Wetting Tracing Paper—Fiber Porous Media Curling Behavior and Mechanisms
This research presents a novel approach to understanding the curling and uncurling behavior of tracing paper when exposed to water, identifying limitations in traditional diffusion-based models like Fick’s second law. While Fick's model adequately represents the uncurling phase, where water content is stable, it falls short during the curling phase due to its inability to account for dynamic changes in diffusivity. Our study identifies capillary action, modeled through Richards' equation, as the primary mechanism in the curling phase, where diffusivity varies with water content due to capillary-driven water movement through the paper's porous structure. Experimental data align well with the Richards' equation model, highlighting a saturation point where curvature peaks, governed by evaporation's impact on moisture balance. To simulate this phenomenon, we developed a finite difference approximation scheme based on Richards' equation, discretizing the spatial domain for detailed control over moisture dynamics and incorporating the Robin boundary condition with virtual points. This approach, combined with evaporation considerations, produces simulation results consistent with observed data, emphasizing evaporation’s role in steady-state moisture gradients and the subsequent deformation mechanics. Our findings further reveal that factors like paper thickness, temperature, and salt concentration significantly influence curling behavior. We established linear correlations between peak time and thickness reciprocal, as well as between peak curvature and thickness squared, supporting theoretical models. Temperature affects both peak curvature and curling rate due to changes in viscosity and surface tension, and higher temperatures prevent full uncurling due to sustained evaporation effects. Increased salt concentration heightens peak curvature without altering expansion ratio, suggesting additional variables in play.