of motion $$\begin{aligned}
\dot{x}_{i}^{\alpha} &= v_{s} p_{i}^{\alpha} + \mathcal{U}^{\alpha}\left( {\bm x}_i \right),   
\label{xdot} \\
\dot{p}_{i}^{\alpha} &= \mathbb{P}_{i}^{\alpha\beta} \left(\mathcal{W}^{\beta\gamma}\left( {\bm x}_i \right) + B \mathcal{E}^{\beta\gamma}\left( {\bm x}_i \right) \right) p_{i}^{\gamma},
\label{pdot}\end{aligned}$$ where the dot denotes the time derivative, the superscript indices denote Cartesian components of vectors, and the subscript indices label the particles. Throughout this work, we utilise the Einstein summation convention for the superscript indices, while no summation is assumed over repeated subscript indices.

Equations of motion and incorporate the following physical ingredients. First of all, each swimmer self-propels with the speed $v_s$ in the direction of its orientation. To induce self-propulsion, swimmers generate long-ranged flows in the suspending fluid [@Lauga2009]. The superposition of these flows at the position of the $i$-th swimmer, $\mathcal{U}^{\alpha}\left( {\bm x}_i \right)$, advects that particle in addition to its self-propulsion, see Eq., and re-orients it according to Jeffrey’s equation . The latter describes the dynamics of a passive particle in an external flow [@kimkarrila], with $$\begin{aligned}
&\mathcal{W}^{\beta\gamma}\left( {\bm x}_i \right) = \frac{1}{2} \left( \nabla^{\gamma}  \mathcal{U}^{\beta}\left( {\bm x}_i \right) - \nabla^{\beta}  \mathcal{U}^{\gamma}\left( {\bm x}_i \right) \right), \\
&\mathcal{E}^{\beta\gamma} \left( {\bm x}_i \right)= \frac{1}{2} \left(\nabla^{\gamma}  \mathcal{U}^{\beta}\left( {\bm x}_i \right) + \nabla^{\beta}  \mathcal{U}^{\gamma}\left( {\bm x}_i \right) \right),
\label{eq:Strain}\end{aligned}$$ 