  New developments in the theory and numerical simulation of a recently
proposed one-dimensional nonlinear time-dependent fluid model [K. Avinash, A.
Bhattacharjee, and S. Hu, Phys. Rev. Lett. 90, 075001 (2003)] for void
formation in dusty plasmas are presented. The model describes an initial
instability caused by the ion drag, rapid nonlinear growth, and a nonlinear
saturation mechanism that realizes a quasi-steady state containing a void. The
earlier one-dimensional model has been extended to two and three dimensions
(the latter, assuming spherical symmetry), using a more complete set of
dynamical equations than was used in the earlier one-dimensional formulation.
The present set of equations includes an ion continuity equation and a
nonlinear ion drag operator. Qualitative features of void formation are shown
to be robust with respect to different functional forms of the ion drag
operator.
