Synopsis-111 analysis of the Maxwell orthogonal rheometer for polymer melts is made by using the constitutive equation of White and JIetzner. The results indicate that the shear iieformation involved is oscillatory and that the storage and loss moduli of the melt may be derived from the measured stress response.The rheology of polymer melts is an area of considerable importance both from a practical standpoint and for understanding material behavior. Recently Maxwell and Chartoff' reported on a new device, termed an orthogonal rheometer, for characterizing polymer melt properties. To date, however, its acceptance has been hindered by the need for an analysis of the manner in which the three forces measured by the device are related to the response of the material to the imposed deformation.The molten sample of thickness I is contained between parallel circular plates, the axes of which are not colinear but separated by a distance a along the y axis. The lower plate is driven at a rotational velocity W . The upper plate is allowed to rotate freely a t the same angular velocity. Three orthogonal forces are measured along the 5 , y, and x axes. We have analyzed the rheonieter by formulating the kinenlatics in a nonorthogonal curvilinear coordinate system in which the motion of the fluid can be easily written. This system, depicted in Figure 2, has coordinates (0', r', 2') related to the Cartesian coordinates (2, y , x ) by Figure 1 depicts the rheometer schematically. 8' = tan-' { [ Y -( U / Z ) Z ] / X~
Fabrication conditions and material rheology control the process of film blowing and limit the possible shapes the bubble may take as well as the ranges and ratios of stresses within the bubble. In order to understand bounds on the stresses during the blowing process, we explore the constraints imposed by force balances, the thin shell approximation, and thermodynamics. We show that the ratio of axial stress to hoop stress is independent of the explicit terms for film thickness, velocity, heat transfer, and the rheology of the material. In addition, we demonstrate that the ratio of the axial stress to the hoop stress can be calculated at any point in the blown-film requiring only values for the pressure drop across the bubble, the shape of the bubble, and the force pulling up the bubble. Experimental results, as well as certain theoretical evidence, strongly indicate that the ratio of axial to hoop stress is everywhere greater than 1 in the standard blown-film process. If this is generally true, then the stress relations we derived can be employed to test the applicability of various theoretical models of the blown-film process.
My fellow authors and I have assembled a series of articles on using rheology to understand the structure and processing of a wide range of materials. We approach this task by presenting an introduction to the concepts of rheology and some illustrative applications, followed by a description of linear vis-coelasticity and a description of the rheological behavior of elastic fluids. These concepts and related tools are then used to describe molten polymers, colloidal suspensions, latex systems, electrorheological fluids, and gels. In each of these areas, we show how rheology provides insights into the structure of materials and the type of information required to process them. We also show that the rheological approach spans macroscopic and microscopic domains. These aspects of rheology are of value to materials scientists and engineers. We hope these examples will clarify the relevance of rheology to materials.If we are successful in this presentation, you will obtain a flavor of the process of rheological studies. While reading through these articles, look for the interplay of the concepts of molecular or domain structures and the flow and deformation of the bulk materials. These articles may even inspire you to examine the role that rheology may play in your own studies.
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