2006-07-21
14:15 at HCI J 543

Influence of configuration-dependent drag on the capillary thinning of filaments of dilute polymer solutions

Ravi Jagadeeshan

Department of Chemical Engineering, Monash University Melbourne, Australia

In a seminal paper, Entov and Hinch (J. Non-Newtonian Fluid Mech., 72: 37-53, 1997) predicted that surface tension causes the diameter of a thin filament of a dilute polymer solution to decrease exponentially in time, before break up. Their model showed that the resulting extensional strain rate corresponds to a Weissenberg (Wi) number of 2/3. Subsequent experimental observations by Anna and McKinley (J. Rheol., 45: 115-138, 2001) of an exponential decrease in the mid-filament diameter, suggested that the measured strain rate could be used with the Wi = 2/3 formula to extract the characteristic large-scale relaxation time of the polymer molecule. Recent studies (Clasen et al., Proc. XIVth Intl. Cong. Rheol. 2004) however show that the relaxation time calculated in this manner displays a curious concentration dependence. We demonstrate in this paper that this anomalous behaviour is due in part to the neglect of the configuration dependence of intramolecular hydrodynamic interactions. We use a set of improved constitutive models for the polymer stress in dilute solutions at the theta state, which account for the influence of configurational anisotropy and fluctuations in hydrodynamic interactions. The predictions obtained for homogeneous simple shear and uniaxial extensional flows are shown to be in good agreement with results of Brownian dynamics simulations of isolated chains with hydrodynamic interactions. Using the simple one-dimensional stress balance proposed by Entov and Hinch, we show that the Wi = 2/3 formula is not generally valid, and leads to an erroneous concentration dependence. Further, incorporating configuration-dependent drag leads to an improved description of the evolution of the mid-filament diameter for some solutions. In other cases, our results indicate that the self-concentrating effect of extensional flows may cause theory to deviate from experiment.