Effect of Weak Inertia on the Chaotic Dynamics of Periodically Forced Neutrally Buoyant Spheroids in Simple Shear Flow

This paper describes the effect of weak inertia on the chaotic dynamics of neutrally buoyant periodically forced spheroids in a simple shear flow. We derive a set of ordinary differential equations governing the motion of periodically forced spheroids in a simple shear flow, valid for small Reynolds number and different particle aspect ratios. We show how the system behavior changes with an increase in Reynolds number and find the existence of a critical Reynolds number at which the system behavior changes from chaos to regular behavior.We analyze the dynamics of the spheroidby varying Reynolds number, particle aspect ratios, initial conditions, and external forces acting on the system. It is observed that the extent of the attractor decreases as we increase Reynolds number for a fixed aspect ratio, initial condition and external force parameter. This happens because of the increase in particle and fluid inertia. Keywords - Spheroid dynamics, Periodically forced, Chaotic dynamics, Neutrally buoyant, Lyapunov exponent