- Email: [email protected]
Acoustic characteristics of fluid interface displacement in drying porous media
International Journal of Multiphase Flow 62 (2014) 30–36
Contents lists available at ScienceDirect
International Journal of Multiphase Flow j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j m u l fl o w
Acoustic characteristics of fluid interface displacement in drying porous media N. Grapsas a, N. Shokri b,⇑ a b
Department of Earth and Environment, Boston University, Boston, MA, USA School of Chemical Engineering and Analytical Science, University of Manchester, Manchester, UK
a r t i c l e
i n f o
Article history: Received 15 November 2013 Received in revised form 28 January 2014 Accepted 30 January 2014 Available online 10 February 2014 Keywords: Fluid interface displacement Evaporation Porous media Particle size Acoustic emission
a b s t r a c t Water evaporation from porous media involves many rapid interfacial jumps at the pore-scale as air invades the pore network and displaces the evaporating fluid. We show that this process produces a crackling noise that can be detected using an acoustic emission (AE) instrument. We investigated the acoustic signature of evaporation from porous media using transparent glass cells packed with five types of sand and glass beads differing in particle size distribution and grains shape. Each sample was mounted on a digital balance, saturated with dyed water, left to evaporate under well-controlled atmospheric conditions, and digitally imaged every 20 min to quantify the dynamics of liquid phase distributions. An AE sensor was fixed to each column to record AE events (hits) and their acoustic features. Results indicate that the cumulative number of AE hits is strongly proportional to total evaporative losses. Additionally, the cumulative number of hits shares an inverse relationship with particle size and a direct relationship with grain irregularity. Analysis of the dynamics of liquid phase distributions reveals a strong correlation between the area invaded by air and the cumulative number of AE hits. Our results suggest that AE techniques may hold the potential to non-invasively analyze evaporation from porous media. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Evaporation from porous media is a process ubiquitous in many industrial and environmental contexts ranging from the drying of catalysts, paper, pharmaceutical products, and porous building materials to water evaporation from soil which influences the hydrological cycle and various biological activities in the vadose zone. Evaporation from saturated porous media typically involves the invasion of pores by a non-wetting gaseous phase (e.g. air) that displaces a resident wetting liquid phase (e.g. water) resulting in the formation of a receding primary drying front, defined as the interface between saturated and partially saturated zones (Shaw, 1987; Shokri et al., 2012). Many studies have investigated the drying of porous materials under various boundary conditions and have analyzed the effects of parameters such as atmospheric conditions, wettability, porous media transport properties, and the physical and chemical properties of evaporating fluids (Scherer, 1990; Laurindo and Prat, 1998; Yiotis et al., 2006; Chapuis and Prat, 2007; Lehmann et al., 2008; ⇑ Corresponding author. Address: School of Chemical Engineering and Analytical Science, The University of Manchester, Sackville Street, Manchester M13 9PL, UK. Tel.: +44 161 3063980. E-mail address: [email protected] (N. Shokri). http://dx.doi.org/10.1016/j.ijmultiphaseflow.2014.01.011 0301-9322/Ó 2014 Elsevier Ltd. All rights reserved.
Faure and Coussot, 2010; Shokri and Salvucci, 2011; Peysson et al., 2011; Shahraeeni and Or, 2010; Smits et al., 2012; Shokri and Sahimi, 2012; Doel et al., 2012; Shokri et al., 2012; Yiotis et al., 2012a,b; Aminzadeh and Or, 2013; Haghighi et al., 2013; Shokri and Or, 2013; Or et al., 2013). When evaporation from saturated porous media initiates, evaporation rates are mainly controlled by atmospheric demand, are rather high, and remain relatively constant – these features characterize what is referred to as stage-1 evaporation (Saravanapavan and Salvucci, 2000; Shokri and Or, 2011). During stage-1, capillary-induced liquid flow transports the liquid from a receding primary drying front (referred to simply as ‘drying front’ from here on) to the surface where water vaporization takes place. When the drying front recedes to a characteristic depth which can be estimated using the capillary pressure–saturation curve of the medium (Lehmann et al., 2008; Shokri and Salvucci, 2011), hydraulic connectivity with the surface disrupts, resulting in a transition to lower evaporative fluxes that marks the onset of stage-2 evaporation. During this period, liquid vaporization occurs inside the porous medium and evaporation becomes limited by vapor diffusion through the overlying dry layer near the surface (Scherer, 1990; Shokri and Or, 2011). It is well-known that air invasion of saturated porous media produces many discrete, rapid pore-scale interfacial bursts known as ‘‘Haines jumps’’ which result from instabilities at the contact lines
N. Grapsas, N. Shokri / International Journal of Multiphase Flow 62 (2014) 30–36
of menisci as pores are drained (Haines, 1930; Lu et al., 1994; Blunt and Scher, 1995; Aker et al., 2000; DiCarlo et al., 2003; Chotard et al., 2006; Crandall et al., 2009; Moebius et al., 2012). Recent studies have shown that these pore-scale events may generate sounds depending on the process under consideration. For example, DiCarlo et al. (2003) found that drainage from porous media generates an acoustic ‘‘crackling noise’’ composed of many individual acoustic events. Using passive acoustic emission (AE) methods often employed to monitor the accumulation of strain in civil structures and in microseismicity studies (Nair and Cai, 2010), each small event was detected as a ‘‘hit’’ and demonstrated to be related to the displacement of the liquid–gas meniscus in porous media. Chotard et al. (2006) reported that these AEs could also be detected during cement drying and that the cumulative number of hits may be related to evaporative mass loss. Further inquiries undertaken recently by Moebius et al. (2012) have revealed that AE hits generated during fluid front displacement in porous media exhibit a dependency on the medium pore size among other factors. Motivated by the widespread importance of drying in porous media and recent advances in the application of AE techniques with regard to transport phenomena in porous media (Sahimi, 2011), this study aims to evaluate the feasibility of applying non-invasive AE techniques to characterize the drying of porous media. Within this context, we present experiments which demonstrate that AEs generated during evaporation are related to Haines jumps and are indeed strongly linked to evaporative mass loss during evaporation from porous media. Additionally, we show that medium particle size and grain surface irregularity also influence the acoustic signature of the evaporation process which will be discussed in detail. 2. Materials and methods The model porous media used in this work consisted of either silica sand or glass beads across a range of particle sizes. Fig. 1 presents the particle size distributions (PSDs) of the media obtained using CAMSIZER Digital Image Processing Particle Size from HORIBA. The sand grains had average particle sizes (diameters, d) of 0.34 mm, 0.58 mm, and 0.89 mm, and the glass beads had average particle sizes of 0.15 mm and 0.53 mm. These particles were selected so that the influence exerted on AE characteristics by changes in particle size and roughness, and by extension pore space geometry, could be assessed. As illustrated in Fig. 1a, the sand sample with an average particle size of 0.58 mm possessed a particle size distribution quite
31
