Experimental, Theoretical and Numerical Evaluation of Wicking Models for Liquid Imbibition in Dry Porous Wicks

Nowadays commercial wicks are utilized by consumer product companies in several important commercial applications including Tiki® Brand torches, the passive lubricants of machine gears, propellant management device, and fragrance dispersion units. Spontaneous imbibition of a liquid into porous wicks, also called wicking, is modeled using the single-phase Darcy’s law after assuming a sharp flow-front marked by full saturation behind the front. An analytical expression for the height of the wicking flow-front as a function of time is tested through comprehensive experiments using different wicks and an oil as the wicking liquid. We proposed a model based on sharp liquid-front where a good match with the experimental data was achieved. However, the proposed model based on the sharp liquid-front fails to account for partial saturation in the wicks. As a result, we applied the Richards equation to predict partial liquid saturations in wicks where the equation is solved numerically in 2-D using COMSOL and analytically in 1-D using Mathematica for glass-fiber wicks after treating them as transversely-isotropic porous media. As a novel contribution, the relative permeability and capillary pressure are determined directly from pore-scale simulations in wick microstructure using the state-of-the-art software GeoDict. The saturation along the wick length is determined experimentally through a new liquid-N2 based freezing technique. After including the gravity effect, good agreements between the numerical/analytical predictions and experimental results are achieved in saturation distributions. We also validated the Richards equation-based model while predicting absorbed liquid-mass into the wick as a function of time. A series of wicking experiments with wicks procured from our industrial partners were conducted where the use of a dyed liquid revealed essentially three types of macroscopic (visual) fronts—sharp, semi-sharp, and diffuse. The particulate wicks (i.e. the wicks formed by sintering polymer beads) invariably formed sharp fronts, while the fibrous wicks (i.e. wicks formed from fibers) formed either semi-sharp or diffuse fronts. The porosity was also found to play a role—the lower-porosity fibrous wicks displayed semi-sharp fronts, while the higher-porosity fibrous wicks caused the fronts to be diffuse. A study of SEM (Scanning Electron Microscopy) micrographs revealed that the latter behavior was caused by clustering of fibers thus leading to the formation of an inhomogeneous porous medium (perhaps promoting finger formation on micro-fronts). The experiments also revealed that the visually-observed fronts, for most parts, achieved a good match with the fronts estimated through the sharp-front mass gain formula. (Such a match was found to be lacking in the fibrous wicks displaying diffuse fronts.) We also investigated two parameters of interest to the users of wicks: 1) steady-state (SS) height reached by the visual front at very large times, 2) the liquid supply rate when the front is near the top. The parameters estimated using our sharp-front model matched well with the experimentally-observed ones. Finally, we conducted a CFD simulation using FLUENT where the flow of wicking liquid through a 2D microstructure made of ellipses of varying aspect ratio was modeled. A series of microstructures were created by varying the ellipse aspect ratio from 1:1 (20*20 µm) to 1:64 (20*1280 µm), with lower values representing particulate porous media and the higher values representing fibrous porous media. To study the effect of porosity, two values of 50% and 70% were considered. The flow simulation in particulate porous media produced somewhat even micro-fronts that indicate a flat visual (macroscopic) front. On the other hand, simulations in fibrous porous media produced highly uneven micro-fronts that point to a semi-sharp or diffuse visual fronts. Increasing the porosity results in clustering of solid phase and leads to further increase in the unevenness of micro-fronts, thus pointing to purely diffuse visual fronts. The evolution of saturation plots along the flow direction, obtained using a grid superimposed on fluid distribution pictures, was also studied and the predictions matched our previous experimental and numerical observations, i.e., particulate media create sharp fronts while fibrous media create diffuse fronts