IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Flow-Induced Concentration Fluctuations in Polymer Solutions

  • Oct. 10, 2016
  • 1:15 p.m.
  • LeConte 312

Abstract

A key assumption underlying many theoretical fluid mechanics studies of complex fluids is that the fluid composition remains homogeneous. Specifically, it is often assumed for polymeric solutions that the concentration of the polymer is independent of position in the rest state and remains so in the presence of flow. On the other hand, many industrial flows of complex fluids are nonhomogeneous.

In this two-part talk, we thus consider both linear and nonlinear effects of perturbations of polymer concentration on the flow of polymer solutions. The theoretical foundation is that of the Helfand-Fredrickson mechanism in which polymer molecules can migrate up stress gradients, toward regions of higher concentration, hence providing a mechanism to enhance naturally occurring thermal fluctuations. In this study, we develop and apply a modernized version of the two fluid model for highly entangled polymer solutions. We use the Rolie-Poly constitutive model, which is known to provide qualitatively reasonable predictions for linear chain polymers over a wide range of strain-rates.

First, we generalize the classical analysis of polymer fluctuations in shear flow to consider the same problem for general linear flows, with an emphasis on extensional and mixed (shear + extensional) flows. In this work we attempt to use concentration fluctuation analysis to devise criteria by which one can ascertain whether being a “strong flow” is sufficient to make scattering patterns appear like a rotated version of pure extension. For the types of polymer solutions of interest to this work, our simulations reveal that scattering patterns under flows that are classified as “strong” (in which extension controls the chain dynamics) may deviate from the behavior expected under extensional flow and reveal a nontrivial influence of shear flow.

Furthermore, we have found that the coupling between stress and concentration yields fundamental changes in even pure shearing flows. Specifically, we have shown that linear shear flow is linearly unstable for ranges of shear rates. Simulations of start-up flow, for both linear shear and Couette flow, show that these instabilities lead to major changes in both the velocity field and concentration profiles, ending in a final steady state that exhibits a shear banded velocity profile, each band corresponding to a different locally uniform polymer concentration.

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