Levich Institute Seminar Announcement, 05/01/2007
Steinman Hall, Room #312
(Chemical Engineering Conference Room)
Professor Robert Armstrong
Massachusetts Institute of Technology
Chemical Engineering Department
"Rheology and Fluid Mechanics of Polymer Solutions Undergoing Rapid Elongational Deformations"
[This is a CCNY/Columbia NSF-IGERT Soft Materials seminar]
Bead-spring kinetic theory models, which we illustrate in this talk by elastic dumbbells, have proven to be very useful in describing the rheological behavior of polymeric liquids and for understanding the response of these liquids in complex flows. In this talk we consider two experiments in which simple bead-spring models have failed to capture key physical observations, and we discuss improvements to the models motivated by these failures. The first experiment is filament stretching, which consists of the sudden startup of uniaxial elongational flow followed by stress relaxation. When stress is plotted against birefringence in this experiment, hysteresis is observed between the growth and relaxation parts of the experiment. Simple bead-spring models do not capture this hysteretic behavior. We analyze the Kramers chain, a fine-scale model for polymer dynamics, in order to assess the validity of the coarser-grained bead-spring models in these deformations. Whereas the spring force is a simple function of the dumbbell length for customary nonlinear elastic springs, we find that the relationship between the ensemble averaged end-to-end force and the extension for a Kramers chain depends on the kinematic history to which it has been subjected. We find that it is essential for a dumbbell model to have an end-to-end force that depends upon the deformation history in order to capture hysteresis in the filament stretching experiment.
We then turn to a discussion of a complex flow, namely flow around a linear, periodic array of cylinders. Viscoelastic liquids in this flow undergo a transition from
steady, two-dimensional flow to a spatially periodic, three-dimensional flow at a critical flow rate. Simple bead-spring models do not correctly capture this flow transition, and we believe that this
shortcoming is due to the failure of these models to describe well the rapid elongational flow in the wake behind the cylinders. In order to address this problem we construct a new bead-spring model
that is simple enough to be used in finite element simulations, and yet captures correctly the dynamics of hysteresis observed in the first experiment. The new model describes a polymer molecule as a
set of identical segments where each segment represents a fragment of the polymer that is short enough so that it can sample its entire configuration space on the time scale of the deformation and
therefore stretches reversibly. As the molecule unravels, the number of segments decreases but the maximum length of each segment increases so that the model accounts for the constant maximum contour
length of the parent molecule. The behavior of this new model in the flow around cylinders will be presented.