  We use the Fokker-Planck equation and its moment equations to study the
collective behavior of interacting particles in unsteady one-dimensional flows.
Particles interact according to a long-range attractive and a short-range
repulsive potential field known as Morse potential. We assume Stokesian drag
force between particles and their carrier fluid, and find analytic
single-peaked traveling solutions for the spatial density of particles in the
catastrophic phase. In steady flow conditions the streaming velocity of
particles is identical to their carrier fluid, but we show that particle
streaming is asynchronous with an unsteady carrier fluid. Using linear
perturbation analysis, the stability of traveling solutions is investigated in
unsteady conditions. It is shown that the resulting dispersion relation is an
integral equation of the Fredholm type, and yields two general families of
stable modes: singular modes whose eigenvalues form a continuous spectrum, and
a finite number of discrete global modes. Depending on the value of drag
coefficient, stable modes can be over-damped, critically damped, or decaying
oscillatory waves. The results of linear perturbation analysis are confirmed
through the numerical solution of the fully nonlinear Fokker-Planck equation.
