Stationary particle currents in sedimenting active matter wetting a wall

Abstract: Recently it was predicted, on the basis of a lattice gas model, that scalar active matter in a gravitational field would rise against gravity up a confining wall or inside a thin capillary - in spite of repulsive particle-wall interactions [Phys. Rev. Lett. 124, 048001 (2020)]. In this paper we confirm this prediction with sedimenting active Brownian particles (ABPs) in a box numerically and elucidate the mechanism leading to the formation of a meniscus rising above the bulk of the sedimentation region. The height of the meniscus increases with the activity of the system, algebraically with the P\'eclet number. The formation of the meniscus is determined by a stationary circular particle current, a vortex, centered at the base of the meniscus, whose size and strength increase with the ABP activity. The origin of these vortices can be traced back to the confinement of the ABPs in a box: already the stationary state of ideal (non-interacting) ABPs without gravitation displays circular currents that arrange in a highly symmetric way in the eight octants of the box. Gravitation distorts this vortex configuration downward, leaving two major vortices at the two side walls, with a strong downward flow along the walls. Repulsive interactions between the ABPs change this situation only as soon as motility induced phase separation (MIPS) sets in and forms a dense, sedimented liquid region at the bottom, which pushes the center of the vortex upwards towards the liquid-gas interface. Self-propelled particles therefore represent an impressive realization of scalar active matter that forms stationary particle currents being able to perform visible work against gravity or any other external field, which we predict to be observable experimentally in active colloids under gravitation.

• The paper demonstrates that sedimenting active matter exhibits stationary vortices and capillary rise at confining walls despite repulsive interactions.
• It employs numerical simulations of active Brownian particles to show that meniscus height scales algebraically with the swimming Péclet number.
• The findings offer practical insights for designing experimental active systems with applications in materials science and biological physics.

Analysis of Stationary Particle Currents in Active Matter Sedimentation

The paper "Stationary particle currents in sedimenting active matter wetting a wall" investigates the complex behavior of active matter systems under sedimentation, specifically focusing on the formation of stationary particle currents and wetting properties against a confining wall. The authors employ active Brownian particles (ABPs) as a model to simulate this behavior.

Summary of Findings

This work provides numerical confirmation for the prediction that scalar active matter under a gravitational field exhibits capillary rise at a confining wall, despite repulsive particle-wall interactions. The study demonstrates this by employing a model of sedimenting ABPs within a box, showcasing the development of a meniscus that rises against the bulk sedimentation.

The mechanisms behind this phenomenon include:

• Vortex Formation: The formation of a prominent stationary circular particle current or vortex is observed. This vortex develops at the base of the meniscus and is vital for the pronounced capillary rise seen in these systems. The size and strength of these vortices increase with the activity of the ABPs.
• Wall Confinement Effects: In the absence of inter-particle interactions, it is revealed that ABPs can still form symmetric current patterns within their confining boundaries. Under the influence of gravity, these patterns morph significantly, leading to two predominant vortices near walls.

Quantitative Results

The analysis indicates that:

• Meniscus Height: The height of the meniscus increases algebraically with the activity of the system, characterized by the swimming Péclet number, Pe_s. Higher activity levels result in more pronounced wall wetting.
• Current Circulation: The strength of the vortices, quantified by integrals over curl amplitudes, also scales with the swimming activity, showcasing a critical link between particle self-propulsion and emergent flow structures.

Theoretical and Practical Implications

From a theoretical standpoint, this study enhances the understanding of non-equilibrium phenomena in active matter. The results illustrate how stationary probability currents—a hallmark of systems away from equilibrium—manifest as real-space particle flows in confined geometries. Such insights could be pivotal in designing active systems where control of movement and spatial organization is required.

Practically, the findings offer predictive means to observe similar behaviors in experimental setups involving active colloids. Given this system's relation to biological analogs (e.g., beneath cell layer dynamics), potential applications could span fields from materials science to biological physics, particularly in developing systems that exploit these active flow properties for transport or mixing at small scales.

Future Directions

Further exploration could investigate the impact of varying boundary shapes and conditions on vortex formation in sedimenting active matter. Additionally, integrating hydrodynamic interactions or more complex particle shapes could yield results more aligned with natural systems or specialized industrial applications. Future research may also explore exploring entropic considerations, to quantitatively connect current strengths with entropy production rates in such dynamic systems. Moreover, extending these studies to 3D geometries and exploring the role of rotational dynamics could provide further insights into the complex behaviors of active fluids.