Brownian dynamics simulations of the stress and molecular configuration ofpolymers in exponential and linearly-ramped shear flow

The rheological and optical properties of dilute polymer solutions during t he startup and subsequent relaxation in exponential shear flow are studied using Brownian dynamics simulations of freely draining, flexible bead-rod c hains. We find that exponential shear flow is capable of effecting large mo lecular deformation for finite shear rates and strains, and furthermore, th e polymer undergoes an initial stress and index of refraction relaxation th at is much faster than a single exponential decay upon cessation of flow. W hen we compare the first normal stress difference (tau(11)-tau(22)) to the corresponding components of the index of refraction tensor, n(11)-n(22), we find that there is hysteresis when plotted over the course of a full start up and relaxation experiment. This is very similar to the hysteresis origin ally discovered by Doyle et al. [J. Non-Newtonian Fluid Mech. 76 (1998) 79- 110] for uniaxial extensional flow. Moreover, the shear components of the s tress and index of refraction tensors (tau(12) and n(12)) also exhibit hyst eretic behavior. However, whereas the hysteresis loop for the 11-22 compone nt traverses up the left branch during startup and relaxes on the right bra nch, that for the 12 component is in the completely opposite direction, i.e . the right branch corresponds to startup and the left branch relaxation. T he presence of stress-index of refraction hysteresis clearly has important implications for the stress-optic rule. We calculate the stress-optic coeff icient for the startup process, and find that the normal and shear componen ts give the same value, but that it is strongly dependent on Wi. This resul t is consistent with that found by Doyle et al. during the startup of stead y shear flow [Doyle and Shaqfeh, Dynamic simulation of freely-draining, fle xible bead-rod chains: startup of extensional and shear flow, J. Non-Newton ian Fluid Mech. 76 (1998) 43-78]. We also simulated shear flows with a line arly ramped shear rate to compare to our results for exponential shear. We find that for comparable final shear rate and time, both exponential and li near ramping shear produce very similar hysteresis effects in both the shea r and normal components suggesting that there may be many unsteady shear fl ow capable of creating large polymer stretch and stress-birefringence hyste resis. Finally, we compare our bead-rod chain simulations to the FENE dumbb ell model, and we find that while the latter can qualitatively capture the normal stress hysteresis, it predicts negligible shear stress hysteresis at equivalent shear rates and shear strains. (C) 1999 Elsevier Science B.V. A ll rights reserved.