Shape dynamics and rheology of dilute suspensions of elastic and viscoelastic particles

This paper examines the shape dynamics of deformable elastic and viscoelastic particles in an ambient Newtonian fluid subjected to simple shear. The are allowed undergo large deformation, with stress determined using neo-Hookean constitutive relation. We first present a method determine initially ellipsoidal that is extension Roscoe ( J. Fluid Mech. , vol. 28, issue 2, 1967, pp. 273–293), originally used at steady state spherical particle. show our recovers earlier results for in-plane trembling tumbling prolate spheroids shear flow, obtained by different approach. then examine oblate triaxial ellipsoids they too, like spheroids, exhibit time-periodic or dynamics, depending on initial aspect ratios particle capillary number $G \equiv \mu \dot {\gamma }/\eta$ where $\mu$ viscosity fluid, $\eta$ modulus $\dot }$ rate. In addition, we find novel wherein extends indefinitely time asymptotically aligns flow axis. demarcate all dynamical regimes parameter space comprising $G$ ratios. When viscoelastic, damped oscillatory observed particles, tumbling–trembling boundary altered so as favour tumbling.