  The ion drag force arising from plasma flow past an embedded spherical grain
is calculated self-consistently and non-linearly using particle in cell codes,
accounting for ion-neutral collisions. Using ion velocity distribution
appropriate for ion drift driven by a force field gives wake potential and
force greatly different from a shifted Maxwellian distribution, regardless of
collisionality. The low-collisionality forces are shown to be consistent with
estimates based upon cross-sections for scattering in a Yukawa (shielded) grain
field, but only if non-linear shielding length is used. Finite collisionality
initially enhances the drag force, but only by up to a factor of 2. Larger
collisionality eventually reduces the drag force. In the collisional regime,
the drift distribution gives larger drag than the shift distribution even at
velocities where their collisionless drags are equal. Comprehensive practical
analytic formulas for force that fit the calculations are provided.
