A mathematical model to study the wall roughness effects on the migration of inertial particles in a shear flow

Separation of particles in a fluid domain is relevant in various industrial applications.  The effect due to the roughness is preponderant compared with that due to fluid inertia so that the Reynolds number is low and the creeping flow equations apply.  The wall roughness is assumed to be rigid and periodic, varied in one direction.  The trajectories of freely moving particles in a shear flow are calculated.

creeping flow
particle migration
rough wall
particle inertia
fluid inertia
  1. Pasol L., Martin M., Ekiel-Jeżewska M. L., Wajnryb E., Bławzdziewicz J., Feuillebois F.  Motion of a sphere parallel to plane walls in a Poiseuille flow. Application to field-flow fractionation and hydrodynamic chromatography.  Chemical Engineering Science.  66 (18), 4078–4089 (2011).
  2. Kim Y. W., Yoo J. Y.  Three-dimensional focusing of red blood cells in microchannel flows for bio-sensing applications.  Biosensors and Bioelectronics.  24 (12), 3677–3682 (2009).
  3. Segré G., Silberberg A.  Radial particle displacements in Poiseuille flow of suspensions.  Nature.  189, 209–210 (1961).
  4. Segré G., Silberberg A.  Behaviour of macroscopic rigid spheres in Poiseuille flow Part 2. Experimental results and interpretation.  Journal of fluid mechanics.  14 (1), 136–157 (1962).
  5. Ho B. P., Leal L. G.  Inertial migration of rigid spheres in two-dimensional unidirectional flows.  Journal of fluid mechanics.  65 (2), 365–400 (1974).
  6. Leal L. G.  Particle motions in a viscous fluid.  Annual Review of Fluid Mechanics.  12, 435–476 (1980).
  7. Saffman P. G.  The lift on a small sphere in a slow shear flow.  Journal of fluid mechanics.  22 (2), 385–400 (1965).
  8. Asmolov E. S.  Dynamics of a spherical particle in a laminar boundary layer.  Fluid Dynamics.  25, 886–890 (1990).
  9. McLaughlin J. B.  Inertial migration of a small sphere in linear shear flows.  Journal of Fluid Mechanics.  224, 261–274 (1991).
  10. Leighton D., Acrivos A.  The lift on a small sphere touching a plane in the presence of a simple shear flow.  Zeitschrift für angewandte Mathematik und Physik ZAMP.  36, 174–178 (1985).
  11. Cherukat P., McLaughlin J. B.  The inertial lift on a rigid sphere in a linear shear flow field near a flat wall.  Journal of Fluid Mechanics.  285, 407 (1995).
  12. Krishnan G. P., Leighton D. T. (Jr.)  Inertial lift on a moving sphere in contact with a plane wall in a shear flow.  Physics of Fluids.  7 (11), 2538–2545 (1995).
  13. Legendre D., Magnaudet J.  The lift force on a spherical bubble in a viscous linear shear flow.  Journal of Fluid Mechanics.  368,  81–126 (1998).
  14. Assoudi R., Lamzoud K., Chaoui M.  Influence of the wall roughness on a linear shear flow.  FME Transactions.  46 (2), 272–277 (2018).
  15. Lamzoud K., Assoudi R., Bouisfi F., Chaoui M.  A spherical particle settling towards a corrugated wall.  Russian Journal of Nonlinear Dynamics.  15 (2), 125–134 (2019).
  16. Chaoui M., Feuillebois F.  Creeping flow around a sphere in a shear flow close to a wall.  The Quarterly Journal of Mechanics and Applied Mathematics.  56 (3), 381–410 (2003).
  17. Yahiaoui S., Feuillebois F.  Lift on a sphere moving near a wall in a parabolic flow.  Journal of Fluid Mechanics.  662, 447–474 (2010).
  18. Assoudi R., Chaoui M., Feuillebois F., Allouche H.  Motion of a spherical particle along a rough wall in a shear flow.  Zeitschrift für angewandte Mathematik und Physik ZAMP.  69, 112 (2018).