such increase in the cluster size is observed only for this interaction range, since WP squirmers with short-range attractions (panel d) develop a ]{} mean cluster-size of $\sim 4$ particles, independently on their hydrodynamic signature.

Fig. \[fig:nct\_xi10\] represents the mean cluster size as a function of time for suspensions where propulsion dominates over attraction ($\xi=10$) of AP squirmers (interacting via long-range (panel-a) or short-range (panel-b) attraction) and of WP squirmers (interacting via long-range (panel-c) or short-range (panel-d) attraction).

![\[fig:nct\_xi10\] Time evolutions of the mean cluster size for squirmers when $\xi=10$ (pullers: red [squares]{} and black [circles]{}; neutral: blue [up triangles]{}; pushers: pink [down-triangles]{} and grey [diamonds]{}). (a) AP squirmers with $r_c=2.5\sigma$ and (b) $r_c=1.5\sigma$, (c) WP squirmers with $r_c=2.5\sigma$ and (d) $r_c=1.5\sigma$. Note the different scale on the y-axis.](ntxi10rc25ttbis.pdf "fig:"){width="0.48\columnwidth"} ![\[fig:nct\_xi10\] Time evolutions of the mean cluster size for squirmers when $\xi=10$ (pullers: red [squares]{} and black [circles]{}; neutral: blue [up triangles]{}; pushers: pink [down-triangles]{} and grey [diamonds]{}). (a) AP squirmers with $r_c=2.5\sigma$ and (b) $r_c=1.5\sigma$, (c) WP squirmers with $r_c=2.5\sigma$ and (d) $r_c=1.5\sigma$. Note the different scale on the y-axis.](ntxi10rc15ttbis.pdf "fig:"){width="0.48\columnwidth"} ![\[fig:nct\_xi10\] Time evolutions of the mean cluster size for squirmers when $\xi=10$ (pullers: red [squares]{} and black [circles]{}; 