similar to the glass bead sample with an average particle size of 0.53 mm. This provided the opportunity to constrain the effects of grain shape and pore roughness on drying behavior since the sand grains were rough and shaped irregularly whereas the glass beads were relatively smooth spheres. Particles were saturated with a dye-water solution and packed uniformly into 8 cm 8 cm 0.5 cm transparent glass Hele–Shaw cells closed on all sides except the top, which was left uncovered to enable evaporation. An identical procedure was used to pack particles into each cell. 5 mL of blue dye was added to 1 L of water and stirred inside of a Tupperware container. Importantly, using dye increased the contrast between the phases present during drying making image segmentation possible. Dry particles were transferred into this solution and mixed to purge trapped air and guarantee complete, uniform saturation. After saturating the particles, some excess ponding solution was transferred into a Hele–Shaw cell to a depth of 1 cm while ensuring that the particles remained submerged and saturated. Using an indented spatula with an effective diameter of 1/3 cm, small amounts of saturated particles were scooped from the Tupperware and transferred into the fluid within the Hele–Shaw cell. Particles were transferred in this manner until they accumulated to a height of 1.5 cm. At this point, a stir was used to gently mix the particles which were then allowed to settle. This procedure of transferring, mixing, and compacting particles was repeated until particles accumulated to 6 cm within each Hele–Shaw cell. This process removed entrapped air bubbles and guarded against the layering effects that result from transferring particles in discrete increments. Managing layering effects is essential to fluid flow or evaporation experimentation as the incremental addition of particles forms distinct strata with independent hydraulic properties. An opaque white plastic backing with a cutout for an AE sensor was taped to the rear of each cell to provide a consistent, uniformly colored backdrop which aided during image segmentation of the transparent glass bead samples. The cells were left to evaporate on digital balances (accurate to 0.01 g) in an environmental chamber set to 35 °C and 30% relative humidity. Mass measurements were recorded every 5 min, and photos of the glass cells were taken every 20 min with a computer-operated digital camera intended to track changes in liquid phase distributions with a spatial resolution of 110 lm. A model R6I-AST Physical Acoustic Corporation resonant AE sensor (45 kHz peak frequency and operating range from 23 dB to 117 dB) with a built in preamplifier was fixed to the rear of each
Fig. 1. (a) Particle size distributions of different sand and glass beads used in the experiments. The numbers in the legends indicate the average particle size of the porous medium in each cell. S and GB refer to sand and glass beads, respectively. (b) Schematic of the experimental setup. Hele–Shaw cells packed with well-defined particle sizes are mounted on digital balances connected to a PC to record the dynamics of water evaporation while changes in liquid phase distribution during evaporation were automatically recorded using a digital camera. An AE sensor was mounted to the rear of each cell using duct tape. (c) Conceptual sketch of a typical acoustic emission signal recorded by the AE machine with its corresponding features.
32
N. Grapsas, N. Shokri / International Journal of Multiphase Flow 62 (2014) 30–36
Hele-Shaw cell on Dow Corning 7 Release Compound and linked to a Physical Acoustics Corporation Micro-II Digital AE system. This setup allowed AE waveforms to be recorded in units of mV and reports individual AE hit features such as absolute energy (hereafter referred to as energy), amplitude, duration, and frequency in addition to tallying the cumulative number of observed hits. An amplitude threshold of 26 (dB) was used to remove background noise. Fig. 1b and c illustrate the experimental setup and the schematic of an AE waveform with the corresponding features. 3. Results and discussion 3.1. Sources of AE hits generated during evaporation from porous media Moebius et al. (2012) have identified five AE-generating mechanisms associated with fluid front displacement in porous media: Haines jumps, liquid bridge rupture, air bubble entrainment and oscillation, interfacial snap-off, and grain collisions. Each source mechanism gives rise to mechanical waves in a unique way. Haines jumps likely release mechanical energy when menisci reduce their interfacial energies during jumps from less stable configurations across larger pore throats to more stable configurations across smaller ones (Quere, 1997). Suspended liquid bridges, which are entrapped saturated regions left behind by the receding drying fronts, rupture when evaporation from their surfaces causes them to shrink until they reach a critical volume (Orr et al., 1975). The magnitude of interfacial energy reductions that occur during these events have been shown to be of similar order to those during Haines jumps, but bridge ruptures are substantially rarer events (Simons et al., 1994). Air bubble entrapment, coalescence and oscillations, which occur when contact lines and fluid displacement fronts reconfigure while abruptly moving across rough surfaces, emit sound either when air becomes entrapped from a free surface or when bubbles snap-off from larger parent gas bodies (Manasseh et al., 2008). Other interfacial snap-off processes (Joekar-Niasar et al., 2008) have been studied comprehensively (Kovscek and Radke, 1996; Gauglitz and Radke, 1989, 1990) and are associated with the release of interfacial energy (Ransohoff et al., 1987). Mechanical collisions of the type that occur between grains during settling or in response to capillary forces and pressure waves have also been identified as one of a host of potential AE sources (Michlmayr et al., 2012). These five phenomena represent the processes which may contribute to the AE signatures detected during our evaporation experiments.
We analyzed the time evolution of the number of AE hits observed, their amplitudes and energies generated during evaporation from porous media. These observables constitute the commonly used AE analytical features. Given that the peak 45 kHz resonant frequency of our sensors corresponds to sound wavelengths in silica of 132 mm which is orders of magnitude larger than the particle diameters in this study, AEs likely undergo little scattering and propagate uniformly (Jia, 2004). The effects of signal attenuation on these observables were ignored due to the small volume of packed sand through which elastic waves had to propagate to reach an AE sensor. 3.2. AE hits and evaporative mass loss When drying initiated, a receding drying front developed in each medium as air began to invade and displace the evaporating water. Fig. 2 presents typical curves illustrating the time evolutions of evaporative mass loss and AE hits generated during evaporation. The observed mass loss pattern dynamics were consistent with data previously reported in literature (Shokri and Or, 2011). High constant drying rates – indicated by the constant slopes of the mass loss curves – are initially present during stage-1 evaporation wherein capillarity draws fluids from the saturated zone to the medium’s surface to evaporate. Discernible changes in drying rates occurred either when the saturated zones became depleted of fluid (which was the case for the sand sample with an average particle size of 0.34 mm) or when a sample entered stage-2 evaporation (as was the case for the sand samples with average particle sizes of 0.58 mm and 0.89 mm and for the glass bead sample with an average particle size of 0.53 mm) when the upward capillary force could no longer overcome the downward gravitational force (viscous forces are negligible in our experiments due to the relatively large particle sizes). As illustrated in Fig. 2, the AE hit rates are found to strongly correlate with mass loss rates in all cases, suggesting a direct relationship between AE hits and mass loss that was first observed by Chotard et al. (2006). Before air began penetrating the pore spaces, the AE hit rates were zero indicating that background noise was not being captured and that the processes by which AEs are produced had not yet commenced. Once air began invading the porous media, stage-1 evaporation started and the highest hit rates were observed. Since the drying rate is faster during stage-1, more pore-scale interfacial jumps are induced causing more AEs to be emitted. After the saturated regime was either exhausted or the process entered stage-2 evaporation, the AE hit rates dropped
Fig. 2. (a–d) The cumulative evaporative losses and cumulative AE hits versus time measured using digital balances and AE sensors during evaporation from sand (S) and glass beads (GB).
