asymptotic self-propelling speed of an isolated squirmer ($v_s= \frac{2}{3} B_1$) [@Prieve; @Stone] and $B_2$ is proportional to the active stress generated on the surrounding fluid. The ratio between active stress and self-propelling velocity, $\beta=B_2/B_1$ [@Ishikawa2006], quantifies the active state of the squirmer and its interaction with the fluid. A positive value of $\beta$ corresponds to the case when thrust is generated in front of the squirmer’s body (puller); a negative value of $\beta$ to the case when thrust is generated at the back (pusher)  [@Ishikawa2007a] and $\beta=0$ corresponds to a neutral swimmer (see Fig. \[fig:Squirmers\]). In our simulations we disregard thermal fluctuations; thus velocity fluctuations are simply induced by the particles’ activity, where $B_2$ can be understood as an effective temperature.

In order to characterize how hydrodynamics affects the assembly of a dilute suspension of Janus swimmers, we model the embedding solvent using a Lattice Boltzmann (LB) method with a D3Q19 three dimensional lattice [@cates_lb; @succi], implemented in a highly parallelized code [@ludwig] that exploit the excellent scalability of LB on supercomputing facilities. Spherical squirmers (with a diameter $\sigma$ of 4.6 lattice nodes [@nguyen]) are individually resolved, imposing a modified bounce-back rule on the one-particle velocity distribution functions to nodes 