Analytical solutions of drying in porous media for gravity-stabilized fronts

Analysis of Drying Front Propagation and Coupled Heat and Mass Transfer During Evaporation From Additively Manufactured Porous Structures Under a Solar Flux

Drying front propagation and coupled heat and mass transfer analysis from porous media is critical for soil-water dynamics, electronics cooling, and evaporative drying. In this study, de-ionized water was evaporated from three 3D printed porous structures (with 0.41 mm, 0.41 mm, and 0.16 mm effective radii, respectively) created out of acrylonitrile butadiene styrene (ABS) plastic using stereolithography technology. The structures were immersed in water until all the pores were invaded and then placed on the top of a sensitive scale to record evaporative mass loss. A 1000 W/m2 heat flux was applied with a solar simulator to the top of each structure to accelerate evaporation. The evaporative mass losses were recorded at 15 min time intervals and plotted against time to compare evaporation rates from the three structures. The evaporation phenomena were captured with a high-speed camera from the side of the structures to observe the drying front propagation during evaporation, and a high-resolution thermal camera was used to capture images to visualize the thermal gradients during evaporation. The 3D-structure with the smallest effective pore radius (i.e., 0.16 mm) experienced the sharpest decrease in the mass loss as the water evaporated from 0.8 g to 0.1 g within 180 min. The designed pore structures influenced hydraulic linkages, and therefore, evaporation processes. A coupled heat-and-mass-transfer model modeled constant rate evaporation, and the falling rate period was modeled through the normalized evaporation rate.

The Role of Discrete Capillary Rings in Mass Transfer From the Surface of a Drying Capillary Porous Medium

The mass exchange between the surface of a model capillary porous medium and the adjacent gas-side boundary layer is studied in the limiting condition of isothermal, slow drying. In order to quantify the role and significance of liquid films in the mass exchange process, three-dimensional pore network Monte Carlo simulations are carried out systematically in the presence and absence of discrete capillary rings. The pore network simulations performed with capillary rings show a noticeable delay in transition from the capillary-supported regime to the diffusion-controlled regime. These simulation results differ significantly from the predictions of classical pore network models without liquid films, and they appear to be more consistent with the experiments conducted with real porous systems. As compared to classical pore network models, the pore network model with rings seems to predict favorably the spatiotemporal evolution of wet and dry patches at the medium surface as well as of their relative contributions to the net mass exchange rate. This is apparent when the analytical solution of the commonly used Schlünder’s model is examined against the numerical simulations conducted using classical and ring pore network models.

Formation of a hard surface layer during drying of a heated porous media

We report surface hardening or crust formation, like caking, during evaporation when a porous medium was heated from above using IR radiation. These crusts had higher strength than their closest counterparts such as sandcastles and mud-peels which essentially are clusters of a partially wet porous medium. Observed higher strength of the crusts was mostly due to surface tension between the solid particles, which are connected by liquid bridges (connate water). Qualitative (FTIR) and quantitative (TGA) measurements confirmed the presence of trapped water within the crust. Based on the weight measurements, the amount of water trapped in the crusts was ~1.5%; trapped water was also seen as liquid bridges in the SEM images. Further, in the fixed particle sizes case, the crust thickness varied slightly (only 10–20 particle diameters for cases with external heating) while with the natural sand whole porous column was crusted; surprisingly, the crust was also found with the hydrophobic glass beads. Fluorescein dye visualization technique was used to determine the crust thickness. We give a power-law relation between the crust thickness and the incident heat flux for various particle sizes. The strength of the crust decreased drastically with increasing hydrophilic spheres diameter while it increased with higher surface temperature.

3D Arrays of Super-Hydrophobic Microtubes from Polypore Mushrooms as Naturally-Derived Systems for Oil Absorption

Porous materials derived from natural resources, such as Luffa sponges, pomelo peel and jute fibres, have recently emerged as oil adsorbents for water purification, due to their suitability, low environmental impact, biodegradability and low cost. Here we show, for the first time, that the porosity of the fruiting body of polypore mushrooms can be used to absorb oils and organic solvents while repelling water. We engineered the surface properties of Ganoderma applanatum fungi, of which the fruiting body consists of a regular array of long capillaries embedded in a fibrous matrix, with paraffin wax, octadecyltrichlorosilane (OTS) and trichloro(1H,1H,2H,2H-perfluorooctyl)silane. Morphological and wettability analyses of the modified fungus revealed that the OTS treatment was effective in preserving the 3D porosity of the natural material, inducing super-hydrophobicity (water contact angle higher than 150°) and improving oil sorption capacity (1.8⁻3.1 g/g). The treated fungus was also inserted into fluidic networks as a filtration element, and its ability to separate water from chloroform was demonstrated.

