From hydrodynamic lubrication to many-body interactions in dense suspensions of active swimmers

TL;DR

This paper investigates how near-field lubrication forces influence the collective behavior of dense suspensions of active swimmers, revealing their significant role in cluster formation and polar order, with a novel numerical approach for large systems.

Contribution

The study introduces an exact calculation of near-field hydrodynamic interactions and a new numerical scheme to analyze large active particle systems with accurate lubrication effects.

Findings

Lubrication forces can dominate long-range interactions in dense suspensions.

Large force dipoles lead to cluster and gel formation, preventing phase separation.

Small force dipoles induce stable polar order driven by near-field interactions.

Abstract

We study how hydrodynamic interactions affect the collective behaviour of active particles suspended in a fluid at high concentrations, with particular attention to lubrication forces which appear when the particles are very close to one another. We compute exactly the limiting behaviour of the hydrodynamic interactions between two spherical (circular) active swimmers in very close proximity to one another in the general setting in both three and (two) dimensions. Combining this with far-field interactions, we develop a novel numerical scheme which allows us to study the collective behaviour of large numbers of active particles with accurate hydrodynamic interactions when close to one another. We study active swimmers whose intrinsic flow fields are characterised by force dipoles and quadrupoles. Using this scheme, we are able to show that lubrication forces when the particles are very close to each other can play as important a role as long-range hydrodynamic interactions in determining their many-body behaviour. We find that when the swimmer force dipole is large, finite clusters and open gel-like clusters appear rather than complete phase separation. This suppression is due to near-field lubrication interactions. For swimmers with small force dipoles, we find surprisingly that a globally polar ordered phase appears because near-field lubrication rather than long-range hydrodnamics dominate the alignment mechanism. Polar order is present for very large system sizes and is stable to fluctuations with a finite noise amplitude. We explain the emergence of polar order using a minimal model in which only the leading rotational effect of the near-field interaction is included. These phenomena are also reproduced in two dimensions.