Effect of liquid films on the isothermal drying of porous media

Pore-network extraction using discrete Morse theory: Preserving the topology of the pore space

Pore-scale modeling based on the 3D structural information of porous materials has enormous potential in assessing physical properties beyond the capabilities of laboratory methods. Such capabilities are pricey in terms of computational expenses, and this limits the applicability of the direct simulations to a small volume and requires high-performance computational resources, especially for multiphase flow simulations. The only pore-scale technique capable of dealing with large representative volumes of porous samples is pore-network (PNM) based modeling. The problem of the PNM approach is that 3D pore geometry first needs to be simplified into a graph of pores and throats that conserve topological and geometrical properties of the original 3D image. While significant progress has been achieved in terms of geometry representation, no methodology provides full conservation of the topological features of the pore structure. In this paper we present a pore-network extraction algorithm for binary 3D images based on discrete Morse theory and persistent homology that by design targets topology preservation. In addition to methodological developments, we also clarify the relationship between topological characteristics of constructed Morse chain complex and pore-network elements. We show that the Euler numbers calculated for PNMs based on our methodology coincide with those obtained using the direct topological analysis. The characteristics of the extracted pore network are calculated for several 3D porous binary images and compared with the results of maximum inscribed balls-based and watershed-based approaches as well as a hybrid approach to support our methodology.

Lattice Boltzmann Modeling of Drying of Porous Media Considering Contact Angle Hysteresis

Drying of porous media is governed by a combination of evaporation and movement of the liquid phase within the porous structure. Contact angle hysteresis induced by surface roughness is shown to influence multi-phase flows, such as contact line motion of droplet, phase distribution during drainage and coffee ring formed after droplet drying in constant contact radius mode. However, the influence of contact angle hysteresis on liquid drying in porous media is still an unanswered question. Lattice Boltzmann model (LBM) is an advanced numerical approach increasingly used to study phase change problems including drying. In this paper, based on a geometric formulation scheme to prescribe contact angle, we implement a contact angle hysteresis model within the framework of a two-phase pseudopotential LBM. The capability and accuracy of prescribing and automatically measuring contact angles over a large range are tested and validated by simulating droplets sitting on flat and curved surfaces. Afterward, the proposed contact angle hysteresis model is validated by modeling droplet drying on flat and curved surfaces. Then, drying of two connected capillary tubes is studied, considering the influence of different contact angle hysteresis ranges on drying dynamics. Finally, the model is applied to study drying of a dual-porosity porous medium, where phase distribution and drying rate are compared with and without contact angle hysteresis. The proposed model is shown to be capable of dealing with different contact angle hysteresis ranges accurately and of capturing the physical mechanisms during drying in different porous media including flat and curved geometries.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s11242-021-01644-9.

Magnetic resonance imaging of enhanced mobility of light non aqueous phase liquid (LNAPL) during drying of water wet porous media

Visualization of NAPLs in multiphase systems in porous media is important for determining contaminant transport in the environment. In this study, magnetic resonance imaging (MRI) was used to confirm the recent observations of mobilisation of a light non aqueous phase liquid (LNAPL) trapped in wet sand under natural drying conditions of the wet porous medium. Visualization of LNAPL (motor oil) and water mobility during the drying of wet glass beads (0.5 mm) in a cylindrical glass column (15 mm ID, 45 mm long) was obtained using spin echo-based NMR microimaging performed at 500 MHz, corresponding to a field of ca. 11.75 T. Sagittal and axial images of LNAPL and water in the porous medium were obtained at a spatial resolution of 59 μm/pixel at different time intervals. A rise of 15-20 mm was observed in the presence of evaporation of water as compared to a 2-3 mm rise in the absence of evaporation in a time span of about 1400 min. The spatio-temporal MRI scans of the water and LNAPL in the glass column reveals that LNAPL rise occurs when the water evaporation front reaches the LNAPL layer. This implied that the enhanced LNAPL rise was strongly linked to the process of water evaporation. A linear correlation of the MRI signal intensities of LNAPL and water with reference to different saturation levels of LNAPL and water in the porous media was obtained. This calibration information was used to quantify the saturation levels of the LNAPL and water during the drying process. These findings show the application of non-invasive techniques such as MRI in quantifying and understanding the mechanism of fate and transport of LNAPLs in porous media, towards effective environmental quality assessment.

