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<p>Understanding how active particles transport in structurally heterogeneous environments is a fundamental and challenging problem, with relevance to biological and synthetic microswimmers in tissues and porous media. Here, using granular experiments and computer simulations, we investigate the long-time diffusion of active tracers in quasi-two-dimensional heterogeneous media. We show that diffusion-structure relations established for passive systems fail to describe active transport across different activity levels. To resolve this, we formulate a modified diffusion-structure relation by incorporating the dimensionless persistence length <i>Q</i>&#xa0;=&#xa0;<i>v</i><sub><i>d</i></sub><i>τ</i><sub><i>r</i></sub>/<i>d</i><sub><i>t</i></sub>, which captures the activity-induced extension of the effective interaction range. The proposed relation yields a consistent collapse within both experimental and simulation datasets across active and passive tracers, diverse environmental structures, and propulsion mechanisms. Our results thus provide a universal predictive framework for transport in non-equilibrium heterogeneous systems.</p>

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A universal scaling law for active diffusion in complex media

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月30日

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  • Qun Zhang,
  • Yuxin Tian,
  • Xue Zhang,
  • Xiaoting Yu,
  • Hongwei Zhu,
  • Ning Zheng,
  • Luhui Ning,
  • Ran Ni,
  • Mingcheng Yang,
  • Peng Liu

摘要

Understanding how active particles transport in structurally heterogeneous environments is a fundamental and challenging problem, with relevance to biological and synthetic microswimmers in tissues and porous media. Here, using granular experiments and computer simulations, we investigate the long-time diffusion of active tracers in quasi-two-dimensional heterogeneous media. We show that diffusion-structure relations established for passive systems fail to describe active transport across different activity levels. To resolve this, we formulate a modified diffusion-structure relation by incorporating the dimensionless persistence length Q = vdτr/dt, which captures the activity-induced extension of the effective interaction range. The proposed relation yields a consistent collapse within both experimental and simulation datasets across active and passive tracers, diverse environmental structures, and propulsion mechanisms. Our results thus provide a universal predictive framework for transport in non-equilibrium heterogeneous systems.