{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"7a9c1522ea1ec4e8c5c51f0b20564e5435241f2407cd67e24f896a20b29edd13","created":"2026-10-03T07:18:03Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"be34c24408310cce1bc67571d2dd9b21905caaae19154ddec9202e2d58bc903e","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"mechanism","assisted_by":[],"external_id":"fluid.contact-lines.dynamic-angle-law","kind":"phenomenon","literature_status":"contested","n":"1","parents":[],"plain":"The angle a moving liquid edge makes with a solid changes with its speed, and two rival theories (bending of the liquid surface by viscous flow, or molecules hopping between surface sites) both fit data once their parameters are adjusted. Which one governs, and under what conditions?","posed_since":"","precise":"Determine whether the dynamic angle $\\theta_d$ as a function of capillary number $Ca = \\eta U / \\gamma$ follows the hydrodynamic Cox-Voinov relation $\\theta_d^3 - \\theta_e^3 = 9 Ca \\ln(L/L_{\\mathrm{micro}})$, the molecular-kinetic relation $U = 2 \\kappa_0 \\lambda \\operatorname{sinh}(\\gamma (\\operatorname{cos} \\theta_e - \\operatorname{cos} \\theta_d) \\lambda^2 / (2 k_B T))$ with hopping frequency $\\kappa_0$ and site spacing $\\lambda$, or a combination, for advancing and receding lines. An answer is a law whose parameters are measured independently rather than fitted, valid for Ca from $1e-6$ to $1e-1$ across viscosity and wettability.","problem_ref":null,"references":"","settled_by":"A data set over five decades of $\\mathrm{Ca}\\ (1e-6\\text{ to }1e-1)$ for liquids of widely varying viscosity on well-characterized surfaces, with $L_{\\mathrm{micro}}$, $\\kappa_{0}$ and $\\lambda$ determined from independent measurements.","status_note":"","title":"Is there a predictive law for dynamic contact angle versus 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