Transient rheology of particle-filled polymer solutions

The transient rheology of polymeric fluids containing embedded particles plays an important role in many industrial processes such as hydraulic fracturing and the manufacture of consumer products, pharmaceuticals, and flexible electronics. We extend our recently developed finite difference method for solving polymer flow around spheroidal particles in spheroidal coordinates to describe the rheology of dilute particle suspensions in polymer fluids. Through hybrid numerical-analytical approaches, we describe the particle stresslet, particle-induced polymer stress, and the overall ensemble-averaged suspension stress. We apply our method to understand start-up shear, large-amplitude oscillatory shear of suspensions of spherical particles, and transient shear of suspensions of high-aspect-ratio spheroids with various initial particle orientations. To explore the dynamic polymer conformational response when a suspension experiences time varying flow-types, we analyze the transient flow in a filament stretching rheometer in which a suspension is subjected to pre-shear followed by extensional motion.