Mathematical Modeling of Mechanical Tone Value Increase across Recycled Testliner
Dynamic impression squeeze on porous recycled testliner forces lateral ink spread, requiring prepress Yule-Nielsen n-factor recalibration to prevent gain.
Hydrodynamic Squeeze Flow
Fluid Displacement
Viscous fluid evacuation governs the lateral expulsion of a liquid film when two solid boundaries approach each other under normal compressive forces. Hydrodynamic squeeze flow describes the transient pressure build-up and outward velocity distribution within thin liquid layers trapped between advancing roll surfaces or printing plates and porous substrates. The process dictates liquid layer thinning before mechanical contact occurs in blade coating, roll metering, and ink transfer units.
Boundary resistance from fluid viscosity counters the closing force of the nip rolls, generating substantial lubricating pressures. The scope terminates where boundary lubrication ends and dry mechanical asperities contact each other across the substrate interface.
Velocity Gradient
Compressive closing speeds force the liquid outward along the cross-machine and machine directions, establishing steep parabolic velocity profiles through the film thickness. High-shear rheology of the coating color or liquid ink controls flow resistance during this rapid lateral displacement. Substrate permeability modifies the classical impermeable squeeze flow model by allowing a portion of the fluid vehicle to drain normally into the porous fiber matrix under generated squeeze pressure.
Micro-roughness on the paperboard surface arrests pure lateral flow, creating localized pressure cells within surface valleys that resist further closure. As film thickness decreases to micro-scale dimensions, shear rates inside the fluid layer can surpass one hundred thousand reciprocal seconds, triggering shear-thinning or dilatant rheological shifts. The resulting normal force pushes the approaching roll surfaces apart until mechanical loading overcomes hydrodynamic lift.
Coating Stability
Premetered slot dies and applicator rolls utilize controlled squeeze mechanics to deposit uniform fluid films across irregular substrate topographies. Improper squeeze dynamics cause coating streak formation, uneven coat weight distribution, and liquid film cavitation along the exit meniscus.