A New Model for Dilute Polymer Solutions in Flows with Strong Extensional
Indranil Ghosh, Yong Lak Joo, Gareth H. McKinley, Robert A. Brown, and Robert C. Armstrong
Department of Chemical Engineering
Massachusetts Institute of Technology
Cambridge, MA 02139-4307 USA
August 27, 2001
Ghosh et al. (2001) demonstrated that the Kramers chain captures the optical and rheological properties of dilute polymer solutions in rapidly varying elongational flows better than the FENE dumbbell model. A new model, based on introducing an adaptive length scale (ALS) as an internal variable, is developed to reproduce the fine scale physics of the Kramers chain. The resulting ALS-model describes the polymer molecule as a set of identical segments in which 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 an imposed deformation and therefore stretch reversibly. As the molecule unravels, the number of segments decreases, but the maximum length of each segment increases, so that the constant maximum contour length of the molecule is preserved. The ALS model gives very good predictions of stress growth in startup of uniaxial elongation and stress-birefringence hysteresis in a uniaxial elongational flow followed by relax-ation. A closed form of the constitutive equation, the ALS-C model, is proposed. The rheolog-ical predictions of the ALS-C model resemble those of the ALS equation. This coupled with its small number of internal degrees of freedom suggests that this constitutive equation may be
useful in modeling complex flows.