Local stress and pressure in an inhomogeneous system of spherical active Brownian particles

Abstract

The stress of a fluid on a confining wall is given by the mechanical wall forces, independent of the nature of the fluid being passive or active. At thermal equilibrium, an equation of state exists and stress is likewise obtained from intrinsic bulk properties; even more, stress can be calculated locally. Comparable local descriptions for active systems require a particular consideration of active forces. Here, we derive expressions for the stress exerted on a local volume of a systems of spherical active Brownian particles (ABPs). Using the virial theorem, we obtain two identical stress expressions, a stress due to momentum flux across a hypothetical plane, and a bulk stress inside of the local volume. In the first case, we obtain an active contribution to momentum transport in analogy to momentum transport in an underdamped passive system, and we introduce an active momentum. In the second case, a generally valid expression for the swim stress is derived. By simulations, we demonstrate that the local bulk stress is identical to the wall stress of a confined system for both, non-interacting ABPs as well as ABPs with excluded-volume interactions. This underlines the existence of an equation of state for a system of spherical ABPs. Most importantly, our calculations demonstrated that active stress is not a wall (boundary) effect, but is caused by momentum transport. We demonstrate that the derived stress expression permits the calculation of the local stress in inhomogeneous systems of ABPs.

A minimal model for structure, dynamics, and tension of monolayered cell colonies

“…Figure 3a shows that the averaged local polarization is zero inside the colony, but points outwards at the boundary. This is in contrast to what is typically found for motility-induced clustering 25,28,[42][43][44] . The reason is that the attractive interactions keep outward-oriented particles at the boundary of the colony-which would otherwise move away-combined with the fluidity of the colony which allows local particle sorting near the boundary, similar to the behavior of isolated self-propelled particles in confinement 41,45 .…”

Computational models for active matter

“…While non-equilibrium active systems usually lack a free energy and equations of state, spherical ABPs are a notable exception. Analytical considerations and simulations yield a pressure equation of state in this case [31,[33][34][35][36]; however, such equation does not exist for nonspherical, elongated ABPs [34].…”

“…Active particles, even with purely repulsive interactions, exhibit novel features, such as motility-induced phase separation (MIPS) [4,5,[21][22][23][24][25][26][27][28], wall accumulation [29][30][31], capillary action in spite of wall-particle repulsion [32], and an active pressure (denoted as swim pressure) [31,[33][34][35][36]. Intuitively, the separation into dense and dilute regions of ABPs is explained by a positive feedback between blocking of persistent particle motion by steric interactions, and an enhanced probability of collisions with further particles at sufficiently large concentrations.…”

Inertial effects of self-propelled particles: From active Brownian to active Langevin motion

“…In case the orientational relaxation is fast, τ r → 0, one may consider the limit of vanishing moment of inertia, J = 0 which was assumed in several recent studies [56][57][58]61 . Correspondigly there is also a second time, the translational relaxation time,…”