Hydrodynamic interactions play a crucial role in the formation of flagellated microswimmer clusters, yet they are still not clearly understood. In this article we try to elucidate the influence mechanism of the flagellum elasticity on the clustering-separation process of two flagellated microswimmers. We first systematically derive an active sphere-rod model from the undulating flagellum model. Based on this simplified model, we then construct autonomous two-dimensional dynamical systems to describe the clustering-separation process of two identical flagellated microswimmers in Newtonian fluid. The theoretical predictions without considering the flagellum elasticity are compared with results from smoothed dissipative particle dynamics simulations in which fluid-structure interactions are fully resolved. The flagellum elasticity is identified to be the key factor that alters the phase portrait and even triggers a clustering-separation transition. The elastic flagella are found to bend under the influence of nonuniform hydrodynamic forces induced by the nearby microswimmer. This bending leads to curved mean centerlines which generate rotational torques on the microswimmers thereby causing them to separate. With the inclusion of the bending effect, the theoretical model is also able to reproduce the clustering-separation transition, and predicts the appearance of a saddle point in a specific phase regime. However, fluid viscoelasticity has a much smaller impact on the phase portrait, it only considerably affects the temporal trajectory of the system. Our results highlight the critical roles that flagellum elasticity may play in the cluster formation of flagellated microswimmers.

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• Biological fluid dynamics
• Low Reynolds number swimmers
• Microswimmers
• Viscoelasticity
• Dissipative particle dynamics