Rotations, Orientations and Collisions of Suspended Particles in Velocity Gradients

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, Jeffery 1 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 described 2 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 .