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

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 hydrodynamics dominates 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.

Emergent vortices and phase separation in systems of chiral active particles with dipolar interactions

“…However, hydrodynamic interactions can have a profound impact on the dynamical self-assembly of active colloidal systems, such as the suppression of MIPS [89][90][91][92] and the emergence of global polar ordering. [93][94][95][96][97] In systems of rotating particles, it is found that hydrodynamic interactions can induce cluster rotation, such that the overall cluster and the individual particles rotate in the same direction. 98 In the present work, we have seen that the giant Type I vortices and circle swimmers rotate in the same direction.…”

Self-propulsion of an active polar drop

“…The advantage of this approach is that the bend (splay) instability is expressed by m = 1 and ψ = Ar (ψ = Ar). It is also convenient to expand other vector fields such as velocity v and force f fields [45],…”

“…Here, we have used incompressibility to simplify the rotational flow. Using the force generated by active stress (67), the cos θ terms in (69) and (70) result in L (a,a) in the linearized matrix (47) for the coefficients of the expansion (45), whereas sin θ terms result in L (b,b) .…”

“…From the boundary condition, (v r (R) − u) · n = 0. Using the self-propulsive velocity u, the tangential velocity at the surface is (v t − u) · t = v s , where the slip velocity, v s is associated with self-propulsive velocity u = −(1/2π) v s tdθ [45]. The velocity field is then expressed as…”

Topical Issue on Advances in Computational Methods for Soft Matter Systems

“…For these systems, the biggest difficulty comes from the need to accurately model the hydrodynamic interactions, which greatly increases the computational cost of the simulations. A brilliant solution to this problem is found in the article by Yoshinaga et al [5], where a new numerical scheme is developed which allows for the simulations of a large number of active particles that have accurate hydrodynamic interactions even when close to each other. The article shows that lubrication forces, often ignored in other methods, are in competition with long-range hydrodynamic forces, and can completely change the behaviour of swimmers.…”