{
  "abstract": "When a micron-sized bubble bursts, capillary waves deform the cavity into a cone that ejects a Worthington jet. The jet is born by inertial focusing, and the local collapse follows self-similar Euler solutions set by the semiangle $β$. Writing $r_j$ and $v_j$ for the dimensionless jet-base radius and velocity, the local Weber number $We_j=r_j v^2_j$ measures inertia relative to capillarity. The theory, supported by accurate numerical simulations gives $r_j\\proptoτ^{α(β)}$ with $α\\simeq0.63$ and, hence $We_j\\gg1$, with $We_j\\to\\infty$ as $r_j\\to0$, so inertia increasingly overwhelms capillarity. In simulations, the interface collapses onto a universal shape for more than two decades in dimensionless time when lengths are scaled using our prediction for $r_j$. For water, this gives incipient radii of $\\mathcal{O}(1)$ nm, predicting nanometric sea-spray aerosols.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.08972",
  "author_total": 3,
  "authors": [
    {
      "name": "José M. Gordillo"
    },
    {
      "name": "Javier Rodríguez-Rodríguez"
    },
    {
      "name": "Vatsal Sanjay"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2hmj72k18v409.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.08972",
  "fulltext_url": null,
  "id": "2hmj72k18v409",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.08972",
  "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",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "2206|Fluid Dynamics and Heat Transfer"
    ]
  ],
  "openalex": "W7168217143",
  "pdf_url": "https://arxiv.org/pdf/2607.08972",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2hmj72k18v409.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:15Z",
      "native_id": "2607.08972",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.08972"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Self-similar Worthington jets",
  "title_text": "Self-similar Worthington jets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:15Z",
  "url": "https://research.draconitic.com/paper/2hmj72k18v409",
  "venue": "arXiv",
  "versions": []
}