N. Grapsas, N. Shokri / International Journal of Multiphase Flow 62 (2014) 30–36
precipitously but maintained proportionality with mass loss. It is important to note that AE hits were only observed while evaporation was active and air invaded the medium, suggesting that AEs dominantly emerged from motions of the air–water interface. This pattern was present for all particle sizes and roughnesses. Fig. 2 shows the great potential of the AE technique to monitor, noninvasively quantify, and analyze the drying of a porous medium. It also illustrates the significant influence of particle size and grain shape (pore geometry) on drying behavior and on the emergent characteristics of AEs which will be discussed in following sections. 3.3. Linking AE hits to fluid invasion patterns The dynamics of liquid phase distributions during evaporation were quantified by segmenting the recorded images into binary data representing the saturated and unsaturated phases following the procedure described in Shokri et al. (2012). Fig. 3 depicts a representative time progression of air invasion and drying front propagation. The white, red, green, and blue regions correspond to air-invaded areas after 5, 10, 15, and 25 h from the onset of evaporation and the black region corresponds to the saturated region after 25 h. We have calculated the time evolution of invaded area for all particle sizes using the segmented images and compared the
33
results to the recorded AE hits. Fig. 4 illustrates that a direct proportionality is shared between the time evolution of AE hits and invaded area (denoted as IA in the figures) during stage-1 evaporation for all particle classes. Any region invaded by air experienced many pore-scale interfacial motions. It follows that any changes in invaded area necessarily stemmed from these porescale interfacial bursts, implying that the number of AE hits recorded directly corresponded to the number of Haines jumps that occurred in the medium. In Fig. 4c, for sand with an average particle size of 0.89 mm, two large steps occur in invaded area approximately half a day into the trial. Inspection of both the raw and binary images recorded at those times reveals massive, rapid invasion events in the area analyzed. These dramatic events can be explained by avalanches of pore invasions which only stop once all the menisci involved stabilize across pore throats smaller than those they originally spanned. Such drastic invasion events were observed only during drying of the largest-diameter particle class due to its volumetrically larger pores. The presence of larger pores reduces the likelihood that a propagating meniscus will attain a stable configuration in a given volume after destabilizing – avalanches also occurred in smaller particle classes but over smaller volumes and areas. The AE hit rate likely remained constant in spite of these avalanches because of the limited image section that was used to assess invaded area; decreased hit rates from regions outside of the analyzed field of view could have compensated for increased hit rates associated with the avalanches. The time resolution of our analysis may also exaggerate the impact of such avalanche events. 3.4. Influence of particle size on the AEs generated during evaporation Hydraulic conductivity, porosity, and in particular the pore geometry of a porous medium are dependent on the constituent grains’ sizes and shapes. Since AEs are generated by meniscus motions in pores, pore-scale configuration may imprint a signature on the crackling sound detected using AE equipment. In the following section, we discuss the effects of particle size and surface irregularity on the characteristics of resulting AEs.
Fig. 3. Typical air invasion patterns at macro-scale during evaporation from sand with an average particle size of 0.58 mm. White, red, green, and blue indicate the invaded region after 5, 10, 15 and 25 h respectively. Black corresponds to the saturated region after 25 h.
3.4.1. AE events as influenced by the medium texture The precise proportionality between AE hits and mass loss in Fig. 2 as well as between AE hits and invaded area in Fig. 4 varies among particle classes. This varying proportionality suggests that
Fig. 4. (a–d) Area of the invaded regions (IA) versus time in glass cells packed with sand (S) and glass beads (GB) with different average particle sizes. The invaded area was delineated by image analysis and compared to the recorded number of AE hits.
34
N. Grapsas, N. Shokri / International Journal of Multiphase Flow 62 (2014) 30–36
volume. Individual displacements would be of smaller volumes, and we would expect them to produce correspondingly fainter emissions since meniscus motions would involve less energy. Thus, AEs generated during drying in media with rough particles and irregular pores would tend to occur at lower amplitudes and energies than for AEs produced during drying in media whose particles and pore spaces are smooth.
Fig. 5. The cumulative number of AE hits observed as a function of the cumulative mass loss for each particle. S and GB refer to sand and glass beads, respectively.
a medium’s particle size, surface roughness, and typical grain (pore) shape influence the characteristics of AEs emitted during evaporation from porous media. This can be rationalized since both pore shape and size influence the pore-scale liquid phase reconfiguration dynamics that ultimately mediate emitted AE signals. Fig. 5 displays the number of AE hits observed as a function of mass loss across all of the particles used in our experiments. This figure shows that hit rate varies indirectly with particle size. Assuming a constant porosity of 0.4 in all cases, a medium consisting of larger particles has larger pores meaning that fewer pores are vacated per given volume of evaporated water. Therefore, when fluid evaporation evacuates an equal volume from two media with distinct particle sizes, more interfacial jumps occur in the finer medium leading to more AE hits. Fig. 5 also suggests that more mass is lost per hit in a coarser-textured medium due to larger pore size, a result consistent with the aforementioned logic. In summary, the total number of hits observed during evaporation from porous media is inversely related to pore size. Pore geometry modifies the dynamics of capillary flow and fluid displacement during evaporation and should thus influence the characteristics of the resulting AEs. To understand the impact exerted by pore geometry, we compare the AE trends exhibited by sand with an average particle size of 0.58 mm to those yielded by glass beads with an average particle size of 0.53 mm. As depicted in Fig. 1, these two samples shared similar average particle sizes and distributions but differed in surface roughness and typical grain shape; the glass beads were smooth spherical particles whereas the sand grains were shaped irregularly. More AEs were detected per unit mass loss in the sand sample than in the similarly-sized glass bead sample. Intuitively, this result makes sense given the jagged nature of pores between rough grains of sand. The small protrusions along their surfaces provide extra locations for a destabilized meniscus to re-adhere, decreasing the displacement of a typical Haines jump but increasing the occurrence frequency for a given
3.4.2. Power–law relation between AE amplitude and event occurrence Fluid invasion in porous media is frequently modeled as a form of invasion percolation with pore-scale burst size distributions that diminish in occurrence with size. Previous studies have found that the statistical distributions of pressure jumps match power–laws (Aker et al., 2000; Måløy et al., 1992; Furuberg et al., 1996) suggesting that AE size distributions may behave similarly. The AE amplitude distributions that emerge during drainage from sand and glass beads display similar power law behavior, but drainage has been shown to yield exponents with lower magnitudes than those produced by imbibition (DiCarlo et al., 2003; Moebius et al., 2012). These exponents describing AE size distributions have also been shown to be strongly influenced by the particle sizes and thus pore sizes of the host medium (Moebius et al., 2012). Here we show that similar scaling behaviors also exist in the context of evaporation and are influenced by particle size, grain shape, and consequently by pore geometry. Fig. 6 displays the amplitude distributions for each particle type used in the present study. Following Moebius et al. (2012) a power law of the form N = a10bA[dB] was fitted to the data where N is the recorded number of AE hits, A is the waveform amplitude in dB, a is the constant of proportionality and b describes the exponent of power law. The curves fitted to these histograms exhibit power laws wherein the number of AEs observed decreases with amplitude for each particle. In all cases, fainter events are more abundant than louder events. Among particles with the same surface roughness, the magnitude of the exponent tends to increase with decreased particle size, indicating that small particles preferentially produce higher proportions of faint AEs relative to large particles. The converse also holds; higher proportions of loud AEs are generated during evaporation from the media with larger particle sizes. Comparing across grain shapes, we find that the smooth spherical glass beads with an average particle size of 0.53 mm exhibit a power law with a less negative value than the similarly sized but irregularly-shaped sand particles of average particle size 0.58 mm – the drying of smoother particles generates AEs with larger amplitudes. In other words, relative to smooth media, evaporation from pore spaces with rough, irregular surfaces produces more numerous AEs albeit at lower amplitudes. 3.4.3. Characteristics of AE hits as influenced by the particle size At a meniscus’ contact line, adhesive forces compete with gravitational, capillary, and viscous forces to stabilize the meniscus.
