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Conduction in heterogeneous systems in the low-frequency regime: variational principles and boundary integral
Francisco J Solis1, Vikram Jadhao2
1School of Mathematical and Natural Sciences, Arizona State University, Glendale, AZ, 85306, USA. francisco.solis@asu.edu.
The European Physical Journal. E, Soft Matter
|September 27, 2024
Summary
This study introduces a new method to analyze heterogeneous materials using dynamic charge at interfaces. This approach simplifies understanding the electrical properties of complex systems like biological tissues and colloidal suspensions.
Area of Science:
- Electromagnetism and Materials Science
- Computational Physics and Engineering
Background:
- Homogeneous materials' response to low-frequency electric fields is defined by complex conductivity.
- Heterogeneous systems' properties depend on constituent components and their arrangement.
- Examples include colloidal suspensions, electrolytes, and biological tissues.
Purpose of the Study:
- To develop a method for characterizing heterogeneous systems using dynamic interfacial charge.
- To express key system properties through this fundamental variable.
- To derive and solve boundary integral equations for charge behavior.
Main Methods:
- Formulation of boundary integral equations for interfacial charges.
- Reconstruction of potentials and fields from solved charge distributions.
- Application of a variational principle to derive system equations.
- Numerical solution using the finite element method.
Main Results:
- A framework is established to describe heterogeneous systems via dynamic interfacial charge.
- Boundary integral equations for charges are derived and solved.
- The variational principle recovers fundamental equations and relates to dissipated power.
Conclusions:
- Dynamic interfacial charge is a powerful variable for analyzing complex materials.
- The derived boundary integral equation method is effective for various heterogeneous systems.
- This approach offers insights into electrical properties and energy dissipation.
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