, paint, and molten polymers. As shown in Figure 7.9, shear stress, t, increases linearly with strain rate, y, for Newtonian fluids. Non-Newtonian fluids may be classified into those that are time dependent or time independent and include viscoelastic fluids. Shear thinning (pseudoplastic) and shear thickening (dilatant) fluids are time independent while rheopectic and thixotropic are time dependent. The shear stress (viscosity) of shear thinning fluids decreases with increasing shear rate and examples include blood and syrup. The viscosity of dilatant fluids increases with shear rate. The viscosity of rheopectic fluids—whipping cream, egg whites—increases with time while thixotropic fluids— paints (other than latex) and drilling muds— decrease their viscosity with the duration of the shear. 

Another approach to miscibility effect on flow is through analysis of the constant stress viscosity-concentration dependence. For solutions of small molecules, the log-additivity rule is most often found ... 

In multiphase polymeric systems the zero-shear Newtonian coefficient of shear viscosity, tjo, is difficult to determine, but the constant stress viscosity, tj , provides an acceptable alternative. The equivalence is easy to note considering superposition of flow curves - if the flow curves superpose at any stress then they also superpose within the Newtonian plateau. 

A fluid can be distinguished from a solid in this discussion of viscosity by its behavior when subjected to a stress (force per unit area) or applied force. An elastic solid deforms by an amount proportional to the applied stress. However, a fluid when subjected to a similar applied stress will continue to deform, i.e., to flow at a velocity that increases with increasing stress. A fluid exhibits resistance to this stress. Viscosity is that property of a fluid which gives rise to forces that resist the relative movement of adjacent layers in the fluid. These viscous forces arise from forces existing between the molecules in the fluid and are of similar character as the shearforces in solids. 

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