Generalizations of a nonlinear fluid model for void formation in dusty plasmas

New developments in the theory and numerical simulation of a recently proposed one-dimensional nonlinear time-dependent fluid model (Avinash K, Bhattacharjee A and Hu S 2003 Phys. Rev. Lett. 90 075001) 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