crossing the solid particle’s boundary (including the slip velocity to impose the squirming motion [@llopis_wall; @ricard_epje]). The total force and torque the fluid exerts on the particle is obtained by imposing that the total momentum exchange between the particle and the fluid nodes vanishes (as a result of the modified bounce-back). While accounting for all forces acting on each squirmer allows to update them dynamically, the torque exerted by the fluid determines the change of the squirmer ’s self-propulsion direction.

The simulated system consists of a suspension of $N=888$ spherical squirmers at $\phi=0.10$ (where $\phi=\frac{\pi}{4} \rho\sigma^2$ and $\rho=N/L^2$) in a quasi two-dimension geometry with periodic boundary conditions ($L\times L \times k \sigma$, with $k=5$ and $L \approx 83 \sigma$) needed to capture three dimensional hydrodynamics effects, [whereas both colloids’ position and orientation are confined to move in 2D]{}. Additionally, we have carried out bigger simulations with $N=3552$ squirmers at the same packing fraction and $L \approx 167 \sigma$, in order to proof that results are not due to finite size effects, specially cases with large cluster sizes.

As in Ref. [@SoftMatter17], we quantify the competition between attractive and self-propelling forces via the dimensionless parameter $$\xi = \frac{F_d}{F_{att}},$$ where $F_d = 