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Updated: Sep 11, 2025
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The Diffusion of Passive Tracers in Laminar Shear Flow
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Anomalous transport models for fluid classification: insights from an experimentally driven approach
Sara Bernardi1,2, Paolo Begnamino3, Marco Pizzi3
1Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy.
Discover Nano
|August 11, 2025
Summary
This study explores electrical transport in micro-gap sensors using mathematical models. The Gaussian Model with a Time-Dependent Diffusion Coefficient best describes anomalous diffusion phenomena, enabling accurate fluid classification.
Area of Science:
- Nanoscale science and technology
- Electrical transport phenomena
- Anomalous diffusion in low-dimensional systems
Background:
- Electrical transport is crucial in nanoscale research.
- Anomalous behaviors in low-dimensional systems present a descriptive challenge.
- Micro-gap sensors immersed in fluids exhibit complex transport properties.
Purpose of the Study:
- To investigate the electrical discharge transport properties in micro-gap sensors across various fluid insulating properties.
- To identify the most effective mathematical model for describing anomalous transport phenomena.
- To develop a data-driven approach for fluid classification based on electrical discharge characteristics.
Main Methods:
- Synergistic combination of experimental data collection and mathematical modeling.
- Calibration and performance analysis of four partial differential equation models: Gaussian Model with Time Dependent Diffusion Coefficient, Porous Medium Equation, Kardar-Parisi-Zhang Equation, and Telegrapher Equation.
- Data fitting techniques to evaluate model accuracy in describing observed electrical discharge behaviors.
Main Results:
- The Gaussian Model with a Time-Dependent Diffusion Coefficient demonstrated superior performance in describing the experimental data.
- This model accurately characterized electrical discharge transport across a spectrum of insulating and conductive fluids.
- The model successfully reproduced diverse behaviors, including clogging and bursts, facilitating fluid classification.
Conclusions:
- The Gaussian Model with a Time-Dependent Diffusion Coefficient is highly effective for characterizing electrical discharges in various fluids.
- The data-driven mathematical modeling approach shows significant potential for accurately predicting and classifying fluids with unknown insulating properties.
- This methodology offers a promising tool for analyzing complex fluid behaviors through electrical transport measurements.
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