Fluid Kinetics
Kinetic equations governing the pressure-driven capillary flow of liquids into porous substrates incorporate both inertial and viscous resistance terms to describe the initial stages of absorption. The mathematical description of this non-equilibrium flow is termed Bosanquet dynamics, which extends the classical Washburn equation to very short time scales. This formulation is highly relevant to high-speed industrial printing, where the contact time between ink and paperboard is measured in milliseconds.
Capillary Flow
Classic penetration models assume that viscous forces dominate the liquid flow from the moment of contact. In contrast, Bosanquet dynamics accounts for the acceleration of the liquid front, where the mass of the fluid resists immediate movement. During the first few microseconds, the flow rate is limited by inertia, which keeps the velocity constant before viscous friction begins to slow the liquid down.
As time progresses, viscosity becomes the dominant factor and the flow transitions to a slower rate.
Substrate Interaction
Paperboard mills utilize these kinetic principles to design specialized coatings that control the initial pick-up of ink resins. Rapid capillary absorption prevents ink spread, while avoiding premature drying on the press. This balance ensures that the ink penetrates to the correct depth during the crucial transfer window.
