FIG 1 - uploaded by Philippe Coussot
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NMR profiles along sample axis at different times (time interval t) (from top to bottom) during drying for bead packings with different particle diameters: (a) 45 000 nm (time interval of 23, then 44 min), (b) 1500 nm (33 min), (c) 1000 nm (36 min), (d) 300 nm (50 min), (e) 80 nm (33 then 44 min), (f) 40 nm (28 min), (g) 12 nm (16 min), and (h) 6 nm (23 min). The first profile with some gradient in saturation is represented by a thicker line. The dotted line corresponds to the first profile after the time interval change. Note that for the sake of clarity data for 300 and 80 nm in the FRP have been smoothened.
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Magnetic resonance imaging visualization down to nanometric liquid films in model porous media with pore sizes from micro- to nanometers enables one to fully characterize the physical mechanisms of drying. For pore size larger than a few tens of nanometers, we identify an initial constant drying rate period, probing homogeneous desaturation, follow...
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Citations
... The drying of a porous medium fully saturated with free water is a process which is relatively well known. For pore sizes larger than a few hundred nanometers and smaller than a few millimeters, as in the case of our cellulose fiber stacks, capillary effects dominate as long as the saturation is not too low [70] and the drying induces a transport of the liquid towards the sample surface where it evaporates. Most of the liquid is extracted during this period and the drying rate is constant. ...
... However, they mentioned little about the transition mechanism from CRP to FRP and the behavior of the drying rate in FRP. Although Thiery et al. [8] used bottomed containers, the effect of gravity was negligible because of their small pore diameters (mostly sub-micrometers). With MRI, they confirmed the growth of the dry region in FRP and showed for the first time that the falling rate can be understood quantitatively by water vapor diffusion through the dry region. ...
... With MRI, they confirmed the growth of the dry region in FRP and showed for the first time that the falling rate can be understood quantitatively by water vapor diffusion through the dry region. Thiery et al. [8] defined the critical saturation, ⟨S⟩ * , as the spatially averaged water saturation when the water saturation gradient appears in the wet region and found that the transition occurs approximately at the same time. They also showed an empirical formula as below: ...
... If water transport in the wet region is regarded as the advection of liquid water driven by capillary pressure gradient and water permeability [8], water saturation must satisfy the following equation: ...
The drying rate profile of granular beds can be divided into the constant rate period (CRP), which is characterized by a nearly constant drying rate, and the falling rate period (FRP), in which the drying rate rapidly decays. In order to explain this behavior quantitatively, we proposed a simple one-dimensional power law model in which the product of the water permeability and the pressure gradient is assumed to be proportional to the cube of the saturation. To test this model, we measured the drying rates of glass beads and hierarchical granular materials produced by sintering and breaking glass beads. Our results and those of previous experiments showed consistency with the power law. The obtained proportional constant of the experimental power law also shows a rough agreement with that estimated from previous studies on water permeability and capillary pressure. Drying behavior in FRP also agrees with our model in some points. The remnant deviation of the model from experimental results may be attributed to the inhomogeneity of granular media, which was qualitatively verified.
... On the other hand, the evaporation/condensation phenomenon has a long development history in thermodynamics and has found a large number of applications in engineering such as steam power 10 and heat exchangers. [11][12][13][14] Considering the phase change in porous media, many studies have focused on the slow phenomenon of drying, [15][16][17][18] which is involved in a number of different applications (e.g., paper, 19 soil, 20 or food 21 drying). Recently, the phase change from ice to vapor sublimation has been introduced in a study on melting snow. ...
This paper investigates acoustic wave propagation in wet rigid-frame porous media accounting for evaporation and condensation. At equilibrium, the solid walls are covered by a thin water film, and water vapor in the air is at its temperature-dependent saturation pressure. Small acoustic perturbations cause water to vaporize or condense, which together with the reversibility of the phase change, lead to a linear problem where the usual local poro-acoustics physics is enriched with the (i) Clapeyron relation linking liquid-wall temperature, vapor pressure, and latent heat of vaporization, (ii) latent heat transfer in the solid frame, (iii) diffusion equation for water vapor in air, and (iv) water vapor's equation of state. The equilibrium temperature highly influences the vapor concentration and the physical parameters of saturated moist air. Using the two-scale asymptotic homogenization method, it is shown that the dynamic permeability is determined similarly to classical porous media, while the effective compressibility is modified by evaporation/condensation and the equilibrium temperature. This modification is influenced by vapor mass and heat flows associated with phase changes through a local fully coupled heat transfer and water vapor diffusion problem, with specific boundary conditions at the gas–water interface. The analysis identifies dimensionless parameters and characteristic frequencies defining the upscaled model's features. Depending on equilibrium temperature, the theory qualitatively and quantitatively determines the characteristics of acoustic waves propagating through the media. The results are illustrated and discussed with analytically developed models.
... Indeed, in general, it is well established that for simple Newtonian fluids, two main drying regimes can be observed [39,48,51,52]: the Constant Rate Period (CRP) where evaporation happens at the surface of the stone and the Falling Rate Period (FRP). During the CRP, the capillary transport to the surface of the porous medium is faster than the mean evaporation speed. ...
