Threshold speed for air entrainment in forced wetting
In plain words
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?
Precise statement
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.
What would settle it
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 in the literature
Unverified 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).