Hierarchical microphase separation in non-conserved active mixtures

Abstract

Non-equilibrium phase separating systems with reactions, such as biomolecular condensates and bacteria colonies, can break time-reversal symmetry (TRS) in two distinct ways. Firstly, the conservative and non-conservative sectors of the dynamics can be governed by incompatible free energies; when both sectors are present, this is the leading-order TRS violation, captured in its simplest form by ‘Model AB’. Second, the diffusive dynamics can break TRS in its own right. This happens only at higher order in the gradient expansion (but is the leading behaviour without reactions present) and is captured by ‘Active Model B+’ (AMB+). Each of the two mechanisms can lead to microphase separation, by quite different routes. Here we introduce Model AB+, for which both mechanisms are simultaneously present, and show that for slow reaction rates the system can undergo a new type of hierarchical microphase separation, which we call ‘bubbly microphase separation’. In this state, small droplets of one fluid are continuously created and absorbed into large droplets, whose length-scales are controlled by the competing reactive and diffusive dynamics.

Hierarchical defect-induced condensation in active nematics

“…As we discuss in more detail below, part of the system's dynamics can be understood in terms of two separate effective free-energy functionals for the non-conservative Q -tensor () and the conservative density field (), similar to related nonequilibrium models discussed recently. 34…”

“…As we discuss in more detail below, part of the system's dynamics can be understood in terms of two separate effective free-energy functionals for the non-conservative Q-tensor (F Q ) and the conservative density field (F F ), similar to related nonequilibrium models discussed recently. 34 Mass-conservation requires that the density obeys a continuity equation q t f = Àq i J i . In general, for symmetry reasons, the current must be the gradient of a scalar quantity and a tensorial quantity containing the Q-tensor.…”

Formation of dissipative structures in microscopic models of mixtures with species interconversion

“…In this form, Eq. 3 is similar to the continuity equations used to describe the dynamic behavior in active matter systems ( 10 , 32 , 43 , 44 ). However, we note that our work is different from other studies of active matter systems as we explicitly consider the evolution of the system toward equilibrium and the behavior at equilibrium.…”

“…Nonequilibrium microphase separation could exist in a wide class of systems, including “active matter systems,” a recent focus of theoretical and experimental studies ( 15 , 45 ), as well as biomolecular condensates (e.g. membraneless organelles), where natural interconversion could be caused by mechanisms like polymerization, protein folding-unfolding, and self-assembly, while forced interconversion could be generated by the nonequilibrium environment of the cell ( 32 , 44 – 53 ). The developed approach could be applicable to understanding and quantitatively describing these phenomena.…”

“…Previous theoretical studies of phase separation in chemically reactive binary mixtures have demonstrated that the formation of steady-state dissipative structures (in systems with a simple A ⇌ B interconversion reaction) is only possible under nonequilibrium conditions ( 10 , 20 , 29 ). In their seminal work, utilizing a scalar field theoretical approach, Li and Cates have shown that different kinds of steady-state structures may be formed in a nonequilibrium system with a combination of diffusion and chemical-reaction dynamics ( 10 , 32 ). In our work, we study the formation of nonequilibrium dissipative structures by investigating three nonequilibrium microscopic models of phase-separating binary systems with mixed dynamics.…”