Shear-Banding In Entangled Polymer Solutions Under Large Amplitude Oscillatory Shear: A Confocal Rheometry Study

Abstract

We use a large aspect-ratio, planar-Couette shear cell to explore the flow properties of entangled polymer solutions, with a special focus on a long-standing problem of shear-banding in polymer solutions/melts. We first analyze the velocity profiles of entangled DNA solutions under large amplitude oscillatory shear (LAOS) inside the shear cell. We vary a gap between the shearing plates and Weissenberg number ($\mathrm{Wi}$) to construct phase diagrams quantifying the degree of wall-slip and shear-banding at different conditions. We observe transitions from normal linear shear profiles to wall-slip dominant and finally to shear-banding profiles with increasing $\mathrm{Wi}$. We further explore the dynamics of micron-sized tracer particles embedded in the solutions to study the microscopic origin of the shear-banding. Tracer particles in the shear frame exhibit transient super-diffusivity and strong dynamic heterogeneity localized in the high-shear-rate band. The probability distribution functions of particle displacements follow a power-law scaling at large displacements, indicating a L\'{e}vy-walk-type motion, reminiscent of tracer dynamics in entangled wormlike micelle solutions and sheared colloidal glasses. We further characterize the length and time scales of the abnormal dynamics of tracer particles. Based on them, we hypothesize that the unusual particle dynamics arise from localized shear-induced chain disentanglement. Next, we experimentally investigate a penetration of edge-induced disturbances and its influence on shear-banding flows. Edge instabilities have been pointed out as one of the possible experimental artifacts leading to apparently heterogeneous shear profiles. Simulations suggested even a mild edge disturbance can penetrate deeply along a vorticity direction to cause apparent gradient-banding of a velocity profile, potentially misleading experimentalists. We measure velocity profiles at different locations to reveal penetrating behavior of edge disturbances and test authenticity of the observed shear-banding flows. Under a weak oscillatory shear ($\mathrm{Wi} < 1$) where DNA solutions display a linear shear profile with wall slip, the penetration depth of the edge disturbance was on the order of the gap thickness , similar to a behavior in Newtonian fluids. Under a strong shear ($\mathrm{Wi} > 1$) where shear-banding flows are developed, the penetration depth was estimated as 20 $H$ along the flow direction while it was still on the order of the gap thickness along the vorticity direction. Furthermore, we find that the shear-banding profiles persist deep inside the sheared fluid, where the influence of edge disturbances diminishes. Our findings suggest a long penetration of the edge disturbance and also demonstrates the authentic nature of the observed shear-banding polymers. Shear-induced microscopic conformational change of individual polymer chains that trigger shear banding still remains an open question. To attain information about chain-end distributions and its dynamics, we synthesize dumbbells consisting of two spherical colloidal tracer particles connected by $\lambda$-DNA linkers and track their 2D-projected configurations and motions in the two shear-bands. We observe preferable alignment along the flow direction, enhanced translation/rotation in the high-shear-rate band. Coupling between translational/rotational dynamics and stronger correlation between chain extension and translation are also found in the high-shear-rate band. We hypothesize a formation of the localized low viscosity zones which allow the enhanced dynamics and chain extension in the high-shear-rate band.