Clumping instability of a falling horizontal lattice

Particle falling through a viscous liquid tend to form clumps under the influence of viscous forces. An analysis of this effect for a falling horizontal lattice indicates that the clumps which form are much larger than expected on the basis of nearest neighbor approximations. This difference in behavior can be traced to the increasing influence of distant neighbors in two dimensions, and suggests that the clumping instability in three dimensions may not be described as a simple extension of the one-dimensional instability.