understand the effect of the hydrodynamic interactions in the collective dynamics of active Janus colloids, inspired by experiments showing flow fields around a single catalytic Janus sphere [@Campbell_FlowFieldJanus].]{}

The manuscript is organised as follows. In section \[model\] we present the anisotropic interaction model, the squirmer model, the lattice Boltzmann methodology and simulations details. In section \[sec:Tools\] we describe the tools used to characterise the Janus squirmers. In section \[sec:Results\] we present all results and discuss our conclusions in section \[sec:Conclusions\].

\[model\]Simulation details
===========================

In this work, we have studied a quasi two dimensional dilute suspension of squirmers [@Lighthill; @Blake; @Pedley:2016] interacting via a Janus anisotropic potential similar to the one used in Ref. [@Stewart_17] for Active Brownian Particles (ABP). In order to model the Janus swimmers, we have introduced a pair potential $V(r_{ij},\theta_i,\theta_j)$ which depends on the distance between two squirmers ($r_{ij}$) and their attractive patches’ orientations $$\begin{aligned}
\label{eq:JanusGralPotential}
%V(r_{ij},\hat{p}_i,\hat{p}_j)= V_{rep}(r_{ij})+V_{att}(r_{ij})\phi(\theta_i,\theta_j)\, .
V(r_{ij},\theta_i,\theta_j)= V_{rep}(r_{ij})+V_{att}(r_{ij})\phi(\theta_i,\theta_j)\,  \end{aligned}$$ where $\theta_i$ is the angle between the patch unit vector $\vec{p_i}$ and the inter-particle vector $\vec{r}_{ji}=\vec{r}_j - \vec{r}_i$; and $\theta_j$ the angle between $\vec{p_j}$ and $\vec{r}_{ij}=-\vec{r}_{ji}$.

$V_{rep}(r_{ij})$ represents a short range soft repulsion [@Allen_Tildesley] (to avoid overlapping) given by

$$\begin{aligned}
\label{eq:SSPotential}
\begin{split}
&V_{rep}\left(r_s\right)= \\ 
&\begin{cases}