Effect of geometry on the dewetting of granular chains by evaporation

Understanding evaporation or drying in granular media still remains complex despite recent advancements. Evaporation depends on liquid transport across a connected film network from the bulk to the surface. In this study, we investigate the stability of film networks as a function of the geometry of granular chains of spherical grains. Using a controlled experimental approach, we vary the grain arrangement or packing and measure the height of the liquid film network during evaporation as packing shifts from loose-packed to close-packed arrangement. This height can be calculated from an equilibrium between hydrostatic pressure and the capillary pressure difference in the vertical film network. Following a simulation approach using Surface Evolver, we evaluate the pressure variation due to dewetting of the meniscus volume in the grains in both the percolating front and evaporating front within the two-phase zone of air/water mixture. Results show good agreement between model and experiment. We find that above a "critical" packing angle, the liquid continuity is broken and films connections fragment into separate, isolated capillary bridges.

Enhanced mobility of non aqueous phase liquid (NAPL) during drying of wet sand

Enhanced upward mobility of a non aqueous phase liquid (NAPL) present in wet sand during natural drying, and in the absence of any external pressure gradients, is reported for the first time. This mobility was significantly higher than that expected from capillary rise. Experiments were performed in a glass column with a small layer of NAPL-saturated sand trapped between two layers of water-saturated sand. Drying of the wet sand was induced by flow of air across the top surface of the wet sand. The upward movement of the NAPL, in the direction of water transport, commenced when the drying effect reached the location of the NAPL and continued as long as there was significant water evaporation in the vicinity of NAPL, indicating a clear correlation between the NAPL rise and water evaporation. The magnitude and the rate of NAPL rise was measured at different water evaporation rates, different initial locations of the NAPL, different grain size of the sand and the type of NAPL (on the basis of different NAPL-glass contact angle, viscosity and density). A positive correlation was observed between average rate of NAPL rise and the water evaporation while a negative correlation was obtained between the average NAPL rise rate and the NAPL properties of contact angle, viscosity and density. There was no significant correlation of average NAPL rise rate with variation of sand grain size between 0.1 to 0.5mm. Based on these observations and on previous studies reported in the literature, two possible mechanisms are hypothesized -a) the effect of the spreading coefficient resulting in the wetting of NAPL on the water films created and b) a moving water film due to evaporation that "drags" the NAPL upwards. The NAPL rise reported in this paper has implications in fate and transport of chemicals in NAPL contaminated porous media such as soils and exposed dredged sediment material, which are subjected to varying water saturation levels due to drying and rewetting.

Experimental investigation of water distribution in a two-phase zone during gravity-dominated evaporation

We characterize the water repartition within the partially saturated (two-phase) zone (PSZ) during evaporation from mixed wettable porous media by controlling the wettability of glass beads, their sizes, and as well the surrounding relative humidity. Here, capillary numbers are low and under these conditions, the percolating front is stabilized by gravity. Using experimental and numerical analyses, we find that the PSZ saturation decreases with the Bond number, where packing of smaller particles have higher saturation values than packing made of larger particles. Results also reveal that the extent (height) of the PSZ, as well as water saturation in the PSZ, both increase with wettability. We also numerically calculate the saturation exclusively contained in connected liquid films and results show that values are less than the expected PSZ saturation. These results strongly reflect that the two-phase zone is not solely made up of connected capillary networks but also made of disconnected water clusters or pockets. Moreover, we also find that global saturation (PSZ + full wet zone) decreases with wettability, confirming that greater quantity of water is lost via evaporation with increasing hydrophilicity. These results show that connected liquid films are favored in more-hydrophilic systems while disconnected water pockets are favored in less-hydrophilic systems.