Historical monuments, outdoor stone sculptures, and artworks made of porous materials are exposed to chemical and physical degradations over time. Presently, the most promising route for consolidation of weakened porous materials is the injection of viscoelastic solutions of polymerizing compounds. Those compounds, after injection, undergo a sol-gel transition inside the porous media through evaporation of the solvent. Finding a suitable gelifying solution as a consolidant calls for understanding the drying kinetics of viscoelastic fluids in porous media. Here, we present a multiscale study of the drying kinetics of fluids during the sol-gel transition in porous materials using NMR and x-ray microtomography techniques. We find that from the early stage of the drying, a heterogeneous desaturation develops and advances from the free surface of evaporation towards the inner parts of the stone. We identify different drying periods, which appear to be dependent on the intrinsic properties of the porous medium influencing strongly the homogeneity of the final gel distribution within a treated stone. Our findings not only are relevant for the consolidation of porous artworks but also for civil and soil engineering processes where the fluids considered are generally more complex than water.
... Mass transfer phenomena between phases are controlled by thermodynamic conditions at the liquid-vapor interfaces within the pores, and these evaporation-condensation processes have been largely studied in the context of porous media drying. [4][5][6][7][8] Direct numerical simulation methods are still being developed and improved to simulate the process of evaporation, such as the volume-of-fluid method, [9][10][11] molecular dynamics, [12][13][14] the level set method, 15,16 and smoothed particle hydrodynamics (SPH). 17,18 However, the competition between drying forces (driven by vapor-liquid equilibrium conditions and thus by the equality of chemical potentials) and capillary forces (i.e., surface tension) becomes exacerbated as pore size decreases. ...
... At each time step, vapor concentration C eq [Eq. (8)] driven by the interface curvature is imposed on gas particles located in the transition band near the liquid interface. The vapor mass injected at a gas particle i is calculated as ...
... With parametrization chosen to reduce computational costs, the capillary pressure was too low for the Kelvin effect to be visible. Thus, the molar mass M in Eq. (8) has been artificially modified by a scaling factor of 3:25 Â 10 8 to increase the Kelvin effect in this test case. ...
Understanding drying processes in nanoporous media is of great importance in many technological and industrial situations. To better understand how gas moves through clayey rocks, of interest for underground disposal of radioactive wastes, we propose using pore-scale direct numerical simulations. In this study, we use the Smoothed Particle Hydrodynamics method, which has proved to be an effective approach for simulating complex fluid dynamics within porous media at the nanoscale. Our simulations consider capillary-dominated two-phase flow with evaporation and condensation at liquid–gas interfaces, coupled to the diffusion of water vapor in the gas phase, as well as the Kelvin effect, which is a specific feature of nanopores. Our evaporation-condensation model is validated against analytical solutions. The size of the compact support of kernel function and the particle density required to obtain accurate and stable results of capillary pressure are investigated. Drying regimes, capillary-driven and evaporated-driven, are explored. A specific effort is made to highlight the influence of the Kelvin effect on desaturation and the creation of preferential paths for gas flow as well as its impact on drying rate. The role of condensation due to local vapor concentration conditions is also emphasized.
... Different particle size ranges are used to regulate the media pore size and maintain medium porosity stability [12]. This approach is used to study various aspects of the drying process, such as the medium temperature [13], porous medium thickness [14], drying stage evolution [15], drying characteristic length L C [16], the average depth of the end of the constant velocity period Lcap [17], and validating Whitaker's model [18]. P. Coussot et al. [11] investigated the drying rate variation with pore size (particle size 4.5-200 µm) in an ethanol-soaked granular bed at 23 • C. The results showed that the descending drying period was caused by evaporation and capillary flow within the medium, with the intensity of the capillary flow depending mainly on the granular particle size. ...
The drying kinetics of porous media are crucial for controlling the drying process, which is a vital component in many processes. A mathematical model of the drying process in a granular bed was developed using Whitaker’s model, and its accuracy was verified through experimental results. The results indicated that the three stages of porous media drying are closely linked to the heat flow to the media and the latent heat of evaporation required by the liquid water inside it. Moreover, as the influence of gravity weakens and the capillary force strengthens, specifically due to the gradual decrease in the pore size of the bed, significant differences in the drying kinetics of the bed are observed, particularly in the third stage of drying, which is most affected. The onset of saturation in the third stage of bed drying varies with the pore size of the particles, with smaller pore sizes exhibiting an earlier onset. Additionally, the temperature change in this stage demonstrates the occurrence of secondary warming as the pore size decreases.
... The same regime change will occur with a given system when the air flux intensity is increased from a very low to a high value or by increasing the sample thickness. This is in agreement with the observations of the water distributions over time during the drying of bead packings with pore sizes ranging from 1 mm to a few nanometers 5,72 or clayey materials. 74 Note that an additional complexity with such systems is that, in contrast with hygroscopic systems, at some stage of drying, an apparently dry region of significant thickness can develop below the free surface, while there is still water below this region. ...
