(98b) Departure From Stokes Drag Coefficients for Spherical and Non-Spherical Particles in Microducts

Drag has been studied in great detail over the last century providing many equations that predict drag at various Reynolds numbers.  Creeping flow has become an increasingly more studied regime with the development of DPD (dissipative particle dynamics) and micro fluidics.  Originally Stokes' Law was generated to describe drag in creeping flow, however it neglects the concepts of wall correction and non uniform velocity profiles.  Fayon and Happel introduced a force correction for sphere sedimentation based on the data obtained by McNown in the early 1960's (Brenner and Happel, 1965).  Fidleris has ran experiments that confirmed that the radius of the sphere divided by the radius of the pipe was the critical parameter when evaluating drag in non uniform flow (Fidleris and Whitmore, 1958).  Levenspiel expanded these empirical equations to include a larger range of Reynolds numbers and different shaped particles (Haider and Levenspiel, 1988).  Recently Ganser generated correction factors K₁ and K₂ along with a C_D function similar to that of Levenspiel to apply for all particles for a large range of Reynolds (Ganser, 1993).  This paper uses computational fluid dynamics to establish the error associated with these equations at low Reynolds number.  Simpler equations using the aspect ratios of (D/H diameter of particle/height of channel) and (L/D length/diameter) are used to describe the geometries of spheres, ellipses, and cylinders.

  References

Haider, A. & Levenspiel, O. (1989). Drag coefficient and Terminal Velocity of Spherical and Nonspherical Particles. Powder Technology, 63-70.

Ganser, G. (1993). A rational approach to drag perdiction of spherical and nonspherical particles. Powder Technology, 143-152.

Happel, J. & Brenner, H. (1965). Low Reynolds Number Hydrodynamics. Englewood Cliffs: Prentice-Hall, Inc.

Fidleris, V. & Whitmore, R. L. (1958). The Physical Interaction of Spherical Particles in Suspension. University of Nottingham, 572-579.