Concentration fluctuations in polymer solutions under mixed flow

Abstract

In this work, we extend the classical analysis of concentration fluctuations in polymer solutions under shear flow to consider the same phenomenology under mixed (shear + extensional) flows. To investigate this phenomenon, we couple stress and concentration using a two-fluid model with fluctuations driven by thermal noise incorporated through a canonical Langevin approach. The polymer stress is governed by the Rolie-Poly model augmented with finite extensibility to account for large stretching of chains at high Weissenberg numbers. Perturbing the equations about homogeneous flow for weak amplitude inhomogeneities, but arbitrary flow strength, we solve for the steady state structure factor (Fourier transformed pair correlation function) under general linear flows using a unique method of characteristics solver. Under shear flow, the model predicts butterfly patterns in accord with previous experimental and theoretical work, including a full rotation of peaks past the flow axis. In addition, the magnitude of the structure factor initially grows with the Weissenberg number until reaching a maximum at intermediate shear rates and decaying thereafter. Under mixed flow, the butterfly patterns as well as the location and magnitude of the peak structure factor are strongly tied to both the flow type parameter and the Weissenberg number (the characteristic strain rate). As expected, for flows characterized as strong, the scattering patterns typically appear like a rotated version of pure extension. However, as the flow type approaches the pure shear limit, the influence of shear flow on the butterfly patterns becomes more pronounced. In particular, for large Weissenberg numbers, contrary to expectations, the flow type need not be very near shear flow in order for the scattering patterns to no longer be simply rotated versions of extensional flow.