{"paper":{"title":"Self-similar Worthington jets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Javier Rodr\\'iguez-Rodr\\'iguez, Jos\\'e M. Gordillo, Vatsal Sanjay","submitted_at":"2026-07-09T22:29:55Z","abstract_excerpt":"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 $\\beta$. 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 $r_j\\propto\\tau^{\\alpha(\\beta)}$ with $\\alpha\\simeq0.63$ and, hence $We_j\\gg1$, with $We_j\\to\\infty$ as $r_j\\to0$, so inertia increasingly o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08972","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.08972/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}