[en] The ion drag force on a spherical dust particle immersed in a flowing plasma with an external electric field is self-consistently calculated using the particle-in-cell code SCEPTIC in the entire range of charge-exchange collisionality. Our results, not based on questionable approximations, extend prior analytic calculations valid only in a few limiting regimes. Particular attention is given to the force direction, shown never to be directed opposite to the flow except in the continuum limit, where other forces are of a much stronger magnitude