Article
| Title: | Multi-scale mathematical models for plasma-liquid interactions (English) |
| Author: | Singh, Abhisek Kumar |
| Author: | Kumar, Punit |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 71 |
| Issue: | 4 |
| Year: | 2026 |
| Pages: | 557-573 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Plasma-liquid interactions (PLIs) occur in a wide range of natural and engineered systems including biomedical sterilization, wastewater treatment, materials synthesis, and electrochemical processing. These interactions span multiple spatial and temporal scales, coupling complex plasma dynamics with liquid phase transport and chemistry. Developing tractable mathematical models that capture the essential physics across scales is crucial to enable predictive simulations, optimize applications, and guide experimental design. This paper reviews the fundamental mathematical frameworks used in modelling PLI systems, with emphasis on multi-scale coupling strategies. We discuss kinetic and fluid descriptions of plasma, continuum models for liquids, interface conditions, and numerical methods for tackling stiff, heterogeneous problems. We synthesize approaches including asymptotic analysis, continuum kinetic hybrid methods, reduced models, and scale separation techniques. Representative case studies illustrate the interplay between disparate scales and highlight challenges such as non-equilibrium effects, interface charge dynamics, and strongly coupled reaction transport phenomena. The review concludes with a discussion of open mathematical problems, emerging multi-physics challenges, and potential directions for future research, particularly in model reduction, rigorous analysis of interface dynamics, and uncertainty quantification. (English) |
| Keyword: | plasma-liquid interactions |
| Keyword: | multi-scale modeling |
| Keyword: | kinetic fluid coupling |
| Keyword: | interface dynamics |
| Keyword: | reaction transport systems |
| Keyword: | asymptotic analysis |
| MSC: | 35K57 |
| MSC: | 35Q35 |
| MSC: | 76X05 |
| MSC: | 82D10 |
| DOI: | 10.21136/AM.2026.0017-26 |
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| Date available: | 2026-09-15T09:44:25Z |
| Last updated: | 2026-09-21 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153749 |
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