The conformation change of model polymers in stochastic flow fields: Flow through fixed beds

Simulations of the conformation change of model polymers in various steady, anisotropic Gaussian random flow fields are presented. These flow fields have been chosen because they are models for the flow through porous media and have been predicted to be “stochastic strong flows” according to the criteria developed by Shaqfeh and Koch [J. Fluid Mech. 244, 17 (1992)]. To be specific, beyond a certain Deborah number (based on the sampling time of a velocity fluctuation), large average conformation change in the polymer is predicted. In our simulations, the polymers are modeled as dumbbells, but beyond this restriction, the assumptions of the theory by Shaqfeh and Koch are removed. Many realizations of the Gaussian fields are synthesized spectrally following a modified version of the method developed by Kraichnan [Phys. Fluids 13, 22 (1970)]. Moreover, the ratio of the mean “plug” flow to the amplitude of the fluctuations is varied from mean-dominant to fluctuation-dominant flows. The simulated conformation change shows that, in fact, these flows are “strong” in the sense that the average second moment of the end-to-end distance becomes large (relative to equilibrium) beyond a critical value of the fluctuation Deborah number. Although qualitatively capturing these trends, the theory by Shaqfeh and Koch underestimates the strength of the flows and thus overestimates the critical Deborah number. We present a new theory which includes spring relaxation and Brownian motion in the sampling of a velocity fluctuation (two factors which were neglected in the existing theory), thereby breaking the fore–aft symmetry of the sampling, thus increasing the average polymer stretch. The new theory quantitatively predicts the simulation results. To the authors knowledge, this is the first evidence via direct simulation that these random flows can produce large conformation change in model polymer molecules, even when the mean flow would produce no such change.