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The lift and drag forces acting on a small spherical particle moving with afinite slip in single-wall-bounded flows are investigated via direct numericalsimulations. The effect of slip velocity on the particle force is analysed as afunction of separation distance for low slip and shear Reynolds numbers($10^{-3} \leq Re_{\gamma}, Re_{\text{slip}} \leq 10^{-1}$) in both quiescentand linear shear flows. A generalised lift model valid for arbitraryparticle-wall separation distances and $Re_{\gamma}, Re_{\text{slip}} \leq10^{-1}$ is developed based on the results of the simulations. The proposedmodel can now predict the lift forces in linear shear flows in the presence orabsence of slip,and in quiescent flows when slip is present. Existing dragmodels are also compared with numerical results for both quiescent and linearshear flows to determine which models capture near wall slip velocities mostaccurately for low particle Reynolds numbers. Finally, we compare the resultsof the proposed lift model to previous experimental results of buoyantparticles and to numerical results of neutrally-buoyant (force-free) particlesmoving near a wall in quiescent and linear shear flows. The generalised liftmodel presented can be used to predict the behaviour of particle suspensions inbiological and industrial flows where the particle Reynolds numbers based onslip and shear are $\mathcal{O}(10^{-1})$ and below.

Lift and drag forces acting on a particle moving in the presence of slip and shear near a wall