In stratified suspensions, we show using a linear stability analysis and large-scale simulations that the vertical density gradient stabilizes long-wavelength fluctuations, resulting in a wavenumber selection at a finite wavelength. In initially well-mixed suspensions, the evolution of the wavelength of the instability can therefore be explained as a consequence of the formation of density gradients in the bulk of the suspensions.
When an external electric field is applied such as in microfluidic applications, and if the particles are polarizable, induced-charge electrophoresis occurs. We use theory and simulations to study this phenomenon, which is shown to cause the alignment of the particles and to drive a stresslet flow in the vicinity of the particles. While this induced flow can result in additional particle pairings, the strong alignment in the direction of the electric field tends to stabilize the suspension, which is observed to become stable for sufficiently strong fields. Upon stabilization, the average sedimentation velocity of the particles is hindered, (rather than enhanced as in the unstable sedimentation) and we present calculations of both the stability boundary in terms of the dimensionless applied field, as well as a theory for the hindered setting function.