Recent experiments and calculations have exhibited apparent steady cus
ps in certain fluid free surfaces driven by a converging subsurface fl
ow. Molecular dynamics simulations are used to elucidate some of the i
ssues raised by this phenomenon, with emphasis on the behavior of the
fluid on very small scales. The similar but different situation of two
immiscible fluids of equal viscosity driven by solid rollers is consi
dered. Molecular scale simulations of the evolution of the separating
interface exhibit a gradual increase of curvature with rotation rate.
However, high curvature interfaces do not reach a steady state, but in
stead drops of the fluid above the free surface are detached. In no ca
se does a true cusp form, and the stress tensor is never unusually lar
ge in the near-cusp region.