... Drying rate starts to decrease since water mass transport is controlled by vapor diffusion to the external surface. The rate of drying depends on the soil moisture conditions and soil hydraulic properties during falling rate period (Brutsaert 1982;Lockington 1994;Shokri and Or 2011;Thiery et al. 2017). The critical moisture content in drying literature is defined as the point at which the transition from the constant rate period to the falling rate period occurs (Sherwood 1929). ...
... In the subsequent part, the drying rate remains almost constant, albeit with some data noise and mild fluctuations. These fluctuations are inevitable under the possibly varying ambient conditions (temperature, relative humidity, and air flow) during the evaporation test since the rate of drying is controlled by external conditions during constant rate period (Scherer 1990, Van Brakel 1980, Shokri et al. 2008, Yiotis et al. 2012and Thiery et al. 2017. For the Ankara clay specimens, the constant rate period for the corrected drying rate curve ascends monotonically until the falling rate period. ...
The effect of microstructure on the hydromechanical behavior of unsaturated soils is an issue that is frequently addressed in literature. A simple procedure is proposed in this study to characterize the soil microstructure through evaporation tests. Time-series gravimetric water content data together with the drying rate curve of an evaporated soil specimen are used to reveal soil’s microstructural properties. The experimental output is used for calibrating the parameter for shear strength model proposed by Alonso et al. (2010). A test program consisting of constant suction and constant water content triaxial tests on various types of soils from non-plastic to highly plastic has been carried out. The shear strength of soils determined from the experiments is predicted with the shear strength model that is calibrated through evaporation tests on the same soils. The model predictions have matched the experimental results satisfactorily. The shear strength of the unsaturated soils is predicted from a quite simple experimental procedure.
... 18,19 The key component of this analysis was the use of insulating nanoparticle films as the sensing layer to capture the vapor. [18][19][20] The dynamics of liquids in nanopore between nanoparticles were studied by using the size of nanoparticles such as drying 21 and condensing 22 processes. In our concept, the condensation and percolation of the vapor into a void space between the nanoparticles were utilized for vapor detection. ...
Rapid electrical analysis of chemical liquids is a promising technique for on-site evaluation. In this study, the electrical impedance response of insulator nanoparticle films with condensed chemical vapors was investigated in structural isomers and polar aprotic chemical liquids. Headspace vapor was condensed in the nanoscale void between the nanoparticles, and ionic conduction subsequently occurred under an AC voltage. The transient electrical impedance response depends on the vapor pressure and conductivity of the liquid isomers. A chemical liquid of the structural isomers was identified by monitoring the impedance during exposure to its headspace vapor. The response time of the film impedance was 10.6, 4.7, 7.5, and 2.4 s for 1-butanol, 2-butanol, 2-methyl-1-propanol, and tert-butyl alcohol, respectively. Furthermore, the current conduction mechanism in the polar aprotic chemicals was discussed. Although these chemicals did not form molecular networks with the hydrogen bonds, the electrical current flowed in the system. We proposed that hydrogen bonds mediated by water molecules were formed and proton hopping through the condensed polar aprotic liquid occurred. This proposed method has the potential to detect protic and aprotic polar chemical vapors.
... In particular, to characterize the transient water distribution, nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) have become versatile tools. NMR-MRI allow to study the evaporation processes noninvasively (Guillot et al., 1991;Koptyug et al., 2000;Saidov et al., 2015;Thiery et al., 2017) and thus have been used for a broad range of applications to study various fluid dynamics in subsurface porous media (Ala-Korpela, 2007;Liao et al., 2021;Liaw et al., 1996;Liu et al., 2018), To date, the experimental evidences have shown interesting and diversified evaporation dynamics from porous media, like the capillary-assisted air invasion or sometimes the emergence of cavitation. ...
Evaporation of water from porous media is essential for a large variety of applications, whereas the opacity of porous matrix imposes considerable challenges in unveiling complicated phase‐change phenomena. Air invasion was previously reported as the major desaturation mechanism, while cavitation in porous media is not well studied. Herein we characterize the transient distribution and evaporation of water in homogeneous tight porous media with nondestructive nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI). By monitoring the amplitude change of NMR transverse relaxation time T2, we investigate the dynamical pore filling status and water content during evaporation. Interestingly, we find that the T2 spectrum shifts immediately after the evaporation starts, indicating the emptying of big pores from the entire medium. Disconnected void clusters at different depths in the porous medium are also observed from MRI scanning and optical images. These observations indicate the emergence of cavitation across the entire porous media along with the evaporation from open surface. Cavitation occurs when the water is stretched to metastable state by large capillary pressure from the evaporating meniscus. By studying the evaporation from hydrophilic membrane‐separated porous media, we further demonstrate the existence of cavitation‐associated evaporation. The preferential water vaporization from the bottom part can still be found from T2 spectrum analysis and optical imaging even when the water‐permeable membrane cuts off possible air invasion. Our findings confirm cavitation‐associated evaporation is one of the primary mechanisms for tight porous media, which provides valuable guidance for evaporation and moisture control.