patch” (WP). When the propulsion direction ($\hat{e}_i$, red arrow in figure \[fig:JanusSquirmers\]-right panel) is pointing against the attractive patch $-\hat{p}_i$ (green arrow in figure \[fig:JanusSquirmers\]-right panel), swimmers are propelling “against the patch” (AP).

![Panel a) WP Janus swimmers. Panel b) AP Janus swimmers. The attractive patch is represented in blue [(dark gray)]{}, and the non-attractive patch is in green [(light gray)]{}. The swimming direction $\hat{e}$ is the red arrow and direction of the attractive patch $\hat{p}$ is the green one. The center-to-center distance between two swimmers $\vec{r_{ij}}$ is the black vector. \[fig:JanusSquirmers\]](WP_pairJanus.pdf "fig:"){width="0.480\linewidth"} ![Panel a) WP Janus swimmers. Panel b) AP Janus swimmers. The attractive patch is represented in blue [(dark gray)]{}, and the non-attractive patch is in green [(light gray)]{}. The swimming direction $\hat{e}$ is the red arrow and direction of the attractive patch $\hat{p}$ is the green one. The center-to-center distance between two swimmers $\vec{r_{ij}}$ is the black vector. \[fig:JanusSquirmers\]](AP_pairJanus.pdf "fig:"){width="0.480\linewidth"}

![image](Sqrmr_Bn1.pdf){width=".32\textwidth"}![image](Sqrmr_Bcero.pdf){width=".32\textwidth"}![image](Sqrmr_Bp1.pdf){width=".362\textwidth"}

A spherical Janus squirmer of radius $R_p$ is characterized by the tangential surface slip velocity, $$\begin{aligned}
 \label{eq:surface_veloc}
\textbf{u}|_{R_p} = \left[ B_1 \sin \theta + B_2 \sin \theta \cos \theta \right] \boldsymbol{\tau}\, ,\end{aligned}$$ where $\boldsymbol{\tau}$ is a unit vector tangential to the particle surface, $B_1$ quantifies the 