{"doi":"10.1017/jfm.2025.10216","title":"Large deformation of elastic capsules under uniaxial extensional flow","abstract":"A spherical capsule (radius $R$ ) is suspended in a viscous liquid (viscosity $\\mu$ ) and exposed to a uniaxial extensional flow of strain rate $E$ . The elasticity of the membrane surrounding the capsule is described by the Skalak constitutive law, expressed in terms of a surface shear modulus $G$ and an area dilatation modulus $K$ . Dimensional arguments imply that the slenderness $\\epsilon$ of the deformed capsule depends only upon $K/G$ and the elastic capillary number ${Ca}=\\mu R E/G$ . We address the coupled flow–deformation problem in the limit of strong flow, ${Ca}\\gg 1$ , where large deformation allows for the use of approximation methods in the limit $\\epsilon \\ll 1$ . The key conceptual challenge, encountered at the very formulation of the problem, is in describing the Lagrangian mapping from the spherical reference state in a manner compatible with hydrodynamic slender-body formulation. Scaling analysis reveals that $\\epsilon$ is proportional to ${Ca}^{-2/3}$ , with the hydrodynamic problem introducing a dependence of the proportionality prefactor upon $\\ln \\epsilon$ . Going beyond scaling arguments, we employ asymptotic methods to obtain a reduced formulation, consisting of a differential equation governing a mapping field and an integral equation governing the axial tension distribution. The leading-order deformation is independent of the ratio $K/G$ ; in particular, we find the approximation $\\epsilon ^{2/3} {Ca}\\approx 0.2753\\ln (2/\\epsilon ^2)$ for the relation between $\\epsilon$ and $Ca$ . A scaling analysis for the neo-Hookean constitutive law reveals the impossibility of a steady slender shape, in agreement with existing numerical simulations. More generally, the present asymptotic paradigm allows us to rigorously discriminate between strain-softening and strain-hardening models.","journal":"Journal of Fluid Mechanics","year":2025,"id":567839,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":0,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9582,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2025-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":1472039,"name":"P. D. Howell","orcid":"0000-0002-6036-3386","position":1,"is_corresponding":false},{"id":255939,"name":"Howard A. Stone","orcid":"0000-0002-9670-0639","position":2,"is_corresponding":false},{"id":1472038,"name":"Ehud Yariv","orcid":"0000-0003-0398-2954","position":0,"is_corresponding":true}],"reference_count":44,"raw_metadata":null,"created_at":"2026-07-19T02:56:48.183032Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}