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Abstract:

We investigate the self-diffusiophoretic motion of a catalytically active spherical particle confined within a wedge-shaped domain. Using the Fourier-Kontorovich-Lebedev transform, we solve the Laplace equation for the concentration field in the diffusion-dominated regime. The method of images is employed to obtain the first and second reflections of the concentration field, accounting for both monopole and dipole contributions of the particle's surface activity. Based on these results, we derive leading-order expressions for the self-induced phoretic velocity in the far-field limit and examine how it varies with the wedge opening angle and the particle's position within the domain. We focus on the contributions to the phoretic velocities arising from phoretic interactions, without accounting for hydrodynamic effects. Our findings reveal that the wedge geometry significantly affects both the magnitude and direction of particle motion. Our study provides a systematic framework for calculating the contributions to the phoretic velocity arising from concentration disturbances near corners, with implications for microfluidic design and control of autophoretic particles in confined geometries.

Abstract:

Proliferation and motility are ubiquitous drivers of activity in biological systems. Here, we study a dense binary mixture of motile and proliferating particles with exclusively repulsive interactions, where homeostasis in the proliferating subpopulation is maintained by pressure-induced removal. Using numerical simulations, we show that phase separation emerges naturally in this system at high density and weak enough self-propulsion. We map the full two-component system to an effective single-component active Brownian particle model that recapitulates this behavior. This allows us to identify the emergent effects of the proliferating matrix on motile particles that interact to produce phase separation: enhanced diffusion, renormalized self-propulsion, reduced persistence, and an effective attraction between motile particles. Our results establish a specific type of phase transition based on these emergent effects and pave a way to reinterpret the physics of dense cellular populations, such as bacterial colonies or tumors, as systems of mixed active matter.

Abstract:

The stochastic dynamics of tracers arising from hydrodynamic fluctuations in a driven electrolyte is studied using a self-consistent field-theory framework in all dimensions. A plethora of scaling behavior that includes two distinct regimes of anomalous diffusion is found, and the crossovers between them are characterized in terms of the different tuning parameters. A short-time ballistic regime is found to be accessible beyond two dimensions, whereas a long-time diffusive regime is found to be present only at four dimensions and above. The results showcase how long-ranged hydrodynamic interactions can dominate the dynamics of nonequilibrium steady states in ionic suspensions and produce strong fluctuations despite the presence of Debye screening.

Abstract:

Interactions between active particles may be non-reciprocal, breaking action-reaction symmetry and leading to novel physics not observed in equilibrium systems. The non-reciprocal Cahn–Hilliard (NRCH) model is a phenomenological model that captures the large-scale effects of non-reciprocity in conserved, phase-separating systems. In this work, we explore the consequences of different variations of this model corresponding to different symmetries, inspired by the importance of symmetry in equilibrium universality classes. In particular, we contrast two models, one with a continuous SO(2) symmetry and one with a discrete C4 symmetry. We analyze the corresponding models by constructing three-dimensional linear stability diagrams. With this, we connect the models with their equilibrium limits, highlight the role of mean composition, and classify qualitatively different instabilities. We further demonstrate how non-reciprocity gives rise to out-of-equilibrium steady states with non-zero currents and present representative closed-form solutions that help us understand characteristic features of the models in different parts of the parameter space.