text: The preceding analysis will not be accurate in the ultra-Stokesian regime. i.e. if the particle Reynolds number is much greater than unity. Assuming a Mach number much less than unity, a generalized form of the Stokes number was demonstrated by Israel & Rosner.
  Where is the "particle free-stream Reynolds number",
  An additional function  was defined by; this describes the non-Stokesian drag correction factor,
  It follows that this function is defined by,
  Considering the limiting particle free-stream Reynolds numbers, as  then  and therefore . Thus as expected there correction factor is unity in the Stokesian drag regime. Wessel & Righi evaluated  for  from the empirical correlation for drag on a sphere from Schiller & Naumann.
  Where the constant . The conventional Stokes number will significantly underestimate the drag force for large particle free-stream Reynolds numbers. Thus overestimating the tendency for particles to depart from the fluid flow direction. This will lead to errors in subsequent calculations or experimental comparisons.