Lift and drag forces acting on a particle moving with zero slip in a linear shear flow near a wall

The lift and drag forces acting on a small spherical particle in a single wall-bounded linear shear flow are examined via numerical computation. The effects of shear rate are isolated from those of slip by setting the particle velocity equal to the local fluid velocity (zero slip), and examining the resulting hydrodynamic forces as a function of separation distance. In contrast to much of the previous numerical literature, low shear Reynolds numbers are considered ($10^{-3} \lesssim Re_{\gamma } \lesssim 10^{-1}$). This shear rate range is relevant when dealing with particulate flows within small channels, for example particle migration in microfluidic devices being used or developed for the biotech industry. We demonstrate a strong dependence of both the lift and drag forces on shear rate. Building on previous theoretical $Re_{\gamma } \ll 1$ studies, a wall-shear-based zero-slip lift correlation is proposed that is applicable when the wall lies both within the inner and outer regions of the disturbed flow. Similarly, we validate an improved wall-shear-based zero-slip drag correlation that more accurately captures the drag force when the particle is close to, but not touching, the wall. Application of the new correlations to predict the movement of a force-free particle shows that the examined shear-based lift force is as important as the previously examined slip-based lift force, highlighting the need to accurately account for shear when predicting the near-wall movement of force-free particles.