{
  "abstract": "Membrane profiling and near-membrane spacers modify concentration polarization by altering fluid flow and the membrane–solution interface. This study examines their combined influence using a two-dimensional Nernst–Planck–Poisson–Navier–Stokes model with a voltage ramp of 5 mV/s. The geometries comprise a smooth membrane without spacers, a profiled membrane without spacers, and six wing arrangements adjacent to a profiled membrane. The feed concentration is 0.01 mol/m3, the protrusion radius is 0.5 mm, and the center-to-center pitch is 1.5 mm. Current data from five identifiable model files are compared over a common interval up to 1.2 V using a dimensionless domain-integrated current. Wing placement affects the current response, while profiling increases the geometric membrane contour by 28.54%. An analytical reference limiting current is calculated using the Levêque equation. The comparison with published three-dimensional results provides qualitative support for the transport mechanism. Systematic numerical uncertainty assessment, quantitative three-dimensional validation, geometry optimization, and energy comparisons at equal salt removal are identified as further research beyond the scope of the present study.",
  "abstract_shown": true,
  "affiliations": [
    "Faculty of Information Technology and Big Data Analysis, Financial University under the Government of the Russian Federation, 125167 Moscow, Russia",
    "Faculty of Architecture and Civil Engineering, RheinMain University of Applied Sciences and Arts, 65197 Wiesbaden, Germany",
    "Faculty of Computer Technologies and Applied Mathematics, Kuban State University, 350040 Krasnodar, Russia",
    "School of Software Engineering, Faculty of Computer Science, HSE University, 109028 Moscow, Russia"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 6,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Anna Ovsyannikova"
    },
    {
      "affs": [
        1
      ],
      "name": "Evgenia Kirillova",
      "orcid": "0000-0002-6797-0920"
    },
    {
      "affs": [
        2
      ],
      "name": "Anna Kovalenko"
    },
    {
      "affs": [
        3
      ],
      "name": "Anastasiia Lelekova"
    },
    {
      "affs": [
        3
      ],
      "name": "Alexandra Ovsyannikova"
    },
    {
      "affs": [
        2
      ],
      "name": "Makhamet Urtenov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/acc8pd8pbcdh5.bib",
  "cited_by": 0,
  "doi": "10.3390/math14203825",
  "fulltext_url": null,
  "id": "acc8pd8pbcdh5",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/20/3825",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2204|Membrane-based Ion Separation Techniques"
    ]
  ],
  "openalex": "W7223158598",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/acc8pd8pbcdh5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14203825",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/20/3825"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "Combined Influence of Membrane Profiling and Wing-Shaped Spacers on Ion Transport: A Two-Dimensional Potentiodynamic Study",
  "title_text": "Combined Influence of Membrane Profiling and Wing-Shaped Spacers on Ion Transport: A Two-Dimensional Potentiodynamic Study",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/acc8pd8pbcdh5",
  "venue": "Mathematics",
  "versions": []
}