Abstract
We derive a microscopic expression for a quantity μ that plays the role of chemical potential of active Brownian particles (ABPs) in a steady state in the absence of vortices. We show that μ consists of (i) an intrinsic chemical potential similar to passive systems, which depends on density and self-propulsion speed, but not on the external potential, (ii) the external potential, and (iii) a newly derived one-body swim potential due to the activity of the particles. Our simulations on ABPs show good agreement with our Fokker–Planck calculations, and confirm that is spatially constant for several inhomogeneous active fluids in their steady states in a planar geometry. Finally, we show that phase coexistence of ABPs with a planar interface satisfies not only mechanical but also diffusive equilibrium. The coexistence can be well-described by equating the bulk chemical potential and bulk pressure obtained from bulk simulations for systems with low activity but requires explicit evaluation of the interfacial contributions at high activity.
Highlights
The non-equilibrium phase behavior of active Brownian particles (ABPs), which constantly convert energy into directed motion, has received considerable attention in recent years
Our Fokker–Planck approach is similar in spirit to that of [9, 26], but defines an expression for the local chemical potential in terms of the new concept of a ‘swim potential’, which is well-defined in planar geometries and curl-free particle fluxes and which may contribute, in these cases, to formulating a theoretical framework
We derive a microscopic expression for the local chemical potential m (z) of ABPs in a spatially inhomogeneous steady state in a planar geometry, for simplicity, with z the normal Cartesian direction
Summary
The non-equilibrium phase behavior of active Brownian particles (ABPs), which constantly convert energy into directed motion, has received considerable attention in recent years. The authors of [12] even proceed and calculate spinodals and binodals on the basis of either a Gibbs–Duhem-like equation or a free energy for the (realistic) case of an incompressible solvent Later, it was argued in [9] that a Maxwell construction on the simulated equation of state does not yield the simulated coexistence densities. Our Fokker–Planck approach is similar in spirit to that of [9, 26], but defines an expression for the local chemical potential in terms of the new concept of a ‘swim potential’, which is well-defined in planar geometries and curl-free particle fluxes and which may contribute, in these cases, to formulating a theoretical framework. We conclude that the swim potential and the chemical potential m (z) is not a state function of the density for a macroscopic system
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