Fig. 6. The amplitude distributions of AEs observed during evaporation for each particle type. The data for (a) S 0.34 mm, S 0.58 mm, and S 0.89 mm are described by beta values of 0.11, 0.07, and 0.06 and for (b) GB 0.15 mm and GB 0.53 mm by 0.11 and 0.06 respectively. S and GB refer to sand and glass beads with the average particle sizes presented in the legend.
N. Grapsas, N. Shokri / International Journal of Multiphase Flow 62 (2014) 30–36
35
Fig. 7. Hit parameters averaged across all AEs recorded during stage-1 evaporation for each particle type. (a) Blue columns correspond to sand particles and red columns to glass beads. Results show that average hit energies trend upward with particle size and that AEs from glass beads exhibit higher energies than those from similarly sized sand grains. (b) Hit energy versus amplitude (A) in a double logarithmic scale. Hit energy (E) scale reasonably with the square of hit amplitudes in all cases. The solid line corresponds to the ideal case where E A2.
The amount of force needed to overcome adhesion depends on the properties of the liquid, the wettability of the surface, and pore geometry among other factors. When the meniscus destabilizes and undergoes a Haines jump, it releases energy in the form of an AE with features influenced by jump dynamics. It is reasonable to assume that hit energies may be imprinted with information about the nature of fluid interaction with the surface from which the meniscus detaches. Extending this logic, the geometry of the pore space (size and roughness) should affect individual AE waveforms either by controlling the nature of the de-pinning event or by modifying jump dynamics. Fig. 7a presents the mean energies observed for samples during stage-1 evaporation. Typical hit energies increase with particle size for both sand and glass beads, a trend aligned with the associated increases in pore size and jump displacement. Comparing the AEs from glass beads with average particle size of 0.53 mm to those from the sand with average particle size 0.58 mm reveals that evaporation from beads generates more energetic AEs on average than it does from sand. Fig. 7b plots hit energy as a function of amplitude in units of Pascal for each particle type in log–log space. Since the energy of an acoustic wave scales with the square of its amplitude (Nakamura et al., 1972), a power law of 2 would emerge in the presence of idealized sound propagation. As indicated in Fig. 7b, the exponents arising from these experiments deviate slightly from the ideal case, seemingly due to a combination of AE sensor detection accuracy and the 26 (dB) threshold used to filter out background noise. Since hit amplitude scales with the square root of hit energy, it follows that any patterns in hit energy will be reflected in hit amplitude. Accordingly, larger particle sizes and smoother surfaces correlate with increased AE amplitude. 4. Summary and conclusions Based on the findings of this paper, AE methods appear capable of non-destructively characterizing evaporation from porous media in real time while revealing information about the host medium and its resident fluid. There might be practical limitations to AE techniques at this stage, but this study illustrates the potential of AE methods in the context of drying – they may be used to noninvasively characterize evaporation rates from soil surfaces composed of varying particle sizes and grain shapes. This represents a crucial step toward developing a direct method for environmental flux measurements. Future work in this direction could focus on unambiguously delineating the source mechanism of AE generation; establishing a quantitative understanding of precisely how the acoustic signature generated during drying relates to pore geometry and pore-scale fluid dynamics; and determining whether the properties of AE waveforms can be used to deduce total evaporative mass loss.
Acknowledgements The authors would like to thank Prof. Dani Or for helpful discussions. We would like to thank Prof. Jonathan D. Woodruff and his graduate student Christine Brandon at University of Massachusetts, Amherst for allowing us to use their CAMSIZER Digital Image Processing (from HORIBA) to analyze the particle size distribution of the materials used in our experiments. References Aker, E., Måløy, K.J., Hansen, A., Basak, S., 2000. Burst dynamics during drainage displacements in porous media: simulations and experiments. Europhys. Lett. 51 (1), 55–61. Aminzadeh, M., Or, D., 2013. Temperature dynamics during nonisothermal evaporation from drying porous surfaces. Water Resour. Res. 49, 7339–7349. http://dx.doi.org/10.1002/2013WR014384. Blunt, M.J., Scher, H., 1995. Pore-level modeling of wetting. Phys. Rev. E 52 (6), 6387–6403. Chapuis, O., Prat, M., 2007. Influence of wettability conditions on slow evaporation in two-dimensional porous media. Phys. Rev. E 75 (4), 046311. Chotard, T., Quet, A., Ersen, A., Smith, A., 2006. Application of the acoustic emission technique to characterise liquid transfer in a porous ceramic during drying. J. Eur. Ceram. Soc. 26 (7), 1075–1084. Crandall, D., Ahmadi, G., Ferer, M., Smith, D.H., 2009. Distribution and occurrence of localized-bursts in two-phase flow through porous media. Physica A 388 (5), 574–584. DiCarlo, D.A., Cidoncha, J.I., Hickey, C., 2003. Acoustic measurements of pore-scale displacements. Geophys. Res. Lett. 30 (17), 1901. Doel, P., Heitman, J., Amoozegar, A., Ren, T., Horton, R., 2012. Quantifying nonisothermal subsurface soil water evaporation. Water Resour. Res. 48, W11503. http://dx.doi.org/10.1029/2012WR012516. Faure, P., Coussot, P., 2010. Drying of a model soil. Phys. Rev. E 82 (3), 036303. Furuberg, L., Måløy, K.J., Feder, J., 1996. Intermittent behavior in slow drainage. Phys. Rev. E 53, 966–977. Gauglitz, P.A., Radke, C.J., 1989. Dynamics of Haines jumps for compressible bubbles in constricted capillaries. AIChE J. 35 (2), 230–240. Gauglitz, P.A., Radke, C.J., 1990. The dynamics of liquid-film breakup in constricted cylindrical capillaries. J. Colloid Interface Sci. 134 (1), 14–40. Haghighi, E., Shahraeeni, E., Lehmann, P., Or, D., 2013. Evaporation rates across a convective air boundary layer are dominated by diffusion. Water Resour. Res. 49, 1602–1610. Haines, W.B., 1930. Studies in the physical properties of soil. V. The hysteresis effect in capillary properties, and the modes of moisture distribution associated therewith. J. Agric. Sci. 20, 97–116. Jia, X., 2004. Codalike multiple scattering of elastic waves in dense granular media. Phys. Rev. Lett. 93 (15), 154303. Joekar-Niasar, V., Hassanizadeh, S.M., Leijnse, A., 2008. Insights into the relationships among capillary pressure, saturation, interfacial area and relative permeability using pore-network modelling. Trans. Porous Media 74 (2), 201–219. Kovscek, A.R., Radke, C.J., 1996. Gas bubble snap-off under pressure-driven flow in constricted noncircular capillaries. Colloids Surf., A 117 (1–2), 55–76. Laurindo, J.B., Prat, M., 1998. Numerical and experimental network study of evaporation in capillary porous media. Drying rates. Chem. Eng. Sci. 53 (12), 2257–2269. Lehmann, P., Assouline, S., Or, D., 2008. Characteristic lengths affecting evaporative drying of porous media. Phys. Rev. E 77 (5), 056309. Lu, T.X., Biggar, J.W., Nielsen, D.R., 1994. Water movement in glass bead porous media: 1. Experiments of capillary rise and hysteresis. Water Resour. Res. 30 (12), 3275–3281.
