Hydrodynamic clustering of two finite-length flagellated swimmers in viscoelastic fluids

Clustering of flagellated microswimmers such as sperm is often mediated by hydrodynamic interactions between them. To better understand the interaction of microswimmers in viscoelastic fluids, we perform two-dimensional simulations of two swimming sheets, using a viscoelastic version of the smoothed dissipative particle dynamics method that implements the Oldroyd-B fluid model. Elasticity of sheets (stiff versus soft) defines two qualitatively different regimes of clustering, where stiff sheets exhibit a much more robust clustering than soft sheets. A formed doublet of soft sheets generally swims faster than a single swimmer, while a pair of two stiff sheets normally shows no speed enhancement after clustering. A pair of two identical swimmers is stable for most conditions, while differences in the beating amplitudes and/or frequencies between the two sheets can destroy the doublet stability. Clustering of two distinct swimmers is most stable at Deborah numbers of De = tau omega approximate to 1 (tau is the relaxation time of a viscoelastic fluid and omega is the beating frequency), in agreement with experimental observations. Therefore, the clustering of two swimmers depends non-monotonically on De. Our results suggest that the cluster stability is likely a dominant factor which determines the cluster size of collectively moving flagellated swimmers.

Automated summary

This study uses two-dimensional simulations in viscoelastic fluids to investigate the interaction of microswimmers. It is found that stiff sheets form stronger clusters than soft sheets. A doublet of soft sheets swims faster than a single swimmer, while a pair of stiff sheets does not show speed enhancement. Clustering of two identical swimmers is stable, but differences in beating amplitudes and frequencies can destroy the stability of the doublet. The stability of two distinct swimmers clustering is most stable at Deborah numbers of De = tau omega approximate to 1, in agreement with experimental observations. Therefore, cluster stability is a key factor in determining the cluster size of flagellated swimmers.