Sedimentation equilibrium as a probe of the pressure equation of state of active colloids

TL;DR

This paper develops a theoretical and computational method to determine the pressure equation of state of active colloids from sedimentation profiles, enabling better understanding and prediction of active matter systems.

Contribution

It introduces a novel approach to extract the pressure EoS of active suspensions from sedimentation profiles using exact mechanical considerations.

Findings

Pressure can be derived from sedimentation profiles in active Brownian particles.

Sedimentation-derived EoS matches results from periodic simulations.

Framework provides a direct, measurable way to characterize active matter.

Abstract

We introduce a theoretical and computational framework for extracting the pressure equation of state (EoS) of an active suspension from its steady-state sedimentation profile. As EoSs are prerequisites for many theories in active matter, determining how pressure depends on key parameters such as density, activity, and interparticle interactions is essential to make quantitative predictions relevant to materials design and engineering applications. Focusing on the one-dimensional active Brownian particle (1D-ABP) model, we show that the pressure measured in a homogeneous periodic system can be recovered from the spatial profiles established in sedimentation equilibrium. Our approach is based on exact mechanical considerations and provides a direct route for determining pressure from experimentally measurable quantities. This work compares sedimentation-derived equations of state with those obtained from periodic simulations, establishing a foundation for using sedimentation as a generic tool to characterize the behavior of active suspensions.