Abstract
It is known that purely repulsive self-propelled colloids can undergo bulk liquid-vapor phase separation. In experiments and large scale simulations, however, more complex steady states are also seen, comprising a dynamic population of dense clusters in a sea of vapor, or dilute bubbles in a liquid. Here we show that these microphase-separated states should emerge generically in active matter, without any need to invoke system-specific details. We give a coarse-grained description of them, and predict transitions between regimes of bulk phase separation and microphase separation. We achieve these results by extending the $\phi^4$ field theory of passive phase separation to allow for all local currents that break detailed balance at leading order in the gradient expansion. These local active currents, whose form we show to emerge from coarse-graining of microscopic models, include a mixture of irrotational and rotational contributions, and can be viewed as arising from an effective nonlocal chemical potential. Such contributions influence, and in some parameter ranges reverse, the classical Ostwald process that would normally drive bulk phase separation to completion.
Highlights
Active colloidal fluids are nonequilibrium systems in which individual particles continually consume fuel in order to self-propel [1,2]
We show that a closely related continuum description—the main difference being that mobility is not constant and that noise is multiplicative—can be obtained from explicit coarse graining of microscopic models of self-propelled particles. This result strongly suggests that the time-reversal symmetry (TRS)-breaking terms in Active Model B (AMB)+ are not forbidden by any microscopic mechanism that we might have overlooked; its prediction of reverse Ostwald regimes is generic, in the same way that Model B is generic for equilibrium binary fluid phase separation [37]
We have presented results for AMB+, a field theory that, at leading order in a gradient expansion, fully generalizes the canonical model of passive phase separation (Model B) to break time-reversal symmetry
Summary
Active colloidal fluids are nonequilibrium systems in which individual particles continually consume fuel in order to self-propel [1,2]. We show that a closely related continuum description—the main difference being that mobility is not constant and that noise is multiplicative—can be obtained from explicit coarse graining of microscopic models of self-propelled particles This result strongly suggests that the TRS-breaking terms in AMB+ are not forbidden by any microscopic mechanism that we might have overlooked; its prediction of reverse Ostwald regimes is generic, in the same way that Model B is generic for equilibrium binary fluid phase separation [37]. (These ideas are studied in a separate paper [42].) In the language of Bray [37], we are interested in phase separation in the neighborhood of the zero-temperature dynamical fixed point, where noise terms might be significant for kinetics (for instance, in allowing nucleation) but do not dominate the steady-state statistics, at least in the equilibrium case of Model B The universality of this fixed point means that qualitative predictions, such as power-law scalings in time for the mean droplet size ðR ∼ t1=3Þ, remain. Analytical results are valid in any dimension d unless otherwise specified
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