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.

Highlights

  • Computer simulations show that our obtained local stress expression agrees quantitatively with the corresponding global stress expression of an ABP system confined between walls for both, non-interacting ABPs as well as ABPs interacting via a Lennard-Jones potential

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Summary

FiriΛi γ

We neglect terms with the averages 〈ΓiriΛi〉; these averages vanish as long as inertia (cf. Eq (1)) is taken into account. This is expected by the equivalence of the stress expressions (21) and (25). Simulation results for the local interparticle force (18), local active (19), and global stress of ABP systems with excluded-volume interactions are depicted in Fig. 5(a) as function of the packing fraction φ. This result confirms that the derived expression is suitable for calculating local stress even in inhomogeneous systems

Summary and Conclusions
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