Self-propelled colloidal objects, such as motile bacteria or synthetic microswimmers, have microscopically irreversible individual dynamics - a feature they share with all living systems. The incoherent behaviour of individual swimmers can then be ha
rnessed (or rectified) by microfluidic devices that create systematic motions impossible in equilibrium. Examples include flow of rotor particles round a circuit, steady rotation of a gear wheel in a bacterial bath, and pumping of bacteria between chambers by funnel gates. Here we present a computational proof-of-concept study, showing that such active rectification devices might be created directly from an unstructured primordial soup of motile particles, solely by using spatially modulated illumination to control their local propulsion speed. Alongside both microscopic irreversibility and speed modulation, our mechanism requires spatial symmetry breaking, such as a chevron light pattern, and strong interactions between particles, such as volume exclusion causing a collisional slow-down at high density. These four factors create a many-body rectification mechanism that generically differs from one-body microfluidic antecedents. Our work suggests that standard spatial-light-modulator technology might allow the programmable, light-induced self-assembly of active rectification devices from an unstructured particle bath.
We derive from first principles the mechanical pressure $P$, defined as the force per unit area on a bounding wall, in a system of spherical, overdamped, active Brownian particles at density $rho$. Our exact result relates $P$, in closed form, to bul
k correlators and shows that (i) $P(rho)$ is a state function, independent of the particle-wall interaction; (ii) interactions contribute two terms to $P$, one encoding the slow-down that drives motility-induced phase separation, and the other a direct contribution well known for passive systems; (iii) $P(rho)$ is equal in coexisting phases. We discuss the consequences of these results for the motility-induced phase separation of active Brownian particles, and show that the densities at coexistence do not satisfy a Maxwell construction on $P$.
