Theory of capillary tension and interfacial dynamics of motility-induced phases

Journal Article · 12 November 2024 · Physical Review. E

DOI: https://doi.org/10.1103/physreve.110.054604 · OSTI ID:2481485

Langford, Luke  ^[1]; Omar, Ahmad K.  ^[2]

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1. Univ. of California, Berkeley, CA (United States)
2. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

The statistical mechanics of equilibrium interfaces has been well-established for over a half century. In the past decade, a wealth of observations have made increasingly clear that a new perspective is required to describe interfaces arbitrarily far from equilibrium. In this work, beginning from microscopic particle dynamics that break time-reversal symmetry, we derive the linear interfacial dynamics of coexisting motility-induced phases. Doing so allows us to identify the athermal energy scale that excites interfacial fluctuations and the nonequilibrium surface tension that resists these excitations. Our theory identifies that, in contrast to equilibrium fluids, this active surface tension contains contributions arising from nonconservative forces which act to suppress interfacial fluctuations and, crucially, is distinct from the mechanical surface tension of Kirkwood and Buff. Here we find that the interfacial stiffness scales linearly with the intrinsic persistence length of the constituent active particle trajectories, in agreement with simulation data. We demonstrate that at wavelengths much larger than the persistence length, the interface obeys surface-area minimizing Boltzmann statistics with our derived nonequilibrium interfacial stiffness playing a role identical to that of equilibrium systems.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Laboratory Directed Research and Development (LDRD) Program
• Grant/Contract Number: SC0024900; AC02-05CH11231
• OSTI ID: 2481485
• Journal Information: Physical Review. E, Journal Name: Physical Review. E Journal Issue: 5 Vol. 110; ISSN 2470-0045
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English