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Scalar φ4 field theory for active-particle phase separation

Author

Listed:
  • Raphael Wittkowski

    (SUPA, School of Physics and Astronomy, University of Edinburgh)

  • Adriano Tiribocchi

    (SUPA, School of Physics and Astronomy, University of Edinburgh)

  • Joakim Stenhammar

    (SUPA, School of Physics and Astronomy, University of Edinburgh)

  • Rosalind J. Allen

    (SUPA, School of Physics and Astronomy, University of Edinburgh)

  • Davide Marenduzzo

    (SUPA, School of Physics and Astronomy, University of Edinburgh)

  • Michael E. Cates

    (SUPA, School of Physics and Astronomy, University of Edinburgh)

Abstract

Recent theories predict phase separation among orientationally disordered active particles whose propulsion speed decreases rapidly enough with density. Coarse-grained models of this process show time-reversal symmetry (detailed balance) to be restored for uniform states, but broken by gradient terms; hence, detailed-balance violation is strongly coupled to interfacial phenomena. To explore the subtle generic physics resulting from such coupling, we here introduce ‘Active Model B’. This is a scalar φ4 field theory (or phase-field model) that minimally violates detailed balance via a leading-order square-gradient term. We find that this additional term has modest effects on coarsening dynamics, but alters the static phase diagram by creating a jump in (thermodynamic) pressure across flat interfaces. Both results are surprising, since interfacial phenomena are always strongly implicated in coarsening dynamics but are, in detailed-balance systems, irrelevant for phase equilibria.

Suggested Citation

  • Raphael Wittkowski & Adriano Tiribocchi & Joakim Stenhammar & Rosalind J. Allen & Davide Marenduzzo & Michael E. Cates, 2014. "Scalar φ4 field theory for active-particle phase separation," Nature Communications, Nature, vol. 5(1), pages 1-9, September.
    • Handle: RePEc:nat:natcom:v:5:y:2014:i:1:d:10.1038_ncomms5351
    DOI: 10.1038/ncomms5351
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    Cited by:

    1. Feng Lin & Xia Li & Shiyu Sun & Zhongyi Li & Chenglin Lv & Jianbo Bai & Lin Song & Yizhao Han & Bo Li & Jianping Fu & Yue Shao, 2023. "Mechanically enhanced biogenesis of gut spheroids with instability-driven morphomechanics," Nature Communications, Nature, vol. 14(1), pages 1-15, December.
    2. Hantaek Bae, 2020. "Global existence of solutions to some equations modeling phase separation of self-propelled particles," Partial Differential Equations and Applications, Springer, vol. 1(6), pages 1-26, December.
    3. Kang Zhang & Wen-Si Hu & Quan-Xing Liu, 2020. "Quantitatively Inferring Three Mechanisms from the Spatiotemporal Patterns," Mathematics, MDPI, vol. 8(1), pages 1-13, January.
    4. Dolachai Boniface & Sergi G. Leyva & Ignacio Pagonabarraga & Pietro Tierno, 2024. "Clustering induces switching between phoretic and osmotic propulsion in active colloidal rafts," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    5. Antonio Lamura & Adriano Tiribocchi, 2021. "Shearing Effects on the Phase Coarsening of Binary Mixtures Using the Active Model B," Mathematics, MDPI, vol. 9(23), pages 1-13, November.
    6. Bae, Hantaek, 2023. "Global existence of unique weak solutions and decay rates of Active model B with the logarithmic Cahn–Hilliard equation in Wiener space," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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