{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"6b2bfecd2cfda2e365e123cf91a1571d00e424095175f573e9ba3f045da4c1ce","created":"2026-10-03T07:18:03Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"50dca9879733c114a2e0825a1c89926027e0e9a98ba29e27be1fd6d110f48f3f","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"fluid.contact-lines.air-entrainment-threshold","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"When a plate or tape is pushed quickly into a liquid, above a critical speed the liquid can no longer wet the solid and a thin air film is dragged in, which ruins coatings. What sets that critical speed?","posed_since":"","precise":"For a solid plunging at speed $U$ into a liquid of viscosity $\\eta$ and surface tension $\\gamma$, surrounded by gas of viscosity $\\eta_g$ and pressure $p$, predict the critical capillary number Ca* = eta U*/gamma for dynamic wetting failure, including its dependence on the viscosity ratio $\\eta_g/\\eta$, on gas rarefaction when the mean free path approaches the air-film thickness, and on the large increase of Ca* when the flow pushes the liquid against the solid (curtain coating). An answer predicts Ca* within experimental error for $\\eta_g/\\eta$ from $1e-6$ to $1e-2$ and across reduced gas pressures.","problem_ref":null,"references":"","settled_by":"A comparison of measured $\\mathrm{Ca}*$ for plunging plates and curtain coating over wide viscosity ratios and gas pressures with a single model of the gas film and the contact line.","status_note":"Lubrication models that include gas viscosity capture the weak viscosity-ratio dependence for simple plunging; the roles of gas rarefaction and of flow assistance remain unsettled as of 2026 (not re-verified for 2024-2026).","title":"Threshold speed for air entrainment in forced 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