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Periodic Precipitation in Hele-Shaw Cells: Mechanism Insights from Experiments and Numerical Simulation Considering
Nobuhiko J Suematsu1,2, Yuhei Onishi1, Masaki Itatani3
1Graduate School of Advanced Mathematical Sciences, Meiji University, 4-21-1, Nakano, Tokyo 164-8525, Japan.
Langmuir : the ACS Journal of Surfaces and Colloids
|November 13, 2025
Summary
This study introduces a Hele-Shaw cell for creating Liesegang patterns without gels. The gap thickness critically controls pattern formation, with a new model explaining precipitate band spacing via nucleation rates.
Area of Science:
- Physical Chemistry
- Materials Science
- Chemical Engineering
Background:
- Liesegang patterns are self-organized precipitate structures.
- Traditional gel-based methods have limitations like undesired chemical interactions.
- A gel-free approach is needed for simplified Liesegang pattern formation.
Purpose of the Study:
- To develop a gel-free method for producing Liesegang patterns using a Hele-Shaw cell.
- To identify critical gap thickness thresholds for flow inhibition and band formation.
- To develop and validate a mathematical model for Liesegang pattern formation based on microscopic dynamics.
Main Methods:
- Utilized a Hele-Shaw cell with a controlled gap (30-225 μm) between glass plates.
- Investigated aqueous solutions of copper(II) chloride (CuCl₂) and potassium chromate (K₂CrO₄).
- Developed a mathematical model based on precipitation dynamics and nucleation rates.
Main Results:
- Identified critical gap thresholds of 110 μm (flow inhibition) and 150 μm (band formation).
- Observed that precipitate band spacing increases with gap thickness below the flow inhibition threshold.
- Numerical simulations confirmed nucleation rate's inverse effect on band spacing, linked to surface area.
Conclusions:
- The Hele-Shaw cell offers a simplified, gel-free method for Liesegang pattern generation.
- The proposed mathematical model accurately reproduces thickness-dependent band spacing.
- This research advances understanding of self-organization phenomena and potential applications.
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