Abstract
Active Brownian particles display self-propelled movement, which can be modelled as arising from a one-body force. Although their interparticle interactions are purely repulsive, for strong self-propulsion, the swimmers phase separate into dilute and dense phases. We describe in detail a recent theory for such motility induced phase-separation. Starting from the continuity equation and the force density balance, the description is based on four superadiabatic contributions to the internal force density. Here the superadiabatic forces are due to the flow in the system and they act on top of the adiabatic forces that arise from the equilibrium free energy. Phase coexistence is described by bulk state functions and agrees quantitatively with Brownian dynamics simulation results from the literature. We describe in detail all analytical steps to fully resolve the spatial and orientational dependence of the one-body density and current. The decomposition into angular Fourier series leads to coupling of total density, polarisation and all higher modes. We describe the power functional approach, including the kinematic dependence of the superadiabatic force fields and the quiet life effect that pushes particles from fast to slow regions and hence induces the phase separation.
Acknowledgments
This paper is dedicated to the memory of Gerhard Findenegg. The authors would like to thank Philip Krinninger, Jeroen Rodenburg, Siddarth Paliwal, Marjolein Dijkstra, René van Roij, René Wittmann, Hartmut Löwen, Thomas Speck, Sven Auschra, Klaus Kroy, Victor Holubec, Nicola Söker, Frank Cichos, Gerhard Gompper, Grzegorz Szamel, Julien Tailleur, Martin Oettel, Bob Evans, Joseph Brader, and Thomas Fischer for inspiring comments and useful discussions. Umberto Marconi is thanked for pointing out typo-graphical errors in two equations.
Disclosure statement
No potential conflict of interest was reported by the authors.