Tunable Long Range Forces Mediated by Self-Propelled Colloidal Hard Spheres

Using Brownian dynamics simulations, we systematically study the effective interaction between two parallel hard walls in a 2D suspension of self-propelled (active) colloidal hard spheres, and we find that the effective force between two hard walls can be tuned from a long range repulsion into a long range attraction by changing the density of active particles. At relatively high densities, the active hard spheres can form a dynamic crystalline bridge, which induces a strong oscillating long range dynamic wetting repulsion between the walls. With decreasing density, the dynamic bridge gradually breaks, and an intriguing long range dynamic depletion attraction arises. A similar effect occurs in a quasi-2D suspension of self-propelled colloidal hard spheres by changing the height of the confinement. Our results open up new possibilities to manipulate the motion and assembly of microscopic objects by using active matter.

Figure 1

(a) Effective forces Fσ/kBT as a function of wall-to-wall distance r at density ρbulkσ2=0.4 with various activity f. (b) Fσ/kBT and the average density ρ¯(r) inside the confinement -0.5r≤x≤0.5r, -0.5W≤y≤0.5W as a function of r with fσ/kBT=40 and ρbulkσ2=0.4. (c) Fσ/kBT as a function of r at ρbulkσ2=0.4 with various Gaussian size polydispersities s. (d) Reduced density distribution log10[ρ(x,y)/ρbulk] of active particles with fσ/kBT=40 at ρbulkσ2=0.4, with a wall-to-wall distance r/σ=2.1,5,10, and 20. (e) Typical snapshots of systems for density distributions in (d), respectively. (f) F/(ρbulkσkBT) for fσ/kBT=40 as a function of wall-to-wall distance r for various particle densities. (g) Fσ2/(WkBT) for a self-propelled ideal particle system with fσ/kBT=40 and ρbulkσ2=0.2 for various wall sizes W. The lines are fits with ∼-exp(-r/ξ). (h) Fσ2/(WkBT) for ideal particles with density ρbulkσ2=0.2 for various self-propulsions and a wall size W/σ=80. (i) Reduced density distribution log10[ρ(x,y)/ρbulk] for ideal particle systems with fσ/kBT=40 and r/σ=2.2,5,10, and 20, where the wall size is W/σ=10, and ρbulkσ2=0.4.

Figure 2

(a) Simple model with one ideal particle (grey square) moving in a 2D square lattice, with two parallel impenetrable walls (dark squares). (b)–(d) Reduced density distributions ρ(x,y)/ρbulk for kswap=0.2,0.5, and 1, respectively. (e) Effective force between two walls F/v0 for various kswap as a function of r. The solid lines are the fits with ∼-exp(-r/ξ). (f) Fitted interaction range ξ in (e) as a function of 1/kswap.

Figure 3

(a) Main: Fσ2/(WkBT) as a function of wall-wall separation r/σ for fσ/kBT=40 in quasi-2D confinement with a varying height H/σ, at fixed 2D number density Nσ2/A=0.4. Inset: a typical system snapshot with two walls as yellow bricks. (b) Fσ3/(WHkBT) as a function of r/σ for fσ/kBT=40 and varying H/σ, where the 3D number density is fixed at Nσ3/(AH)=0.2.