Rotation and alignment of rods in two-dimensional chaotic flow

Abstract

We study the dynamics of rod shaped particles in two-dimensional electromagnetically driven fluid flows. Two separate types of flows that exhibit chaotic mixing are compared: one with time-periodic flow and the other with constant forcing but nonperiodic flow. Video particle tracking is used to make accurate simultaneous measurements of the motion and orientation of rods along with the carrier fluid velocity field. These measurements allow a detailed comparison of the motion and orientation of rods with properties of the carrier flow. Measured rod rotation rates are in agreement with predictions for ellipsoidal particles based on the measured velocity gradients at the center of the rods. There is little dependence on length for the rods we studied (up to 53% of the length scale of the forcing). Rods are found to align weakly with the extensional direction of the strain-rate tensor. However, the alignment is much stronger with the direction of Lagrangian stretching defined by the eigenvectors of the Cauchy–Green deformation tensor. A simple model of the stretching process predicts the degree of alignment of rods with the stretching direction.