Evaporation kinetics of continuous water and dispersed oil droplets

Drying of volatile oil droplets immersed in a continuous water phase was observed and analysed. Drying sample solutions were sandwiched between two glass plates and the water and oil phases were observed by confocal microscopy. In the initial stage of drying, evaporation of water was dominant and drying of the oil droplets was negligible. However, the rate of water evaporation decreased when the oil droplets were compressed. Comparison of experimental data with a diffusion model of water vapour showed that the decline in drying rates occurred earlier in the experiment than in the theoretical prediction. This implies that compression and narrowing of water paths caused the decline in the rate of water evaporation. After most water had evaporated, evaporation of the oil droplets occurred. The oil droplets did not shrink isotropically and the air-liquid interface invaded into the drying oil droplets. Cross-sectional observation by z-scanning revealed direct exposure of the oil droplets and they were pinned by the residual water phase. The water network between the oil droplets collapsed after the oil droplets had evaporated. The correlation between changes in structures and drying kinetics in both liquid phases was discussed.

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.

Visualization of water drying in porous materials by X-ray phase contrast imaging

We present in this study results from X-ray tomographic microscopy with synchrotron radiation performed both in attenuation and phase contrast modes on a limestone sample during two stages of water drying. No contrast agent was used in order to increase the X-ray attenuation by water. We show that only by using the phase contrast mode it is possible to achieve enough water content change resolution to investigate the drying process at the pore-scale. We performed 3D image analysis of the time-differential phase contrast tomogram. We show by the results of such analysis that it is possible to obtain a reliable characterization of the spatial redistribution of water in the resolved pore system in agreement with what expected from the theory of drying in porous media and from measurements performed with other approaches. We thus show the potential of X-ray phase contrast imaging for pore-scale investigations of reactive water transport processes which cannot be imaged by adding a contrast agent for exploiting the standard attenuation contrast imaging mode.

MRI evidence for a receding-front effect in drying porous media

After drying colloidal particles suspended in a porous medium a concentration gradient appears. Using ^{1}H MRI we propose a protocol to observe simultaneously the distributions of air, liquid, and colloid through the unsaturated solid porous structure. Thus we show that the above phenomenon comes from a receding-front effect: The elements migrate towards the free surface of the sample and accumulate in the remaining liquid films. Our understanding of the process makes it possible to establish a simple model without diffusion predicting the drying rate and the concentration distribution in time, in excellent agreement with the experimental observations.

Liquid transport facilitated by channels in Bacillus subtilis biofilms

Many bacteria on earth exist in surface-attached communities known as biofilms. These films are responsible for manifold problems, including hospital-acquired infections and biofouling, but they can also be beneficial. Biofilm growth depends on the transport of nutrients and waste, for which diffusion is thought to be the main source of transport. However, diffusion is ineffective for transport over large distances and thus should limit growth. Nevertheless, biofilms can grow to be very large. Here we report the presence of a remarkable network of well-defined channels that form in wild-type Bacillus subtilis biofilms and provide a system for enhanced transport. We observe that these channels have high permeability to liquid flow and facilitate the transport of liquid through the biofilm. In addition, we find that spatial variations in evaporative flux from the surface of these biofilms provide a driving force for the flow of liquid in the channels. These channels offer a remarkably simple system for liquid transport, and their discovery provides insight into the physiology and growth of biofilms.

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.

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

We develop a mathematical model for the drying of porous media in the presence of gravity. The model incorporates effects of corner flow through macroscopic liquid films that form in the cavities of pore walls, mass transfer by diffusion in the dry regions of the medium, external mass transfer over the surface, and the effect of gravity. We consider two different cases: when gravity opposes liquid flow in the corner films and leads to a stable percolation drying front, and when it acts in the opposite direction. In this part, we develop analytical results when the problem can be cast as an equivalent continuum and described as a one-dimensional (1D) problem. This is always the case when gravity acts against drying by opposing corner flow, or when it enhances drying by increasing corner film flow but it is sufficiently small. We obtain results for all relevant variables, including drying rates, extent of the macroscopic film region, and the demarkation of the two different regimes of constant rate period and falling rate period, respectively. The effects of dimensionless variables, such as the bond number, the capillary number, and the Sherwood number for external mass transfer are investigated. When gravity acts to enhance drying, a 1D solution is still possible if an appropriately defined Rayleigh number is above a critical threshold. We derive a linear stability analysis of a model problem under this condition that verifies front stability. Further analysis of this problem, when the Rayleigh number is below critical, requires a pore-network simulator which will be the focus of future work.

