Geometrical confinements and depletion interactions

Confinement-induced alternating interactions between inclusions in an active fluid

In a system of colloidal inclusions suspended in an equilibrium bath of smaller particles, the particulate bath engenders effective, short-ranged, primarily attractive interactions between the inclusions, known as depletion interactions, that originate from the steric depletion of bath particles from the immediate vicinity of the inclusions. In a bath of active (self-propelled) particles, the nature of such bath-mediated interactions can qualitatively change from attraction to repulsion, and they become stronger in magnitude and range of action as compared with typical equilibrium depletion interactions, especially as the bath activity (particle self-propulsion) is increased. We study effective interactions mediated by a bath of active Brownian particles between two fixed, impenetrable, and disk-shaped inclusions in a planar (channel) confinement in two dimensions. Confinement is found to strongly influence the effective interaction between the inclusions, specifically by producing alternating interaction profiles with possible attractive and repulsive regions in sufficiently narrow channels. We study the dependence of the ensuing interactions on different system parameters and the orientational (parallel versus perpendicular) configuration of the inclusion pair relative to the channel walls. The confinement effects are largely regulated by the layering of active particles next to the surface boundaries, both of the inclusions and the channel walls that counteract one another in accumulating the active particles in their own proximities. In narrow channels, the combined effects due to the channel walls and the inclusions lead to peculiar structuring of active particles (reminiscent of wavelike interference patterns) within the channel.

Entropic forces and directed alignment of hard squares in suspensions of rods and disks

We use Monte Carlo simulations in two dimensions to study the depletion forces between two hard squares in a suspension of hard rods or disks. We determine the effects of size and concentration of rods and disks on the potential of mean force between the squares. Both rods and disks produce a short-range depletion attraction between the two squares. The depletion interaction can be strong enough to outweigh the (rotational) entropic repulsion between the squares at certain sizes and concentrations of the rods and disks. We also probe the relative orientation that two squares adopt as they approach each other and we observe rich behavior, in which the relative orientation depends on the size, concentration, and shape of the depletion agent. Simple models based on the ideas of Asakura and Oosawa [J. Chem. Phys. 22, 1255 (1954)] can explain trends in the potentials of mean force obtained from the simulations.