Drying kinetics driven by the shape of the air/water interface in a capillary channel

We look at the drying process in a simple glass channel with dominant capillary effects as is the case in microfluidics. We find drying kinetics commonly observed for confined geometry, namely a constant period followed by a falling rate period. From visualization of the air/water interface with high resolution, we observe that the drying rate decreases without a drying front progression although this is the usually accepted mechanism for confined geometries. We show with FEM that in our specific geometry the falling rate period is due to changes in the shape of the air-water interface at the free surface where most evaporation occurs. Our simulations show that the sensitivity of the drying rate to the shape of the first air-water interface from the sample free surface implies that slight changes of the wetting or pinning conditions can significantly modify the drying rate.

Simple analytical model of evapotranspiration in the presence of roots

Evaporation of water out of a soil involves complicated and well-debated mechanisms. When plant roots are added into the soil, water transfer between the soil and the outside environment is even more complicated. Indeed, plants provide an additional process of water transfer. Water is pumped by the roots, channeled to the leaf surface, and released into the surrounding air by a process called transpiration. Prediction of the evapotranspiration of water over time in the presence of roots helps keep track of the amount of water that remains in the soil. Using a controlled visual setup of a two-dimensional model soil consisting of monodisperse glass beads, we perform experiments on actual roots grown under different relative humidity conditions. We record the total water mass loss in the medium and the position of the evaporating front that forms within the medium. We then develop a simple analytical model that predicts the position of the evaporating front as a function of time as well as the total amount of water that is lost from the medium due to the combined effects of evaporation and transpiration. The model is based on fundamental principles of evaporation fluxes and includes empirical assumptions on the quantity of open stomata in the leaves, where water transpiration occurs. Comparison between the model and experimental results shows excellent prediction of the position of the evaporating front as well as the total mass loss from evapotranspiration in the presence of roots. The model also provides a way to predict the lifetime of a plant.

Drying in porous media with gravity-stabilized fronts: experimental results

In a recent paper [Yiotis et al., Phys. Rev. E 85, 046308 (2012)] we developed a model for the drying of porous media in the presence of gravity. It incorporated effects of corner film flow, internal and external mass transfer, and the effect of gravity. Analytical results were derived when gravity opposes drying and hence leads to a stable percolation drying front. In this paper, we test the theory using laboratory experiments. A series of isothermal drying experiments in glass bead packings saturated with volatile hydrocarbons is conducted. The transparent glass cells containing the packing allow for the visual monitoring of the phase distribution patterns below the surface, including the formation of liquid films, as the gaseous phase invades the pore space, and for the control of the thickness of the diffusive mass boundary layer over the packing. The experimental results agree very well with theory, provided that the latter is generalized to account for the effects of corner roundness in the film region (which was neglected in the theoretical part). We demonstrate the existence of an early constant rate period (CRP), which lasts as long as the films saturate the surface of the packing, and of a subsequent falling rate period (FRP), which begins practically after the detachment of the film tips from the external surface. During the CRP, the process is controlled by diffusion within the stagnant gaseous phase in the upper part of the cells, yielding a Stefan tube problem solution. During the FRP, the process is controlled by diffusion within the packing, with a drying rate inversely proportional to the observed position of the film tips in the cell. Theoretical and experimental results compare favorably for a specific value of the roundness of the films, which is found to be constant and equal to 0.2 for various conditions, and verify the theoretical dependence on the capillary Ca(f), Bond Bo, and Sherwood Sh numbers.

Structure of drying fronts in three-dimensional porous media

Evaporation in a three-dimensional (3D) porous medium, a sand column saturated by water, was studied using synchrotron x-ray tomography. Three-dimensional images of the medium with a resolution of 7 μm were obtained during the evaporation. The entire column was scanned seven times, resulting in nearly 10(4) 2D cross sections and illustrating the spatial distribution of air, liquid, and solid phases at the pore scale. The results were analyzed in order to gain new insights and better understanding of the characteristics of the drying front that was formed when the liquid-filled pores were invaded by air, as well as the structure of the liquid phase as it was dried. The analysis indicates that the liquid phase has a self-similar fractal structure, with its fractal dimension D(f) in all the cross sections being a function of the water content or saturation. In addition, D(f) for the 3D liquid structure, as well as its density correlation function, were computed using the 3D images. A crossover length scale ξ was identified that separates the fractal regime from the compact geometry. For length scales r>ξ, the density correlation function approaches asymptotically the water content of the porous medium. The drying front is shown to be rough and multi-affine, rather than self-affine. Its properties were also computed using the 3D images. The roughness characteristics agree with those for imbibition in porous media, but not with those of fracture surfaces and crack lines.