The effect of stratification on the wave number selection in the instability of sedimenting spheroids

It is well known that a dilute suspension of spheroids sedimenting under gravity at low Reynolds number is unstable to density fluctuations as a result of hydrodynamic interactions [D. L. Koch and E. S. G. Shaqfeh, J. Fluid Mech. 209, 521 (1989)]. Using a linear stability analysis, it is shown that a vertical density gradient in such a suspension can lead to a wave number selection by damping fluctuations at long wavelengths. A scaling for the most unstable wavelength, or characteristic size of the density fluctuations, is obtained in terms of the background stratification and volume fraction, and is compared to results from numerical simulations in stratified particulate suspensions using methods that we have developed previously. In initially homogeneous suspensions, simulations show a continuous decay of the size of the density fluctuations over time, which we demonstrate can be attributed to the development of stratification inside the suspension. (c) 2006 American Institute of Physics.