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.
Inclined Sedimentation of Suspensions: Theoretical and Experimental Investigation into the Boycott Effect
The Boycott Effect is a phenomenon where sedimentation rate can be increased by tilting the container which holds the suspension, making it a way to increase the efficiency of the process without additional energy input. This makes the Boycott Effect valuable in speeding up and optimising a multitude of industrial applications such as wastewater management and food processing, all of which employ sedimentation to separate particulate matter from the fluids in which they are suspended in. Thus, it is imperative to model the Boycott Effect accurately for a wide range of cases, including arbitrary shaped containers and suspensions of various concentrations without the need to run costly, computationally expensive numerical simulations. In this project I investigated the inclined sedimentation of suspensions both theoretically and experimentally. Experimentally, two image tracking programs were created and tested out on my own experimental videos. I demonstrated the use of a novel method for making use of the Beer-Lambert Law to optically keep track of local concentration of suspensions. This method allows more information to be gathered about the sedimentation process in a very low-cost, non-equipment intensive or invasive way. Theoretically, I expanded upon the well-known analytical 2D PNK theory by accounting for concentration-hindering and sediment build-up effects, as well as the geometrical theory for 3D cylindrical geometries. All parts of the theoretical model were verified with experimental data and shown to have good agreement. (233 words)