36
N. Grapsas, N. Shokri / International Journal of Multiphase Flow 62 (2014) 30–36
Måløy, K.J., Furuberg, L., Feder, J., Jossang, T., 1992. Dynamics of slow drainage in porous media. Phys. Rev. Lett. 68 (14), 2161–2164. Manasseh, R., Riboux, G., Risso, F., 2008. Sound generation on bubble coalescence following detachment. Int. J. Multiphase Flow 34 (10), 938–949. Michlmayr, G., Cohen, D., Or, D., 2012. Sources and characteristics of acoustic emissions from mechanically stressed geologic granular media – a review. Earth Sci. Rev. 112 (3–4), 97–114. Moebius, F., Canone, D., Or, D., 2012. Characteristics of acoustic emissions induced by fluid front displacement in porous media. Water Resour. Res. 48 (12), 11507–11519. Nair, A., Cai, C.S., 2010. Acoustic emission monitoring of bridges: review and case studies. Eng. Struct. 32 (6), 1704–1714. Nakamura, Y., Veach, C.L., McCauley, B.O., 1972. Amplitude distribution of acoustic emission signals. Acous. Emiss., ASTM STP 505, 164–186. Or, D., Lehmann, P., Shahraeeni, E., Shokri, N., 2013. Advances in soil evaporation physics – a review. Vadose Zone J. 12 (4), 1–16. http://dx.doi.org/10.2136/ vzj2012.0163. Orr, F.M., Scriven, L.E., Rivas, A.P., 1975. Pendular rings between solids—meniscus properties and capillary force. J. Fluid Mech. 67, 723–742. Peysson, Y., Fleury, M., Blazquez-Pascual, V., 2011. Drying rate measurements in convection- and diffusion-driven conditions on a shaly sandstone using Nuclear Magnetic Resonance. Trans. Porous Media 90 (3), 1001–1016. Quere, D., 1997. Inertial capillarity. Europhys. Lett. 39 (5), 533–538. Ransohoff, T.C., Gauglitz, P.A., Radke, C.J., 1987. Snap-off of gas bubbles in smoothly constricted noncircular capillaries. AIChE J. 33 (5), 753–765. Sahimi, M., 2011. Flow and Transport in Porous Media and Fractured Rock: From Classical Methods to Modern Approaches. Wiley-VCH Publishers, Weinheim, Germany (773 pp.). Saravanapavan, T., Salvucci, G.D., 2000. Analysis of rate-limiting processes in soil evaporation with implications for soil resistance models. Adv. Water Resour. 23, 493–502. http://dx.doi.org/10.1016/S0309-1708(99)00045-7.
Scherer, G.W., 1990. Theory of drying. J. Am. Ceram. Soc. 73, 3–14. Shahraeeni, E., Or, D., 2010. Pore-scale analysis of evaporation and condensation dynamics in porous media. Langmuir 26 (17), 13924–13936. Shaw, T.M., 1987. Drying as an immiscible displacement process with fluid counterflow. Phys. Rev. Lett. 59 (15), 1671–1674. Shokri, N., Or, D., 2011. What determines drying rates at the onset of diffusion controlled stage-2 evaporation from porous media? Water Resour. Res. 47, W09513. http://dx.doi.org/10.1029/2010WR010284. Shokri, N., Or, D., 2013. Drying patterns of porous media containing wettability contrasts. J. Colloid Interface Sci. 391, 135–141. Shokri, N., Sahimi, M., 2012. The structure of drying fronts in three-dimensional porous media. Phys. Rev. E 85, 066312. Shokri, N., Salvucci, G., 2011. Evaporation from porous media in the presence of a water table. Vadose Zone J. 10, 1309–1318. http://dx.doi.org/10.2136/ vzj2011.0027. Shokri, N., Sahimi, M., Or, D., 2012. Morphology, propagation, dynamics and scaling characteristics of drying fronts in porous media. Geophys. Res. Lett. 39, L09401. http://dx.doi.org/10.1029/2012GL051506. Simons, S.J.R., Seville, J.P.K., Adams, M.J., 1994. An analysis of the rupture energy of pendular liquid bridges. Chem. Eng. Sci. 49 (14), 2331–2339. Yiotis, A.G., Tsimpanogiannis, I.N., Stubos, A.K., Yortsos, Y.C., 2006. Pore-network study of the characteristic periods in the drying of porous materials. J. Colloid Interf. Sci. 297, 738–748. Yiotis, A.G., Salin, D., Tajer, E.S., Yortsos, Y.C., 2012a. Analytical solutions of drying in porous media for gravity-stabilized fronts. Phys. Rev. E 85, 046308. Yiotis, A.G., Salin, D., Tajer, E.S., Yortsos, Y.C., 2012b. Drying in porous media with gravity-stabilized fronts: experimental results. Phys. Rev. E 86, 026310.
