화학공학소재연구정보센터
Journal of Rheology, Vol.46, No.5, 1057-1089, 2002
A new model for dilute polymer solutions in flows with strong extensional components
Ghosh et al. (2001) demonstrated that the Kramers chain captures the optical and theological properties of dilute polymer solutions in rapidly varying elongational flows better than the finitely extensible nonlinear elastic 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 relaxation. A closed form of the constitutive equation, the ALS-C model, is proposed. The theological 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.