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  • Letter
  • Open Access

Self-organized criticality driven by droplet influx and random fusion

Bohan Lyu1 and Jie Lin1,2,*

  • 1Peking-Tsinghua Center for Life Sciences, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871, China
  • 2Center for Quantitative Biology, Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871, China

  • *Contact author: linjie@pku.edu.cn
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Phys. Rev. Research 7, L022060 – Published 9 June, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L022060

Abstract

The droplet size distribution typically decays exponentially in solutions formed by liquid-liquid phase separation. Nevertheless, a power-law distribution of nucleolus volumes has been observed in amphibian oocytes, which appears similar to the cluster size distribution in reaction-limited aggregation. In this work, we study the mechanism of power-law distributed droplet sizes and unveil a self-organized criticality driven by droplet influx and random fusion between droplets. Surprisingly, the droplet size dynamics is governed by a Smoluchowski equation similar to the cluster size in aggregation systems. The system reaches a critical state as the area fraction approaches the critical value at which the droplet size has a power-law distribution with an exponent of 1.5. The system is also spatially scale-free, with a divergent correlation length at the critical state, marked by giant droplet-density fluctuations and power-law decay of the pair correlation function.

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Phys. Rev. Research 7, L022060– Published 9 June, 2025
  • Received 17 February 2025
  • Accepted 23 May 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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