Contents lists available at ScienceDirect
International Journal of Multiphase Flow j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j m u l fl o w
Acoustic characteristics of fluid interface displacement in drying porous media N. Grapsas a, N. Shokri b,⇑ a b
Department of Earth and Environment, Boston University, Boston, MA, USA School of Chemical Engineering and Analytical Science, University of Manchester, Manchester, UK
a r t i c l e
i n f o
Article history: Received 15 November 2013 Received in revised form 28 January 2014 Accepted 30 January 2014 Available online 10 February 2014 Keywords: Fluid interface displacement Evaporation Porous media Particle size Acoustic emission
a b s t r a c t Water evaporation from porous media involves many rapid interfacial jumps at the pore-scale as air invades the pore network and displaces the evaporating fluid. We show that this process produces a crackling noise that can be detected using an acoustic emission (AE) instrument. We investigated the acoustic signature of evaporation from porous media using transparent glass cells packed with five types of sand and glass beads differing in particle size distribution and grains shape. Each sample was mounted on a digital balance, saturated with dyed water, left to evaporate under well-controlled atmospheric conditions, and digitally imaged every 20 min to quantify the dynamics of liquid phase distributions. An AE sensor was fixed to each column to record AE events (hits) and their acoustic features. Results indicate that the cumulative number of AE hits is strongly proportional to total evaporative losses. Additionally, the cumulative number of hits shares an inverse relationship with particle size and a direct relationship with grain irregularity. Analysis of the dynamics of liquid phase distributions reveals a strong correlation between the area invaded by air and the cumulative number of AE hits. Our results suggest that AE techniques may hold the potential to non-invasively analyze evaporation from porous media. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Evaporation from porous media is a process ubiquitous in many industrial and environmental contexts ranging from the drying of catalysts, paper, pharmaceutical products, and porous building materials to water evaporation from soil which influences the hydrological cycle and various biological activities in the vadose zone. Evaporation from saturated porous media typically involves the invasion of pores by a non-wetting gaseous phase (e.g. air) that displaces a resident wetting liquid phase (e.g. water) resulting in the formation of a receding primary drying front, defined as the interface between saturated and partially saturated zones (Shaw, 1987; Shokri et al., 2012). Many studies have investigated the drying of porous materials under various boundary conditions and have analyzed the effects of parameters such as atmospheric conditions, wettability, porous media transport properties, and the physical and chemical properties of evaporating fluids (Scherer, 1990; Laurindo and Prat, 1998; Yiotis et al., 2006; Chapuis and Prat, 2007; Lehmann et al., 2008; ⇑ Corresponding author. Address: School of Chemical Engineering and Analytical Science, The University of Manchester, Sackville Street, Manchester M13 9PL, UK. Tel.: +44 161 3063980. E-mail address: [email protected] (N. Shokri). http://dx.doi.org/10.1016/j.ijmultiphaseflow.2014.01.011 0301-9322/Ó 2014 Elsevier Ltd. All rights reserved.
Faure and Coussot, 2010; Shokri and Salvucci, 2011; Peysson et al., 2011; Shahraeeni and Or, 2010; Smits et al., 2012; Shokri and Sahimi, 2012; Doel et al., 2012; Shokri et al., 2012; Yiotis et al., 2012a,b; Aminzadeh and Or, 2013; Haghighi et al., 2013; Shokri and Or, 2013; Or et al., 2013). When evaporation from saturated porous media initiates, evaporation rates are mainly controlled by atmospheric demand, are rather high, and remain relatively constant – these features characterize what is referred to as stage-1 evaporation (Saravanapavan and Salvucci, 2000; Shokri and Or, 2011). During stage-1, capillary-induced liquid flow transports the liquid from a receding primary drying front (referred to simply as ‘drying front’ from here on) to the surface where water vaporization takes place. When the drying front recedes to a characteristic depth which can be estimated using the capillary pressure–saturation curve of the medium (Lehmann et al., 2008; Shokri and Salvucci, 2011), hydraulic connectivity with the surface disrupts, resulting in a transition to lower evaporative fluxes that marks the onset of stage-2 evaporation. During this period, liquid vaporization occurs inside the porous medium and evaporation becomes limited by vapor diffusion through the overlying dry layer near the surface (Scherer, 1990; Shokri and Or, 2011). It is well-known that air invasion of saturated porous media produces many discrete, rapid pore-scale interfacial bursts known as ‘‘Haines jumps’’ which result from instabilities at the contact lines
N. Grapsas, N. Shokri / International Journal of Multiphase Flow 62 (2014) 30–36
of menisci as pores are drained (Haines, 1930; Lu et al., 1994; Blunt and Scher, 1995; Aker et al., 2000; DiCarlo et al., 2003; Chotard et al., 2006; Crandall et al., 2009; Moebius et al., 2012). Recent studies have shown that these pore-scale events may generate sounds depending on the process under consideration. For example, DiCarlo et al. (2003) found that drainage from porous media generates an acoustic ‘‘crackling noise’’ composed of many individual acoustic events. Using passive acoustic emission (AE) methods often employed to monitor the accumulation of strain in civil structures and in microseismicity studies (Nair and Cai, 2010), each small event was detected as a ‘‘hit’’ and demonstrated to be related to the displacement of the liquid–gas meniscus in porous media. Chotard et al. (2006) reported that these AEs could also be detected during cement drying and that the cumulative number of hits may be related to evaporative mass loss. Further inquiries undertaken recently by Moebius et al. (2012) have revealed that AE hits generated during fluid front displacement in porous media exhibit a dependency on the medium pore size among other factors. Motivated by the widespread importance of drying in porous media and recent advances in the application of AE techniques with regard to transport phenomena in porous media (Sahimi, 2011), this study aims to evaluate the feasibility of applying non-invasive AE techniques to characterize the drying of porous media. Within this context, we present experiments which demonstrate that AEs generated during evaporation are related to Haines jumps and are indeed strongly linked to evaporative mass loss during evaporation from porous media. Additionally, we show that medium particle size and grain surface irregularity also influence the acoustic signature of the evaporation process which will be discussed in detail. 2. Materials and methods The model porous media used in this work consisted of either silica sand or glass beads across a range of particle sizes. Fig. 1 presents the particle size distributions (PSDs) of the media obtained using CAMSIZER Digital Image Processing Particle Size from HORIBA. The sand grains had average particle sizes (diameters, d) of 0.34 mm, 0.58 mm, and 0.89 mm, and the glass beads had average particle sizes of 0.15 mm and 0.53 mm. These particles were selected so that the influence exerted on AE characteristics by changes in particle size and roughness, and by extension pore space geometry, could be assessed. As illustrated in Fig. 1a, the sand sample with an average particle size of 0.58 mm possessed a particle size distribution quite
31
