  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.
