Extensional rheology of dilute suspensions of spheres in polymeric liquids

Abstract

The extensional rheology of dilute suspensions of spheres in viscoelastic or polymeric liquids is studied computationally. At low polymer concentration (c) and Deborah number (De), a wake of highly stretched polymers forms downstream of the particles due to larger local velocity gradients than the imposed flow, indicated by a positive deviation in local De. This increases the suspension's extensional viscosity with time and De for De less than 0.5. When De exceeds 0.5 (the coil-stretch transition), the fully stretched polymers from the far field collapse in regions with lower local velocity gradients around the particle's stagnation points, reducing suspension viscosity relative to the polymer-only liquid. The interaction between local flow and polymers intensifies with increasing c. Highly stretched polymers impede local flow, reducing local De, while it increases in regions with collapsed polymers. Initially, increasing c aligns local De and polymer stretch with far-field values, diminishing particle-polymer interaction effects. However, beyond a certain c, a new mechanism emerges. At low c, fluid three particle radii upstream exhibits increased local De, stretching polymers beyond their undisturbed state. As c increases, this deviation becomes negative, collapsing polymers and resulting in increasingly negative stress from particle-polymer interactions at large De and time. At high c, this negative interaction stress scales as c squared, surpassing the linear increase in polymer stress, making dilute sphere suspensions more effective at reducing the viscosity of viscoelastic liquids at larger De and c.