LOW-REYNOLDS-NUMBER MOTION OF PARTICLES WITH 2 OR 3 PERPENDICULAR PLANES OF SYMMETRY

For a particle with two or three perpendicular planes of symmetry rotating at low Reynolds number in a Couette flow field, there are three orbits in which the motion is simply periodic. The three scalars Bi involved in Bretherton's shape tensor are found experimentally from periods of rotation in these orbits. Experiments on right parallelepipeds, ranging from thin platelets through cubes to rectangular section rods, are described. Each of the Bi is found to depend on the aspect ratio of one of the particle cross-sections, with only slight influence from its third dimension. Results are expressed in terms of a relationship between this aspect ratio and that of an equivalent ellipse, incorporating a weak function of the third particle dimension. The equations of motion governing a general doubly periodic motion, and incorporating experimental Bi values, are integrated numerically and compared satisfactorily with experimental observations. © 1979, Cambridge University Press