Dynamic Surface Tension in High Speed Liquid Curtain Coating
Dynamic surface tension controls curtain coating stability and heel air entrainment, dictating run speed, defect rates, and operational packaging costs.
Weber Number
Dimensionless Ratio
Fluid mechanics equations utilize momentum ratios to evaluate the competition between kinetic disruption and cohesive surface tension forces in free-surface liquid flows. The weber number defines the quotient of fluid inertia against capillary surface tension, calculated using fluid density, characteristic velocity, surface curvature length and liquid surface energy. High values denote systems where kinetic energy dominates, promoting droplet atomization, fluid splashing and liquid sheet fragmentation.
Low values characterize flows where surface tension forces hold the fluid together, maintaining coherent liquid curtains, stable menisci and uniform laminar boundary interfaces.
Coating Stability
Application of functional barrier formulations onto high-speed paperboard webs relies on maintaining an optimal weber number across metering and transfer zones. In curtain coating stations, the falling liquid curtain must remain stable against ambient air draughts and dynamic mechanical vibrations across widths exceeding five metres. The liquid sheet must operate above a critical minimum value to prevent edge pull-in and premature film collapse caused by surface tension pulling the curtain into localized streams.
Operating at excessively high values, however, causes the impacting liquid curtain to entrain micro-air pockets as it collides with the fast-moving paper web, generating micro-pinholes in food barrier coatings. In spray sizing and pigment shower applications, this dimensionless value dictates the median droplet size distribution, ensuring that atomized coatings wet the fibrous paper surface without forming irregular droplet bounce patterns. Formulators adjust surface tension by dosing specialized wetting agents while adjusting coating solid contents to maintain hydrodynamic stability across wide machine speed envelopes.
Calculation Limit
Analytical utility of the weber number breaks down when dealing with highly non-Newtonian formulations where fluid dynamic viscosity dominates both inertia and surface tension forces. Under extreme viscous shear regimes, the Ohnesorge number or the Capillary number provides the primary governing framework for droplet breakup and dynamic film extension. Highly porous, absorbent paper surfaces also invalidate conventional fluid boundary assumptions by extracting carrier water through rapid capillary suction before the liquid momentum can equilibrate.
Dynamic surface tension variations occurring within millisecond timescales behind advancing coating blades further complicate theoretical calculations relying on static equilibrium surface energy values.