Development of a thickness prediction model for the coffee-staining effect based on the ink spreadability of a tensioned web

Tension is an influential parameter affecting thickness in roll-to-roll systems. Thickness prediction and uniformity control of functional layers in roll-to-roll continuous production systems are critical issues, but research on thickness prediction considering tension remains limited. This study developed a new thickness prediction model based on operating tension. By analyzing the spreading mechanism under tension and the coffee-stain effect caused by drying, we applied these insights to roll-to-roll slot-die coating. Tension within the roll-to-roll system affects the contact angle of sessile droplets on the web. As tension increases, the surface roughness of the substrate decreases, lowering the contact angle. Moreover, as tension decreases, surface roughness increases, raising the contact angle. This relationship determines spreadability, which directly affects the width and thickness of the coated layer. Additionally, the capillary flow rate, which transports particles from the center to the edge during evaporation, varies with the contact angle. Evaporation of droplets with a low contact angle intensifies capillary flow, yielding a thicker coffee-stain than droplets with a high contact angle. The newly developed tension-based thickness prediction model exhibited 43.1 % higher accuracy than traditional models, elucidating coated layer variation with tension. The results demonstrate that reducing tension decreases coffee-stain thickness in functional layers, improving thickness uniformity. This study proposes controlling substrate tension to adjust the contact angle to address thickness non-uniformity in roll-to-roll coating processes. This model significantly advances functional layer manufacturing.