  We analyze the dynamics of concentrated polymer solutions modeled by a 2D
Smoluchowski equation. We describe the long time behavior of the polymer
suspensions in a fluid. \par When the flow influence is neglected the equation
has a gradient structure. The presence of a simple flow introduces significant
structural changes in the dynamics. We study the case of an externally imposed
flow with homogeneous gradient. We show that the equation is still dissipative
but new phenomena appear. The dynamics depend on both the concentration
intensity and the structure of the flow. In certain {\it limit cases} the
equation has a gradient structure, in an appropriate reference frame, and the
solutions evolve to either a steady state or a tumbling wave. For small
perturbations of the gradient structure we show that some features of the
gradient dynamics survive: for small concentrations the solutions evolve in the
long time limit to a steady state and for high concentrations there is a
tumbling wave.
