Capillary Interfacial Tension in Active Phase Separation

Abstract

In passive fluid-fluid phase separation, a single interfacial tension sets both the capillary fluctuations of the interface and the rate of Ostwald ripening. We show that these phenomena are governed by two different tensions in active systems, and compute the capillary tension σcw which sets the relaxation rate of interfacial fluctuations in accordance with capillary wave theory. We discover that strong enough activity can cause negative σcw. In this regime, depending on the global composition, the system self-organizes, either into a microphase-separated state in which coalescence is highly inhibited, or into an 'active foam' state. Our results are obtained for Active Model B+, a minimal continuum model which, although generic, admits significant analytical progress.

Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production

“…Extensions of Model B have recently played a crucial role in understanding phase separation in active systems. In the simplest setting [ 10 , 31 , 32 , 33 ], these theories only retain the evolution of the density field , while hydrodynamic [ 34 , 35 ] or polar [ 36 , 37 ] fields can be added if the phenomenology requires. The top-down construction of these field theories, via conservation laws and symmetry arguments, closely retraces the path leading to Model B for passive phase separation [ 7 ].…”

Intrinsic structure perspective for MIPS interfaces in two-dimensional systems of active Brownian particles

“…However, a clear agreement has not been reached on the physical properties such as the surface tension. 3,31–35 The main reason behind this disagreement can be summarised as the difference between considering activity that gives rise to a spatially uniform stress (the swim pressure 36–38 ) or activity that gives rise to a spatially varying body force. 3,39…”

“…However, a clear agreement has not been reached on the physical properties such as the surface tension. 3,[31][32][33][34][35] The main reason behind this disagreement can be summarised as the difference between considering activity that gives rise to a spatially uniform stress (the swim pressure [36][37][38] or activity that gives rise to a spatially varying body force. 3,39 Even though the swim pressure has been successfully used to determine the onset of MIPS, 21,[40][41][42][43][44][45] when dealing with localised phenomena, adding the swim pressure to the total pressure results in a negative surface tension, that in equilibrium phase coexistence would imply an unstable interface.…”

Intrinsic structure perspective for MIPS interfaces in two dimensional systems of Active Brownian Particles

“…Trying to understand this non-equilibrium phase separation via a mechanical equation of state, one could draw similarities with the interfacial properties of equilibrium phases. However, a clear agreement has not been reached on the physical properties such as the surface tension [3,[31][32][33][34][35]. The main reason behind the disagreement can be summarised in the difference between considering activity giving rise to a spatially uniform stress (the swim pressure [36][37][38]) or activity giving rise to a spatially varying body force [3,39].…”

“…The authors of Ref. [34] have recently demonstrated, for a minimum continuum active model, how a negative capillary tension may result into a microphase-separated state or into an active foam state, rather than the MIPS of a large dense cluster.…”