similar to the glass bead sample with an average particle size of 0.53 mm. This provided the opportunity to constrain the effects of grain shape and pore roughness on drying behavior since the sand grains were rough and shaped irregularly whereas the glass beads were relatively smooth spheres. Particles were saturated with a dye-water solution and packed uniformly into 8 cm 8 cm 0.5 cm transparent glass Hele–Shaw cells closed on all sides except the top, which was left uncovered to enable evaporation. An identical procedure was used to pack particles into each cell. 5 mL of blue dye was added to 1 L of water and stirred inside of a Tupperware container. Importantly, using dye increased the contrast between the phases present during drying making image segmentation possible. Dry particles were transferred into this solution and mixed to purge trapped air and guarantee complete, uniform saturation. After saturating the particles, some excess ponding solution was transferred into a Hele–Shaw cell to a depth of 1 cm while ensuring that the particles remained submerged and saturated. Using an indented spatula with an effective diameter of 1/3 cm, small amounts of saturated particles were scooped from the Tupperware and transferred into the fluid within the Hele–Shaw cell. Particles were transferred in this manner until they accumulated to a height of 1.5 cm. At this point, a stir was used to gently mix the particles which were then allowed to settle. This procedure of transferring, mixing, and compacting particles was repeated until particles accumulated to 6 cm within each Hele–Shaw cell. This process removed entrapped air bubbles and guarded against the layering effects that result from transferring particles in discrete increments. Managing layering effects is essential to fluid flow or evaporation experimentation as the incremental addition of particles forms distinct strata with independent hydraulic properties. An opaque white plastic backing with a cutout for an AE sensor was taped to the rear of each cell to provide a consistent, uniformly colored backdrop which aided during image segmentation of the transparent glass bead samples. The cells were left to evaporate on digital balances (accurate to 0.01 g) in an environmental chamber set to 35 °C and 30% relative humidity. Mass measurements were recorded every 5 min, and photos of the glass cells were taken every 20 min with a computer-operated digital camera intended to track changes in liquid phase distributions with a spatial resolution of 110 lm. A model R6I-AST Physical Acoustic Corporation resonant AE sensor (45 kHz peak frequency and operating range from 23 dB to 117 dB) with a built in preamplifier was fixed to the rear of each
Fig. 1. (a) Particle size distributions of different sand and glass beads used in the experiments. The numbers in the legends indicate the average particle size of the porous medium in each cell. S and GB refer to sand and glass beads, respectively. (b) Schematic of the experimental setup. Hele–Shaw cells packed with well-defined particle sizes are mounted on digital balances connected to a PC to record the dynamics of water evaporation while changes in liquid phase distribution during evaporation were automatically recorded using a digital camera. An AE sensor was mounted to the rear of each cell using duct tape. (c) Conceptual sketch of a typical acoustic emission signal recorded by the AE machine with its corresponding features.
32
N. Grapsas, N. Shokri / International Journal of Multiphase Flow 62 (2014) 30–36
Hele-Shaw cell on Dow Corning 7 Release Compound and linked to a Physical Acoustics Corporation Micro-II Digital AE system. This setup allowed AE waveforms to be recorded in units of mV and reports individual AE hit features such as absolute energy (hereafter referred to as energy), amplitude, duration, and frequency in addition to tallying the cumulative number of observed hits. An amplitude threshold of 26 (dB) was used to remove background noise. Fig. 1b and c illustrate the experimental setup and the schematic of an AE waveform with the corresponding features. 3. Results and discussion 3.1. Sources of AE hits generated during evaporation from porous media Moebius et al. (2012) have identified five AE-generating mechanisms associated with fluid front displacement in porous media: Haines jumps, liquid bridge rupture, air bubble entrainment and oscillation, interfacial snap-off, and grain collisions. Each source mechanism gives rise to mechanical waves in a unique way. Haines jumps likely release mechanical energy when menisci reduce their interfacial energies during jumps from less stable configurations across larger pore throats to more stable configurations across smaller ones (Quere, 1997). Suspended liquid bridges, which are entrapped saturated regions left behind by the receding drying fronts, rupture when evaporation from their surfaces causes them to shrink until they reach a critical volume (Orr et al., 1975). The magnitude of interfacial energy reductions that occur during these events have been shown to be of similar order to those during Haines jumps, but bridge ruptures are substantially rarer events (Simons et al., 1994). Air bubble entrapment, coalescence and oscillations, which occur when contact lines and fluid displacement fronts reconfigure while abruptly moving across rough surfaces, emit sound either when air becomes entrapped from a free surface or when bubbles snap-off from larger parent gas bodies (Manasseh et al., 2008). Other interfacial snap-off processes (Joekar-Niasar et al., 2008) have been studied comprehensively (Kovscek and Radke, 1996; Gauglitz and Radke, 1989, 1990) and are associated with the release of interfacial energy (Ransohoff et al., 1987). Mechanical collisions of the type that occur between grains during settling or in response to capillary forces and pressure waves have also been identified as one of a host of potential AE sources (Michlmayr et al., 2012). These five phenomena represent the processes which may contribute to the AE signatures detected during our evaporation experiments.
We analyzed the time evolution of the number of AE hits observed, their amplitudes and energies generated during evaporation from porous media. These observables constitute the commonly used AE analytical features. Given that the peak 45 kHz resonant frequency of our sensors corresponds to sound wavelengths in silica of 132 mm which is orders of magnitude larger than the particle diameters in this study, AEs likely undergo little scattering and propagate uniformly (Jia, 2004). The effects of signal attenuation on these observables were ignored due to the small volume of packed sand through which elastic waves had to propagate to reach an AE sensor. 3.2. AE hits and evaporative mass loss When drying initiated, a receding drying front developed in each medium as air began to invade and displace the evaporating water. Fig. 2 presents typical curves illustrating the time evolutions of evaporative mass loss and AE hits generated during evaporation. The observed mass loss pattern dynamics were consistent with data previously reported in literature (Shokri and Or, 2011). High constant drying rates – indicated by the constant slopes of the mass loss curves – are initially present during stage-1 evaporation wherein capillarity draws fluids from the saturated zone to the medium’s surface to evaporate. Discernible changes in drying rates occurred either when the saturated zones became depleted of fluid (which was the case for the sand sample with an average particle size of 0.34 mm) or when a sample entered stage-2 evaporation (as was the case for the sand samples with average particle sizes of 0.58 mm and 0.89 mm and for the glass bead sample with an average particle size of 0.53 mm) when the upward capillary force could no longer overcome the downward gravitational force (viscous forces are negligible in our experiments due to the relatively large particle sizes). As illustrated in Fig. 2, the AE hit rates are found to strongly correlate with mass loss rates in all cases, suggesting a direct relationship between AE hits and mass loss that was first observed by Chotard et al. (2006). Before air began penetrating the pore spaces, the AE hit rates were zero indicating that background noise was not being captured and that the processes by which AEs are produced had not yet commenced. Once air began invading the porous media, stage-1 evaporation started and the highest hit rates were observed. Since the drying rate is faster during stage-1, more pore-scale interfacial jumps are induced causing more AEs to be emitted. After the saturated regime was either exhausted or the process entered stage-2 evaporation, the AE hit rates dropped
Fig. 2. (a–d) The cumulative evaporative losses and cumulative AE hits versus time measured using digital balances and AE sensors during evaporation from sand (S) and glass beads (GB).
