The hydrodynamic theory of particle movement in non-Newtonian fluids is addressed from a theological perspective. The shear rate due to particle-to-fluid relative movement, the particle Reynolds number in non-Newtonian fluids, and a general form of Stokes' equation for non-Newtonian fluids are proposed. It is concluded that the fluid drag on a sphere moving in a yield-shear thinning or Bingham plastic fluid is jointly determined by the yield stress and viscosity. For fine particles, the influence of the yield stress becomes dominant. From this conclusion it can be deducted that the dense medium separation of fine and/or near density particles is most affected by the medium yield stress.