Drying of a model soil

Drying experiments have been carried out with model soils made of different pastes filling granular packings. A detailed information concerning the time evolution of the water saturation distribution inside the sample was obtained from magnetic resonance imaging measurements. This study makes it possible to understand the physical origin of the drying characteristics of these materials. The drying curves exhibit a constant-rate period (CRP) and a falling-rate period (FRP) but the relative durations of these periods depend on the paste structure. With a kaolin suspension the CRP lasts down to very low water densities and is associated with a homogeneous drying of the paste throughout the sample. With a bentonite suspension the CRP is shorter and the drying in the FRP results from a complex process involving fractures progressing downward through the pasty matrix. With a gel the CRP period is even shorter and the drying in the FRP results from the progression of a dry front through the packing as a result of the shrinkage of the gel matrix. This provides an overview of the main possible processes at work when drying a soil as a function of its components along with some practical means for slowing down drying from soils.

Evaporation and capillary coupling across vertical textural contrasts in porous media

High and nearly constant evaporation rates from initially saturated porous media are sustained by capillary-driven flow from receding drying front below the evaporating surface. The spatial extent of continuous liquid pathways in homogeneous porous medium is defined by its hydraulically connected pore size distribution. We consider here evaporative losses from porous media consisting of two hydraulically coupled dissimilar domains each with own pore and particle size distributions separated by sharp vertical textural contrast. Evaporation experiments from texturally dissimilar media were monitored using neutron transmission and dye pattern imaging to quantify water distribution and drying front dynamics. Drying front invades exclusively coarse-textured domain while fine-textured domain remains saturated and its surface continuously coupled with the atmosphere. Results show that evaporation from fine-textured surface was supplied by liquid flow from adjacent coarse domain driven by capillary pressure differences between the porous media. A first characteristic length defining limiting drying front depth during which fine sand region remains saturated is deduced from difference in air-entry pressures of the two porous media. A second characteristic length defining the end of high evaporation rate includes the extent of continuous liquid films pinned in the crevices of the pore space and between particle contacts in the fine medium. We established numerically the lateral extent of evaporation-induced hydraulic coupling that is limited by viscous losses and gravity. For certain combinations of soil types the lateral extent of hydraulic coupling may exceed distances of 10 m. Results suggest that evaporative water losses from heterogeneous and coupled system are larger compared with uncoupled or homogenized equivalent systems.

Three periods of drying of a single square capillary tube

The drying kinetics of a porous medium is classically described in three main periods, which depend on the interplay between the external and internal mass transfers during evaporation. The first period is described as essentially depending on the external mass transfer, whereas the third period is dominated by the internal mass transfer. The second period is a crossover period. We show experimentally that a similar drying kinetics can be obtained from a much simpler system owing to the effect of corner liquid films: a capillary tube of square cross section.

Characteristic lengths affecting evaporative drying of porous media

Evaporation from porous media involves mass and energy transport including phase change, vapor diffusion, and liquid flow, resulting in complex displacement patterns affecting drying rates. Force balance considering media properties yields characteristic lengths affecting the transition in the evaporation rate from a liquid-flow-based first stage limited only by vapor exchange with air to a second stage controlled by vapor diffusion through the medium. The characteristic lengths determine the extent of the hydraulically connected region between the receding drying front and evaporating surface (film region) and the onset of flow rate limitations through this film region. Water is displaced from large pores at the receding drying front to supply evaporation from hydraulically connected finer pores at the surface. Liquid flow is driven by a capillary pressure gradient spanned by the width of the pore size distribution and is sustained as long as the capillary gradient remains larger than gravitational forces and viscous dissipation. The maximum extent of the film region sustaining liquid flow is determined by a characteristic length L_{C} combining the gravity characteristic length L_{G} and viscous dissipation characteristic length L_{V} . We used two sands with particle sizes 0.1-0.5 mm ("fine") and 0.3-0.9 mm ("coarse") to measure the evaporation from columns of different lengths under various atmospheric evaporative demands. The value of L_{G} determined from capillary pressure-saturation relationships was 90 mm for the coarse sand and 140 mm for the fine sand. A significant decrease in drying rate occurred when the drying front reached the predicted L_{G} value (viscous dissipation was negligibly small in sand and L_{C} approximately L_{G} ). The approach enables a prediction of the duration of first-stage evaporation with the highest water losses from soil to the atmosphere.

