A model for the depletion layer prediction in a dilute suspension of rigid rod-like particles under shear flows in the entire range of Peclet numbers

Abstract We derived a model to predict the concentration profile, or the center-of-mass distribution, of rod-like particles near a wall under shear flows. Various excluded volume mechanisms of a rod near a wall for each Peclet number (a ratio of shear rate and diffusivity) regime were incorporated into the model through a steric factor concept. At low and moderate Peclet numbers, the steric factor is mainly determined by the ratio of the restricted/unrestricted rod orientation distributions. However, at high Peclet number, the ratio between the rod penetration time in a depletion layer and the Jeffery orbit frequency mainly affects the steric factor. The predicted concentration profiles showed a good agreement with the results from previous works.