Colloidal hydrodynamic interactions in viscoelastic fluid

Abstract: The motion of suspended colloidal particles generates fluid disturbances in the surrounding medium that create interparticle interactions. While such colloidal hydrodynamic interactions (HIs) have been extensively studied in viscous Newtonian media, comprehensive understanding of HIs in viscoelastic fluids is lacking. We develop a framework to quantify HIs in viscoelastic fluids with high spatiotemporal precision by trapping colloids and inducing translation-rotation hydrodynamic coupling. Using solutions of wormlike micelles (WLMs) as a case study, we discover that HIs are strongly time-dependent and depend on the structural memory generated in the viscoelastic fluid, in contrast to "instantaneous" HIs in viscous Newtonian fluids. We directly measure time-dependent HIs between a stationary probe and a driven particle during transient start-up, developing on the WLM relaxation timescale. Following the sudden cessation of the driven particle, we observe an intriguing flow reversal in the opposing direction, lasting for a time about ten times larger than the WLM relaxation time. We corroborate our observations with analytical microhydrodynamic theory, direct numerical solutions of a continuum model, and particle-based Stokesian dynamics simulations. We find that the structural recovery of the WLMs from a nonlinear strain can generate anisotropic and heterogeneous stresses that produce flow reversals and hydrodynamic attraction among colloids. Measured heterogeneities indicate a breakdown of standard continuum models for constitutive relations when the size of colloids is comparable to the length scales of the polymeric constituents and their entanglement lengths.