Modeling Hygral Stress Profiles and Edge Waving in High-Bulk Recycled Cartonboard Skids
Modeling transient moisture gradients and hygral stress in high-bulk recycled cartonboard skids establishes barrier wrap limits to prevent press edge waving
Fickian Moisture Diffusion
Vapor Transport
Water vapor transport through porous cellulose structures follows mathematical laws governed by concentration gradients within the paper matrix. Physical testing identifies fickian moisture diffusion as the mass transfer process where moisture flux remains directly proportional to the local concentration gradient. Outer coating layers slow this molecular transport rate across the sheet thickness.
Gradient Mechanism
Cellulose fibers absorb water molecules from ambient air through hydrogen bonding at accessible hydroxyl sites. As surface layers reach equilibrium with ambient humidity, moisture moves deeper into the dry core of the board through random thermal motion. Diffusion coefficients depend heavily on ambient temperature, internal pore structure, and fiber density within individual board plies.
Dense calendered sheets present narrower pore networks that restrict vapor movement, whereas high-bulk uncalendered grades allow faster moisture transfer. Extruded polyolefin or bio-polymer barrier coatings disrupt this transport path by presenting hydrophobic surfaces with low permeability values. Converting operations track moisture penetration rates to prevent dimensional instability and curl during offset printing runs.
Environmental Boundary
Standard moisture transport models assume fixed diffusion coefficients across moderate humidity ranges. Extreme relative humidity conditions cause moisture-dependent swelling that alters pore geometry and accelerates transport rates. Fickian moisture diffusion governs the rate of dimensional changes in paperboard packaging during environmental transitions.