Angular dynamics of small particles in fluids

Abstract: This thesis concerns the angular motion of small particles suspended in fluid flows. A small particle experiences a hydrodynamic torque due to the local fluid velocity, and this torque leads to rotational motion. When inertial effects are negligible the torque on an ellipsoidal particle is given by Jeffery's theory [Jeffery, G. B. Proc. R. Soc. Lond. A 102, 161–179 (1922)]. In this thesis and the appended papers I describe three studies that all relate to this well-known result. First, we derive an effective equation of motion for the orientation of a spheroid in a simple shear flow, valid for small values of the shear Reynolds number $\textrm{Re}_s=sa^2/\nu$, where $s$ is the shear rate, $a$ the particle size and $\nu$ the kinematic viscosity of the suspending fluid. In absence of inertia the equation of motion has infinitely many periodic solutions, the 'Jeffery orbits'. We show how this degeneracy is lifted by the effects of inertia. Second, we describe experimental observations of the orientational dynamics of asymmetric particles advected in a microchannel. We record several trajectories with each particle by resetting the initial condition with an optical trap. We find that the dynamics depend sensitively on both particle shape and initial conditions. This confirms earlier theoretical results, which are also described in this thesis. Third, we discuss the angular dynamics of axisymmetric particles in turbulent and random flow. In these flows the statistical averages of the angular dynamical quantities depend crucially on the intricate correlations between the particle orientation, angular velocity, and the flow vorticity relative to the principal straining directions of the fluid flow. We illustrate this by direct numerical simulation, experimental measurements and statistical model calculations. Finally, this thesis contains an introduction to the field aimed at new students, as well as an accessible popular science introduction to low Reynolds particle dynamics.