{
  "abstract": "We develop a computational framework to investigate the flow kinematics of viscoplastic materials, described by the Herschel-Bulkley model, in vane-in-cup rheometers. Numerical simulations are performed using augmented Lagrangian finite element and regularised finite volume methods for two- and three-dimensional configurations, respectively, to characterise the hydrodynamics and yielding behaviour over a broad range of effective parameters. Three types of vanes are investigated: conventional 4- and 6-arm bespoke vanes and a 24-arm fractal vane (Owens et al., J. Rheol., vol. 64(3), 2020, 643-662). Our previous two-dimensional study (Chaparian et al., J. Non-Newtonian Fluid Mech., vol. 307, 2022, 104857) demonstrated the superiority of the fractal vane over conventional N-arm designs. The bespoke vanes produce highly non-uniform yielding, leading to significant deviations from the circular Couette analogy, whereas the 24-arm fractal vane generates nearly axisymmetric yield surfaces that effectively \"cloak\" the vane geometry. Consequently, the resulting flow closely resembles the azimuthal shear in a conventional \"bob & cup\" rheometer, providing substantially more accurate rheological measurements. Building on these findings, the present study revisits the torque-to-stress and rotation-to-strain rate conversions used in vane-in-cup rheometry. In particular, we re-examine the circular Couette analogy that underpins both the physical interpretation of the flow and the extraction of flow curves from raw rheometric data. Based on our extensive two- and three-dimensional simulations, we identify limitations of the existing conversion relations and propose improved closure expressions that enable more accurate determination of material's rheological properties. Furthermore, the three-dimensional flow structures and yielding patterns within the vane-in-cup fixtures are characterised.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02115",
  "author_total": 4,
  "authors": [
    {
      "name": "James Malcolm"
    },
    {
      "name": "Clare McColgan"
    },
    {
      "name": "Emma Mullarkey"
    },
    {
      "name": "Emad Chaparian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6wtakgk8g00cp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02115",
  "fulltext_url": null,
  "id": "6wtakgk8g00cp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02115",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.soft"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02115",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6wtakgk8g00cp.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.02115",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02115"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.soft",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Three-dimensional computational rheometry of viscoplastic fluids in vane-in-cup fixtures",
  "title_text": "Three-dimensional computational rheometry of viscoplastic fluids in vane-in-cup fixtures",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:18Z",
  "url": "https://research.draconitic.com/paper/6wtakgk8g00cp",
  "venue": "arXiv",
  "versions": []
}