The orientation dynamics of anisotropic particles in shearing flows

Abstract

The thesis investigates the first effects of micro-scale inertia and stochastic orientation fluctuations on the orientation dynamics of spheroids in shearing flows. The first chapter of the thesis focuses on a single spheroid in a planar linear flow and the long-time orientation dynamics of the spheroid set up by weak inertial effects is identified. The second chapter of the thesis focuses on estimating the viscosity of a dilute suspension of spheroids in a simple shear flow. It turns out that the inertia sets up a unique steady state orientation distribution, and therefore a unique viscosity, for a dilute suspension of prolate spheroids of all aspect ratios, and of oblate spheroids with aspect ratios greater than 0.14. A stochastic orientational decorrelation mechanism is needed to render the viscosity unique for a dilute suspension of (oblate) spheroids with aspect ratios smaller than 0.14. Rotary Brownian motion is considered as a canonical example for the decorrelation mechanism. Interestingly, the steady state orientation distribution in the presence of both inertia and rotary Brownian motion lends itself to a novel thermodynamic interpretation and leads to the identification of the ‘Tumbling-spinning transition’ in an anisotropic particle suspension. The ‘Tumbling-spinning transition’ has striking similarities to the coil-stretch transition of high molecular weight polymers in extension-dominated flows. This interpretation is also explained in the second chapter of thesis. In the third chapter the long-time orientation dynamics of a spheroid sedimenting in a simple shear flow is analyzed. The fourth chapter investigates the effect of inertia on the time period of rotation of a spheroid in a simple shear flow, a canonical rheological flow, and a specific instance of a planar linear flow, is also quantified.