Dimensionless Fluid Metric
Dimensionless hydrodynamic ratios quantify the relative magnitude of viscous forces against surface tension forces acting across a liquid-gas or liquid-liquid boundary. The metric is computed as the product of dynamic fluid viscosity and characteristic interface velocity divided by the surface tension of the fluid. In roll coating, blade metering, and fluid delivery systems, capillary number governs whether a flowing liquid film remains stable or breaks into ribbing, air entrainment, or misting defects.
Higher coating speeds or elevated fluid viscosities increase the value, pushing the fluid transfer zone toward hydrodynamic instability. The formulation ceases to follow pure capillary-driven leveling once viscous stresses dominate interfacial forces at elevated values.
Metering Stability
Blade and metering size press operations depend on maintaining the operating point below critical instability thresholds. In forward roll coating, exceeding a critical capillary number initiates meniscus breakdown, creating longitudinal ribs along the machine direction that fail to level before drying. Low values signify that surface tension dominates, smoothing surface irregularities and closing fluid discontinuities before the wet film enters the drying section.
For pigmented coating formulations applied to packaging paperboard, this balance dictates the runnability boundary where coater speeds can be increased without producing streaks, film splitting defects, or curtain instability.
Substrate Interaction
Wetting dynamics between an aqueous formulation and the porous paper web shift as fluid velocities rise on modern high-speed coaters. Dynamic contact angles deviate substantially from static measurements when dynamic fluid displacement outpaces spontaneous capillary absorption into the fibre network. The effective penetration depth of liquid phases into base board pores drops at very high processing speeds, altering coating adhesion and anchor patterns.
Controlling dynamic viscosity through shear-thinning additives allows converters to suppress viscous instabilities while keeping dynamic surface tension low enough to promote rapid substrate wetting.
