particles form dimers on average. A similar behavior is observed for WP squirmers with short-range interactions, with slightly larger fluctuations in the mean cluster size for weak pullers at long times.]{}

Having established the conditions needed for clustering to appear, we represent in Fig. \[fig:MeanClustersBetas\] the mean cluster size as a function of $\beta$ for $r_c=2.5 \sigma$ (panel a) and $r_c=1.5 \sigma$ (panel b). [^2]

![\[fig:MeanClustersBetas\]Mean cluster size for suspensions with (a) $r_c=2.5\sigma$ and (b) $r_c=1.5\sigma$ in steady-state for WP ($\xi=10$, $\xi=1$ and $\xi=0.1$, square symbols) and AP ($\xi=10$ and $\xi=1$, circular symbols) ](meanclustersize2p5.pdf "fig:"){width="0.48\columnwidth"} ![\[fig:MeanClustersBetas\]Mean cluster size for suspensions with (a) $r_c=2.5\sigma$ and (b) $r_c=1.5\sigma$ in steady-state for WP ($\xi=10$, $\xi=1$ and $\xi=0.1$, square symbols) and AP ($\xi=10$ and $\xi=1$, circular symbols) ](meanclustersize1p5.pdf "fig:"){width="0.48\columnwidth"}

[As shown in figure \[fig:MeanClustersBetas\], when $\xi=1$ WP swimmers mostly form tetramers and trimers, while WP swimmers with $\xi=10$ form dimers. The clusters observed for WP squirmers have an average size rather insensitive to the squirmer hydrodynamic signature for these two interaction strength $\xi = \{1$,$10$} and the two interaction ranges studied here.]{}

[ For lower values of $\xi$, the dependence on $\beta$ becomes more evident for WP squirmers with $\xi=0.1$ (gray squares on panel-b): 