Modeling Hydrolyzed Reactive Dye Diffusion Resistance in High Cover Factor Cotton Twills
High cover factor twills restrict intra-yarn mass transport, requiring wash-off temperatures above 85 degrees Celsius to desorb trapped hydrolyzed reactive dye.
Renkin Friction Factor
Transport Metric
Dimensionless correction coefficients account for the increased hydrodynamic resistance experienced by a molecule diffusing through a narrow pore. The Renkin friction factor quantifies the reduction in diffusion rate that occurs when the size of the dye molecule approaches the diameter of the water-filled pores in the fiber. This coefficient ranges from zero to one as the pore restriction increases.
Pore Geometry
Cylindrical channels within the swollen polymer matrix limit the path of migrating chemical species. The Renkin friction factor adjusts the bulk diffusion coefficient to reflect the steric hindrance and viscous drag within these micro-channels. This adjustment is essential for accurate modeling of synthetic fiber dyeing.
Fiber Penetration
Dye molecules cannot penetrate crystalline regions and must move through amorphous zones instead. Calculating the Renkin friction factor helps chemists select dye structures that navigate restricted fiber pathways. This improves the final color uniformity.
Hydrodynamic Limit
Extreme pore restriction causes the factor to approach zero, which prevents any significant molecular transport from occurring. When the Renkin friction factor drops below critical thresholds, dyeing times increase exponentially and surface deposition occurs instead of true penetration. This boundary defines the maximum molecular weight of dyes suitable for dense microfibers.