Abstract
The pressure of suspensions of self-propelled objects is studied theoretically and by simulation of spherical active Brownian particles (ABPs). We show that for certain geometries, the mechanical pressure as force/area of confined systems can be equally expressed by bulk properties, which implies the existence of a nonequilibrium equation of state. Exploiting the virial theorem, we derive expressions for the pressure of ABPs confined by solid walls or exposed to periodic boundary conditions. In both cases, the pressure comprises three contributions: the ideal-gas pressure due to white-noise random forces, an activity-induced pressure ("swim pressure"), which can be expressed in terms of a product of the bare and a mean effective particle velocity, and the contribution by interparticle forces. We find that the pressure of spherical ABPs in confined systems explicitly depends on the presence of the confining walls and the particle-wall interactions, which has no correspondence in systems with periodic boundary conditions. Our simulations of three-dimensional ABPs in systems with periodic boundary conditions reveal a pressure-concentration dependence that becomes increasingly nonmonotonic with increasing activity. Above a critical activity and ABP concentration, a phase transition occurs, which is reflected in a rapid and steep change of the pressure. We present and discuss the pressure for various activities and analyse the contributions of the individual pressure components.
Highlights
Living matter composed of active particles, which convert internal energy into systematic translational motion, is a particular class of materials typically far from equilibrium
Since the surface element is small, the vector ri is essentially the same for all particles interacting with DS and can be replaced by the vector r of that element
The same applies to the normal ni, i.e., ni = n, where n is the local normal at DS
Summary
Living matter composed of active particles, which convert internal energy into systematic translational motion, is a particular class of materials typically far from equilibrium. As an important first step, we demonstrate that the mechanical pressure of a confined fluid can be equivalently represented by the virial of the surface forces for particular geometries such as a cuboid and a sphere. This has important implications, since it provides a relation of the mechanical. By Brownian dynamics simulations, we determine pressure– concentration relationships of active Brownian particles in three-dimensional periodic systems for various propulsion velocities. Appendix D establishes the relation between the mechanical pressure and the surface virial for active systems.
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