Rheological flows viscometric

A kinematic flow classification can be based on Q. If the flow is extensional Ck = 0, for viscometric flow = 1 and for flow which is rigid rotational - oo similarly, a rheological flow classification based on can be formulated. When the flow is viscometric = 0, if the flow has extensional characteristics > 0, and for a flow which has rigid rotational characteristics < 0. This seems to be the most satisfactory flow classification yet devised the distinction between a kinematic and a rheological classification is particularly useful and significant. The criticism of this classification made by Huilgol is false, as Astarita has shown. 

The theoretical basis for spatially resolved rheological measurements rests with the traditional theory of viscometric flows [2, 5, 6]. Such flows are kinematically equivalent to unidirectional steady simple shearing flow between two parallel plates. For a general complex liquid, three functions are necessary to describe the properties of the material fully two normal stress functions, Nj and N2 and one shear stress function, a. All three of these depend upon the shear rate. In general, the functional form of this dependency is not known a priori. However, there are many accepted models that can be used to approximate the behavior, one of which is the power-law model described above. 

Pipkin,A.C. Small displacements superposed on viscometric flow. Trans. Soc. Rheology 12, 397-408 (1968). 

Markovitz,H. Small deformations superimposed-cm steady viscometric flows. In Onogi,S. (Ed.) Proc. 5th Intemat. Cong Rheology, Vol. I, pp. 499-510. Maryland University Park Press 1970. 

It is important to note that the rheological material functions obtained experimentally, using rheometers, are evaluated in simple flows, which are often called viscometric or rheometric. A viscometric flow is defined as one in which only one component of the velocity changes in only one spatial direction, vx (y). Yet these material functions are used to describe the more complex flow situations created by polymer processing equipment. We assume, therefore, that while evaluated in simple flows, the same rheological properties also apply to complex ones. 

Three kinds of viscometric flows are used by rheologists to obtain rheological polymer melt functions and to study the rheological phenomena that are characteristic of these materials steady simple shear flows, dynamic (sinusoidally varying) simple shear flows, and extensional, elongational, or shear-free flows. 

Fig. 3.1 Examples of simple, viscometric, shear-flow rheometer geometries, la, 2a and 3 are steady while lb and 2b are dynamic rheological property... 

Finally, at higher particulate loadings, above 50% vol, the rheological behavior of filled melts is dominated by particle-to-particle interactions, due to both interparticle forces and physical flow-caused movement hindrances of the suspended particulates, particularly during pressure flows. One consequence of this is the creation of a particulate-free wall film that creates a lubricity slip layer and pluglike flows. Such slip velocities have to be considered in flow rate versus pressure drop design expressions, as well as the viscometric rheological characterization (91). 

Techniques for measuring rheological properties of polymeric materials have been well described previously by others (e.g., Whorlow, 1980 Macosko, 1994). The text by Van Wazer et al. (1963) is still a valuable reference that explains in detail many facets of earlier attempts to measure rheological properties of polymeric materials as well as basic equations of viscometric flows. The unique nature of fluid foods prompted this author to review both the rheological properties of fluid foods and their measurement about 30 years ago (Rao, 1977a, 1977b). Subsequent efforts on rheology of foods include those of Rao (1992, 2005) and Steffe (1996). 

Some of the most difficult material properties of fluid and semisolid foods to determine experimentally are viscometric functions and steady shear rheological properties. The flow properties of a liquid and semisolid food system should be measured in the following instances ... 

This brings in the need to study the behavior of pol5mieric liquid in simple flows and for simple systems, with the hope that the knowledge gained can be appropriately used in a complex flow pattern. The word rheology is defined as the science of deformation and flow. Rheology involves measurements in controlled flow, mainly the viscometric flow in which the velocity gradients are nearly uniform in space. In these simple flows, there is an applied force where the velocity (or the equivalent shear rate) is measured or vice versa. 

Housiadas KD, Tanner RI (2009) On the rheology of a dilute suspension of rigid spheres in a weakly viscoelastic matrix fluid. J Non-Newtonian Huid Mech 2009 162 88-92 Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29 329-349 Huilgol RR (2006) On the derivation of the symmetric and asymmetric Hele-Shaw flow equations for viscous and viscoplastic fluids using the viscometric fluidity function. J Non-Newtonian Fluid Mech 138 209-213... 

Solution Rheology. Solutions of polyacrylamides tend to behave as pseudoplastic fluids in viscometric flows. Dilute solutions are Newtonian (viscosity is independent of shear rate) at low shear rates and transition to pseudoplastic, shear thinning behavior above a critical value of the shear rate. This critical shear rate decreases with the polymer molecular weight, polymer concentration, and the thermodynamic quality of the solvent. A second Newtonian plateau at high shear rates is not readily seen, probably because of mechanical degradation of the chains... 

The viscosity function rj (referred to as the steady shear viscosity), the primary and secondary normal stress coefficients ij/, and respectively, are the three viscometric functions which completely determine the state of stress in any rheologically steady shear flow. They are defined as follows ... 

Although most viscometric and rheological studies are carried out in simple shear flows such as rotational viscometers, real flows experienced by real liquids are very often extensional (stretching or elongational) in nahire, and for some liquids there can be a very large difference between their shear and extensional viscosities. 

Rheological measurements are performed so as to obtain a test fluid s material functions. Under viscometric flows we have seen that the shear viscosity and the primary and secondary normal stress differences suffice to rheologically characterize the fluid. If the flow field is extensional and the material is able to attain a state of dynamic equilibrium, then one measures the extensional viscosity otherwise, we measure the extensional viscosity growth or decay functions. In this section, we will examine steady and dynamic shear plus uniaxial extensional tests, since these make up the majority of routine rheological characterization. 

Here the usual rheological convention is used, with x being the flow direction, y the shear and z the neutral directions this simple shear flow is the prototypical viscometric motion. ... 

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