{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"a3f17cba444052668395e74bd701b58ae50f6349e180dffc53621a201c61ed7b","created":"2026-10-03T07:18:03Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"26fb722bca6ed28f7eab7f5669b19e9f16243705a1aa68d3e40ff91d9034e14f","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"mechanism","assisted_by":[],"external_id":"fluid.elastic-turbulence.maximum-drag-reduction","kind":"phenomenon","literature_status":"contested","n":"1","parents":[],"plain":"Polymers can cut pipe friction a great deal, but adding more stops helping beyond a limiting friction curve that is the same for all polymers. Why this limit exists and is universal is not understood.","posed_since":"","precise":"In turbulent pipe flow of polymer solutions, the Fanning friction factor f approaches Virk's maximum drag reduction asymptote $1/\\sqrt{f} = 19.0\\operatorname{log10}(\\mathrm{Re}\\sqrt{f}) - 32.4$, independent of polymer species. Identify the flow state that realizes it (elasto-inertial turbulence driven by polymer stress, or marginally sustained Newtonian-like turbulence), derive the asymptote, and explain why friction can fall below it toward laminar values.","problem_ref":null,"references":"","settled_by":"A derivation of the asymptote from the dynamics of the identified flow state, confirmed by DNS of a constitutive model reproducing the measured friction curve.","status_note":"Elasto-inertial turbulence (Samanta et al. 2013) and friction below the asymptote after relaminarization (Choueiri, Lopez, Hof 2018) favour an elasto-inertial origin; a predictive derivation is lacking.","title":"Origin and universality of the maximum drag reduction asymptote","topic_ref":"b3c75da8fa5e430744454ba9d543f14e3e260933f89d866cf5e627ef69411678"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"56f73c68c59c36091293e78a0554cf8d8188ba8b18861846f4072605a8871989","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"040f8242a796a4cf9d1f5c436d223e1e36c0dcc10cf5f6fbc4a14a0c601e0e1f","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"TrHK3DwKZPF4dhe2pWMCpi41Btm8j98U5kQuaAO8jF_bc0TWuqb552rdXmoNYOlPdndMhf2cC8jhPsIsSzNKAg"},"schema":"pubphys.envelope/1"},"record_hash":"56f73c68c59c36091293e78a0554cf8d8188ba8b18861846f4072605a8871989","leaf_index":1410}