Simple shear flow rheological response

The steady and dynamic drag-induced simple shear-flow rheometers, which are limited to very small shear rates for the steady flow and to very small strains for the dynamic flow, enable us to evaluate rheological properties that can be related to the macromolecular structure of polymer melts. The reason is that very small sinusoidal strains and very low shear rates do not take macromolecular polymer melt conformations far away from their equilibrium condition. Thus, whatever is measured is the result of the response of not just a portion of the macromolecule, but the contribution of the entire macromolecule. 

Rheological Response of Polymer Melts in Steady Simple Shear-Flow Rheometers... 

Aside from the simple shearing motion, the response of visco-elastic materials in a variety of other well-defined flow configmations including the cessation/initiation of flow, creep, small amplitude sinusoidal shearing, etc. also lies in between that of a perfectly viscous fluid and a perfectly elastic solid. Conversely, these tests may be used to infer a variety of rheological information about a material. Detailed discussions of the subject are available in a number of books, e.g. see Walters [1975] and Makowsko [1994]. 

In order to characterize polymeric fluids and to test rheological equations of state it is customary to use simple, well defined flows. The two main flows are simple shear and simple elongational. These are shown schematically in Figure 1. In shear flow, material planes (see Figure 1) move relative to each other without being stretched, whereas in extensional flow the material elements are stretched. These two different flow histories generate different responses in not only flexible chain polymers but in liquid crystalline polymers. When these flows are carried... 

Two separate theoretical analyses of polymer molecular behavior in solution have been carried out by Bueche (12) and Graessley (13). Both analyses predict a pseudoplastic rheology for polymer solutions in simple shear. However, Bueche s explanation is based on the response of independent polymer molecules to a shearing flow field and Graessley s explanation is based on the response of entangled molecules when placed in a shearing flow field. 

Rheology is the science of the deformation and flow of matter. It provides information on the mechanical response to a dynamic stress or strain. Recall that stress (a) is the force per unit area and so has units N m or Pa. Strain (e) is the relative change in length of the sample and is dimensionless. A simple shear deformation is illustrated in Fig. 1.9. The bottom plate is fixed but the top plate is moved at a speed Vx in the x direction. If the gap between the plates is filled with a simple liquid like water, it is observed that the shear stress is proportional to the velocity gradient dvx/dy. 

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