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Self-Organized Homogenization of Flow Networks

Julien Bouvard1,*, Swarnavo Basu2,*, Charlott Leu3, Onurcan Bektas2,3,4, Joachim O. Rädler3, Gabriel Amselem1,†, and Karen Alim2,‡

  • *These authors contributed equally to this work.
  • †Contact author: gabriel.amselem@polytechnique.edu
  • ‡Contact author: k.alim@tum.de
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Phys. Rev. X 15, 041038 – Published 26 November, 2025

DOI: https://doi.org/10.1103/j5ch-4vkh

Abstract

From the vasculature of animals to the porous media making up batteries, the core task of flow networks is to transport solutes and perfuse all cells or media equally with resources. Yet, living flow networks have a key advantage over porous media: They are adaptive, and they self-organize their geometry for homogeneous perfusion throughout the network. Here, we show that artificial flow networks can also self-organize toward homogeneous perfusion by the versatile adaption of controlled erosion. Flowing a pulse of cleaving enzyme through a network patterned into an erodible hydrogel, with initial channels disparate in width, we observe a homogenization in channel resistances. Experimental observations are matched with numerical simulations of the diffusion-advection-sorption dynamics of an eroding enzyme within a network. Analyzing transport dynamics theoretically, we show that homogenization only occurs if the pulse of the eroding enzyme lasts longer than the time it takes any channel to equilibrate to the pulse concentration. The equilibration time scale derived analytically is in agreement with simulations. Lastly, we show both numerically and experimentally that erosion leads to the homogenization of complex networks containing loops. Erosion being an omnipresent reaction, our results pave the way for a very versatile self-organized increase in the performance of porous media.

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Popular Summary

Flow networks—from animal blood vessels to the porous structures inside batteries—share a common goal: to deliver fluids or solutes evenly throughout their systems. Living networks naturally adjust their architecture to maintain uniform flow, but artificial networks typically lack this self-organizing ability. In this study, we demonstrate a simple yet powerful method to help inanimate flow networks achieve similar self-organization using controlled pulsing of an erosive chemical. This approach allows the network to restructure itself so that all channels carry fluid more evenly, improving overall performance.

We create flow networks patterned into erodible hydrogels and introduce a pulse of a cleaving enzyme that gradually dissolves the material. Over time, the resistances of individual channels become more balanced, leading to more uniform flow. Using simulations to describe these experiments, we find that successful homogenization occurs only when the enzyme pulse lasts longer than the time it takes fluid in each channel to reach equilibrium. From this, we derive a simple analytical rule that predicts how long a pulse must last to achieve homogenization. Applying this rule, we can balance flow even in complex networks that contain multiple loops.

Our findings reveal a general strategy for reducing disorder in artificial flow networks through erosion-driven self-organization. Because this mechanism depends only on basic material and flow properties, it can be applied broadly to systems made from erodible materials. This principle could guide the design of next-generation porous materials and devices, including more efficient batteries, reactors, and filtration systems.

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Phys. Rev. X 15, 041038– Published 26 November, 2025
  • Received 4 April 2025
  • Accepted 3 November 2025
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