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Beyond Murray's Law: Resistance Matching Principle for Optimal Fluid Transport in Hierarchical Nanomaterials
Jian Cao1,2, Xueting Deng1,2, Zehui Liu1,2
1State Key Laboratory of Materials-Oriented and Chemical Engineering, Nanjing Tech University, Nanjing 211816, China.
ACS Nano
|January 7, 2026
Summary
Murray's law, a century-old principle for biological transport, is updated for nanoscale engineering. This revised law accounts for fluid slip and confinement, enabling better design of hierarchical nanomaterials for diverse applications.
Area of Science:
- Nanotechnology
- Fluid Dynamics
- Thermodynamics
Background:
- Murray's law, established for biological vascular systems, guides hierarchical nanomaterial design.
- Nanoscale fluid behavior deviates from classical assumptions due to slip and confinement effects.
Purpose of the Study:
- To extend Murray's law for nanoscale applications by incorporating fluid slip and confinement.
- To establish a generalized resistance matching principle for designing hierarchical nanomaterials.
Main Methods:
- Quantitative calculations integrating slip boundary conditions and confinement effects.
- Experimental validation in carbon and zeolite nanosystems.
Main Results:
- Demonstrated a transition from viscous flow to slip-driven transport at the nanoscale.
- Identified significant deviations from classical Murray's law predictions at the nanoscale.
- Validated the generalized resistance matching principle in diverse nanosystems.
Conclusions:
- The adapted Murray's law and resistance matching principle offer a framework for rational nanomaterial engineering.
- This work bridges biological principles with nanofluidics, impacting catalysis, membranes, and energy storage.
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