Influence of wettability conditions on slow evaporation in two-dimensional porous media

We study numerically the influence of the wettability condition on slow evaporation in two-dimensional pore square networks of aspect ratio 1. We show how evaporation in a hydrophobic network can be simulated numerically by combining imbibition rules and the computation of diffusion transport in the gas phase. Then we conduct a statistical study of drying in hydrophilic or hydrophobic networks based on pore network simulations. We concentrate on the situation where the external transfer resistance and liquid film effect are negligible and the invasion is dominated by capillary effects. It is found that drying in a hydrophilic network is significantly faster than in a hydrophobic one. The dimensionless overall drying time is found to be network size dependent, approaching exponentially a limit for large size hydrophilic networks. The dimensionless average overall drying time is 0.93 and 0.75 in hydrophobic and hydrophilic large networks, respectively. Other properties, such as the overall saturation and the evaporation flux (through the concept of equivalent flat front position) are also studied. In a last part the impact of liquid film flow on the overall drying time fluctuation is briefly investigated for the case of hydrophilic networks. It is found that the films dampen the drying time fluctuations.

Pore-network study of methane hydrate dissociation

A two-dimensional pore-network model based on invasion percolation is used to study the patterns obtained from the release of methane during the dissociation of methane hydrates (without including dissociation kinetics) caused by a sudden pressure reduction in the system below the hydrate equilibrium pressure. The concept of the critical gas saturation S(gc) (volume fraction of the gas phase at the onset of bulk gas flow) is introduced to analyze gas hydrate dissociation. The effects of throat-size distribution (corresponding to off-shore oceanic sediments or on-shore sediments under permafrost), applied pressure difference across the network, and initial hydrate saturation on the resulting gas patterns and on the critical gas saturation are examined to determine the possibility of producing methane. As expected, large throat sizes or wide throat distributions, large pressure drops, and higher initial hydrate saturation act as promoters for the production of the released gas. For typical deep ocean sediments with small pore sizes and low hydrate saturation, it may be difficult to produce methane resulting from hydrate dissociation.

Pore-network study of the characteristic periods in the drying of porous materials

We study the periods that develop in the drying of capillary porous media, particularly the constant rate (CRP) and the falling rate (FRP) periods. Drying is simulated with a 3-D pore-network model that accounts for the effect of capillarity and buoyancy at the liquid-gas interface and for diffusion through the porous material and through a boundary layer over the external surface of the material. We focus on the stabilizing or destabilizing effects of gravity on the shape of the drying curve and the relative extent of the various drying periods. The extents of CRP and FRP are directly associated with various transition points of the percolation theory, such as the breakthrough point and the main liquid cluster disconnection point. Our study demonstrates that when an external diffusive layer is present, the constant rate period is longer.

Strongly accelerated and humidity-independent drying of nanochannels induced by sharp corners

Measurements are shown indicating that the drying rate of nanochannels can be enhanced by up to 3 orders of magnitude relative to drying by vapor diffusion, and that the drying rate is independent of the relative humidity of the environment up to a relative humidity of more than 90%. Micromachined Pyrex glass nanochannels of 72 nm height and with sharp corners (corner angles 7 degrees) were used. Available theory shows that the sharp corners function as a low-resistance pathway for liquid water, siphoning (wicking) the water to a location close to the channel exit before it evaporates. The described phenomena are of importance for the understanding of drying processes in industry and agriculture. The introduction of sharp corners or grooves can furthermore be beneficial for the functioning of microheat pipes and capillary-pumped loops.