Rheology and Kinetic Theory of Polymeric Liquids

Abstract

Previous reviews of kinetic theory of macromolecules in the Annual Review of Physical Chemistry have been concerned primarily with (a) equilibrium properties, and departures from equilibrium that include only linear viscoelastic phenomena; (b) very simple flows, such as simple shear flows of the form Vx = k(t)y, where k(t) is often taken to be a small-amplitude sinusoidal function; (c) the shear stress 'yx in shear flows (as opposed to the normal stresses 'XX' Tyy, Tzz); and (d) molecular models of polymers that incorporate linear or Hookean springs. However, they have generally ignored the relation with modern continuum mechanics. These previous reviews have certainly reflected the chief concerns and accomplishments of polymer chemistry investigations during the �st two decades, and it is generally acknowledged that many unresolved problems remain in these areas. In this review the four aspects listed above are deemphasized and attention is focused on the following : (a) nonlinear viscoelastic properties, such as shear-rate-dependent viscosity and normal stress coefficients in steady shear flow and their time-dependent counter­ parts, (b) large-deformation flows including viscometric flows, elongational flows, radial flows, and time-dependent flows, (c) the complete stress tensor expressions from kinetic theory and the measurement of components of the stress tensor other than 'yx in steady shear flow, (d) molecular models involving nonlinear springs or constraints that may be capable of better describing the observed rheological phe­ nomena in terms of internal structural changes, and (e) the use of modern continuum mechanics to provide a framework for presenting kinetic theory results, analyzing rheological experiments, and solving polymer fluid dynamics problems. Interest in these areas has been steadily growing and reflects the observation of new rheo­ logical phenomena, the advances in rheological instrumentation, and the increased activity in computer modeling of polymer processing operations.