Ratio Value
Dimensionless ratio used to predict the stability of liquid films during high-speed textile coating or dyeing. The dynamic capillary number quantifies the competition between viscous forces that drag fluid along and surface tension that resists the deformation of the liquid interface. This calculation allows engineers to set the maximum speed for a specific coating formulation.
Viscous Force
High velocities in the coating head increase the numerator of the equation. When the dynamic capillary number rises, the viscous forces dominate, often leading to thicker liquid films or air entrainment at the point of contact. This effect is particularly evident in high-speed padding operations where the fabric enters the bath at several meters per second.
Surface Tension
Resistance to the expansion of the liquid surface depends on the chemical composition of the dye bath or coating mix. If the dynamic capillary number is too low, the surface tension prevents the liquid from wetting the fibres quickly enough for uniform coverage. Surfactants are typically added to lower the surface tension, which keeps the ratio within an acceptable range for the specific speed of the production line.
This adjustment ensures that the liquid can bridge the gaps between yarns without collapsing into droplets before the drying process begins.
Coating Stability
Maintaining a stable meniscus requires the operator to balance the machine speed with the fluid properties. If the dynamic capillary number exceeds a critical threshold, the liquid film may break or form ribs, resulting in uneven application across the web. Laboratory testing establishes these limits by measuring the viscosity and surface tension of each new formulation before it is used in bulk production.
