Rotations, Orientations and Collisions of Suspended Particles in Velocity Gradients

Abstract

PARTICLES suspended in a liquid subjected to a velocity gradient undergo rotational and translational movements. For fluid velocities u, v, w, along the x-, y- and z-axes given by u = Gy, and v,w = 0, Jeffery¹ has shown that a prolate spheroid of axial ratio r, in the absence of Brownian motion and interaction with other particles, rotates with a period in a fixed spherical elliptical orbit described² by where λ is the angle between the z-axis and the x–z projection of the main particle axis and C is the orbit constant. The particle, when viewed as its projection on the shear planes, should therefore appear to oscillate between ± λ_max. = tan⁻¹ Cr.