(a) Predicted velocity of a particle under a background Poiseuille flow (⁠|$f=0$|⁠) for varying |$\alpha $|⁠. Graphs are shown for the MoR (solid lines) and our finite element implementation for different |$\varepsilon $| (squares, triangles and circles), as well as for the implementations by Murata (1981) and Bungay & Brenner (1973) which are valid for small and tightly-fitting rigid particles, respectively. (b) Log-log plots of the norm of the absolute error between the non-linear FEM solution and the MoR solutions, increasing |$\varepsilon $| for three different particle sizes. In each case, the non-linear particle velocity is smaller than the MoR prediction (see, for example, the inset in (a)). Linear lines of best fit are also presented, omitting the clear non-linear trend for |$\varepsilon> 0.5$|⁠. The average slope across the three lines is |$2.17$|⁠.