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

TL;DR

This paper develops a generalized model for lift and drag forces on small particles near walls in shear flows, incorporating slip effects, validated by simulations and applicable to biological and industrial suspensions.

Contribution

A new generalized lift model for particles with slip near walls in low Reynolds number shear flows, validated against simulations and experiments.

Findings

The model accurately predicts lift forces across various particle-wall distances.

Existing drag models are evaluated for near-wall slip velocity accuracy.

Comparison with experimental data confirms the model's applicability.

Abstract

The lift and drag forces acting on a small spherical particle moving with a finite slip in single-wall-bounded flows are investigated via direct numerical simulations. The effect of slip velocity on the particle force is analysed as a function of separation distance for low slip and shear Reynolds numbers ($10^{-3} \leq Re_{\gamma}, Re_{\text{slip}} \leq 10^{-1}$) in both quiescent and linear shear flows. A generalised lift model valid for arbitrary particle-wall separation distances and $Re_{\gamma}, Re_{\text{slip}} \leq 10^{-1}$ is developed based on the results of the simulations. The proposed model can now predict the lift forces in linear shear flows in the presence or absence of slip,and in quiescent flows when slip is present. Existing drag models are also compared with numerical results for both quiescent and linear shear flows to determine which models capture near wall slip velocities most accurately for low particle Reynolds numbers. Finally, we compare the results of the proposed lift model to previous experimental results of buoyant particles and to numerical results of neutrally-buoyant (force-free) particles moving near a wall in quiescent and linear shear flows. The generalised lift model presented can be used to predict the behaviour of particle suspensions in biological and industrial flows where the particle Reynolds numbers based on slip and shear are $\mathcal{O}(10^{-1})$ and below.