Extensional rheology of dilute suspensions of spheres in polymeric liquids

The extensional rheology of dilute suspensions of spheres in viscoelastic/polymeric liquids is studied computationally. At low polymer concentration c and Deborah number De (imposed extension rate times polymer relaxation time), a wake of highly stretched polymers forms downstream of the particles due to larger local velocity gradients than the imposed flow, indicated by Δ Delocal> 0 . This increases the suspension’s extensional viscosity with time and De for De < 0.5 . When De exceeds 0.5, the coil-stretch transition value, the fully stretched polymers from the far-field collapse in regions with Δ Delocal < 0 (lower velocity gradient) around the particle’s stagnation points, reducing suspension viscosity relative to the particle-free liquid. The interaction between local flow and polymers intensifies with increasing c . Highly stretched polymers impede local flow, reducing Δ Delocal , while Δ Delocal increases in regions with collapsed polymers. Initially, increasing c aligns Δ Delocal and local 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 Δ Delocal > 0 , stretching polymers beyond their undisturbed state. As c increases, however, Δ Delocal in this region 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 c² , surpassing the linear increase of particle-free polymer stress, making dilute sphere concentrations more effective at reducing the viscosity of viscoelastic liquids at larger De and c .