Fluctuations and Instability in Sedimentation

This review concentrates on the fluctuations of the velocities of sedimenting spheres, and on the structural instability of a suspension of settling fibers. For many years, theoretical estimates and numerical simulations predicted the fluctuations of the velocities of spheres to increase with the size of the container, whereas experiments found no such variation. Two ideas have increased our understanding. First, the correlation length of the velocity fluctuations was found experimentally to be 20 interparticle separations. Second, in dilute suspensions, a vertical variation in the concentration due to the spreading of the front with the clear fluid can inhibit the velocity fluctuations. In a very dilute regime, a homogeneous suspension of fibers suffers a spontaneous instability in which fast descending fiber-rich columns are separated by rising fiber-sparse columns. In a semidilute regime, the settling is hindered, more so than for spheres.