Shear-rate-dependent flow

Standard Test Method for Apparent Viscosity of Adhesives Having Shear-Rate Dependent Flow Properties, ASTM D2556, Am Soc. Testing and Materials. 1997. 

ASTM D2556-93a (1997) Standard test method for apparent viscosity of adhesives having shear-rate-dependent flow properties. 

The option of shear rate control in rotational viscosimeters makes it possible to detect shear rate dependent flow phenomena. Variants with high-precision motors and torque sensors are called rheometers and are used in research projects above and beyond the viscosimetry (see also 115, 17, 18]). In these instruments, other measurement systems besides the cylinder geometries are used, that are described in the following chapters. 

For many low-molecular-weight liquids, viscosity is a material property and, by definition, only depends on thermodynamic state variables such as temperature, pressure, and concentration. These fluids are collectively termed Newtonian Liquids because they satisfy Newton s law of viscosity, Ts = p(dw ,/dy) = py, where p, the Newtonian viscosity, is independent of or y. The viscosity of many polymer melts and solutions depends on thermodynamic state variables and flow conditions (Xj and y, in the above example). In these systems, viscosity is not a material property because it cannot be uniquely defined from the knowledge of the thermodynamic state of the fluid alone. It is nonetheless possible to define an apparent viscosity, ri(y)=Ts(y)/y, that quantifies the shear rate-dependent flow resistance. A plot of q(y) versus y for a particular fluid is therefore termed its flow curve. 

Polymers in solution or as melts exhibit a shear rate dependent viscosity above a critical shear rate, ycrit. The region in which the viscosity is a decreasing function of shear rate is called the non-Newtonian or power-law region. As the concentration increases, for constant molar mass, the value of ycrit is shifted to lower shear rates. Below ycrit the solution viscosity is independent of shear rate and is called the zero-shear viscosity, q0. Flow curves (plots of log q vs. log y) for a very high molar mass polystyrene in toluene at various concentrations are presented in Fig. 9. The transition from the shear-rate independent to the shear-rate dependent viscosity occurs over a relatively small region due to the narrow molar mass distribution of the PS sample. 

Qualitatively, the same behaviour is observed for the flow curves at a fixed polymer concentration with various molar masses (Fig. 10). The shear rate depend-... 

The coordinates (x, y, z) define the (velocity, gradient, vorticity) axes, respectively. For non-Newtonian viscoelastic liquids, such flow results not only in shear stress, but in anisotropic normal stresses, describable by the first and second normal stress differences (oxx-Oyy) and (o - ozz). The shear-rate dependent viscosity and normal stress coefficients are then [1]... 

The usual approach for non-Newtonian fluids is to start with known results for Newtonian fluids and modify them to account for the non-Newtonian properties. For example, the definition of the Reynolds number for a power law fluid can be obtained by replacing the viscosity in the Newtonian definition by an appropriate shear rate dependent viscosity function. If the characteristic shear rate for flow over a sphere is taken to be V/d, for example, then the power law viscosity function becomes... 

In steady shear flows, only the shear-rate dependence of viscosity is well documented in terms of molecular structure effects. Molecular theories are more... 

Viscoelastic behavior is classified as linear or non-linear according to the manner by which the stress depends upon the imposed deformation history (SO). Insteady shear flows, for example, the shear rate dependence of viscosity and the normal stress functions are non-linear properties. Linear viscoelastic behavior is obtained for simple fluids if the deformation is sufficiently small for all past times (infinitesimal deformations) or if it is imposed sufficiently slowly (infinitesimal rate of deformation) (80,83). In shear flow under these circumstances, the normal stress differences are small compared to the shear stress, and the expression for the shear stress reduces to a statement of the Boltzmann superposition principle (15,81) ... 

Similar arguments can be raised against internal viscosity as a primary cause of shear rate dependence in the viscosity. A recent review (339a) has shown that current many-bead theories predict differences in y0 and co0 when e is small and chosen to fit the oscillatory data. The approximate nature of these analyses leaves serious doubts about their predictions in steady-state flow, however. A new... 

A final piece of evidence against both finite extensibility and internal viscosity is provided by flow birefringence studies. One would expect each to produce variations in the stress optical coefficient with shear rate, beginning near the onset of shear rate dependence in the viscosity (307). Experimentally, the stress-optical coefficient remains constant well beyond the onset of shear rate dependence in r for all ranges of polymer concentration (18,340). 

The Eyring analysis does not explicity take chain structures into account, so its molecular picture is not obviously applicable to polymer systems. It also does not appear to predict normal stress differences in shear flow. Consequently, the mechanism of shear-rate dependence and the physical interpretation of the characteristic time t0 are unclear, as are their relationships to molecular structure and to cooperative configurational relaxation as reflected by the linear viscoelastic behavior. At the present time it is uncertain whether the agreement with experiment is simply fortuitous, or whether it signifies some kind of underlying unity in the shear rate dependence of concentrated systems of identical particles, regardless of their structure and the mechanism of interaction. 

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