N. Grapsas, N. Shokri / International Journal of Multiphase Flow 62 (2014) 30–36
precipitously but maintained proportionality with mass loss. It is important to note that AE hits were only observed while evaporation was active and air invaded the medium, suggesting that AEs dominantly emerged from motions of the air–water interface. This pattern was present for all particle sizes and roughnesses. Fig. 2 shows the great potential of the AE technique to monitor, noninvasively quantify, and analyze the drying of a porous medium. It also illustrates the significant influence of particle size and grain shape (pore geometry) on drying behavior and on the emergent characteristics of AEs which will be discussed in following sections. 3.3. Linking AE hits to fluid invasion patterns The dynamics of liquid phase distributions during evaporation were quantified by segmenting the recorded images into binary data representing the saturated and unsaturated phases following the procedure described in Shokri et al. (2012). Fig. 3 depicts a representative time progression of air invasion and drying front propagation. The white, red, green, and blue regions correspond to air-invaded areas after 5, 10, 15, and 25 h from the onset of evaporation and the black region corresponds to the saturated region after 25 h. We have calculated the time evolution of invaded area for all particle sizes using the segmented images and compared the
33
results to the recorded AE hits. Fig. 4 illustrates that a direct proportionality is shared between the time evolution of AE hits and invaded area (denoted as IA in the figures) during stage-1 evaporation for all particle classes. Any region invaded by air experienced many pore-scale interfacial motions. It follows that any changes in invaded area necessarily stemmed from these porescale interfacial bursts, implying that the number of AE hits recorded directly corresponded to the number of Haines jumps that occurred in the medium. In Fig. 4c, for sand with an average particle size of 0.89 mm, two large steps occur in invaded area approximately half a day into the trial. Inspection of both the raw and binary images recorded at those times reveals massive, rapid invasion events in the area analyzed. These dramatic events can be explained by avalanches of pore invasions which only stop once all the menisci involved stabilize across pore throats smaller than those they originally spanned. Such drastic invasion events were observed only during drying of the largest-diameter particle class due to its volumetrically larger pores. The presence of larger pores reduces the likelihood that a propagating meniscus will attain a stable configuration in a given volume after destabilizing – avalanches also occurred in smaller particle classes but over smaller volumes and areas. The AE hit rate likely remained constant in spite of these avalanches because of the limited image section that was used to assess invaded area; decreased hit rates from regions outside of the analyzed field of view could have compensated for increased hit rates associated with the avalanches. The time resolution of our analysis may also exaggerate the impact of such avalanche events. 3.4. Influence of particle size on the AEs generated during evaporation Hydraulic conductivity, porosity, and in particular the pore geometry of a porous medium are dependent on the constituent grains’ sizes and shapes. Since AEs are generated by meniscus motions in pores, pore-scale configuration may imprint a signature on the crackling sound detected using AE equipment. In the following section, we discuss the effects of particle size and surface irregularity on the characteristics of resulting AEs.
Fig. 3. Typical air invasion patterns at macro-scale during evaporation from sand with an average particle size of 0.58 mm. White, red, green, and blue indicate the invaded region after 5, 10, 15 and 25 h respectively. Black corresponds to the saturated region after 25 h.
3.4.1. AE events as influenced by the medium texture The precise proportionality between AE hits and mass loss in Fig. 2 as well as between AE hits and invaded area in Fig. 4 varies among particle classes. This varying proportionality suggests that
Fig. 4. (a–d) Area of the invaded regions (IA) versus time in glass cells packed with sand (S) and glass beads (GB) with different average particle sizes. The invaded area was delineated by image analysis and compared to the recorded number of AE hits.
34
N. Grapsas, N. Shokri / International Journal of Multiphase Flow 62 (2014) 30–36
volume. Individual displacements would be of smaller volumes, and we would expect them to produce correspondingly fainter emissions since meniscus motions would involve less energy. Thus, AEs generated during drying in media with rough particles and irregular pores would tend to occur at lower amplitudes and energies than for AEs produced during drying in media whose particles and pore spaces are smooth.
Fig. 5. The cumulative number of AE hits observed as a function of the cumulative mass loss for each particle. S and GB refer to sand and glass beads, respectively.
a medium’s particle size, surface roughness, and typical grain (pore) shape influence the characteristics of AEs emitted during evaporation from porous media. This can be rationalized since both pore shape and size influence the pore-scale liquid phase reconfiguration dynamics that ultimately mediate emitted AE signals. Fig. 5 displays the number of AE hits observed as a function of mass loss across all of the particles used in our experiments. This figure shows that hit rate varies indirectly with particle size. Assuming a constant porosity of 0.4 in all cases, a medium consisting of larger particles has larger pores meaning that fewer pores are vacated per given volume of evaporated water. Therefore, when fluid evaporation evacuates an equal volume from two media with distinct particle sizes, more interfacial jumps occur in the finer medium leading to more AE hits. Fig. 5 also suggests that more mass is lost per hit in a coarser-textured medium due to larger pore size, a result consistent with the aforementioned logic. In summary, the total number of hits observed during evaporation from porous media is inversely related to pore size. Pore geometry modifies the dynamics of capillary flow and fluid displacement during evaporation and should thus influence the characteristics of the resulting AEs. To understand the impact exerted by pore geometry, we compare the AE trends exhibited by sand with an average particle size of 0.58 mm to those yielded by glass beads with an average particle size of 0.53 mm. As depicted in Fig. 1, these two samples shared similar average particle sizes and distributions but differed in surface roughness and typical grain shape; the glass beads were smooth spherical particles whereas the sand grains were shaped irregularly. More AEs were detected per unit mass loss in the sand sample than in the similarly-sized glass bead sample. Intuitively, this result makes sense given the jagged nature of pores between rough grains of sand. The small protrusions along their surfaces provide extra locations for a destabilized meniscus to re-adhere, decreasing the displacement of a typical Haines jump but increasing the occurrence frequency for a given
3.4.2. Power–law relation between AE amplitude and event occurrence Fluid invasion in porous media is frequently modeled as a form of invasion percolation with pore-scale burst size distributions that diminish in occurrence with size. Previous studies have found that the statistical distributions of pressure jumps match power–laws (Aker et al., 2000; Måløy et al., 1992; Furuberg et al., 1996) suggesting that AE size distributions may behave similarly. The AE amplitude distributions that emerge during drainage from sand and glass beads display similar power law behavior, but drainage has been shown to yield exponents with lower magnitudes than those produced by imbibition (DiCarlo et al., 2003; Moebius et al., 2012). These exponents describing AE size distributions have also been shown to be strongly influenced by the particle sizes and thus pore sizes of the host medium (Moebius et al., 2012). Here we show that similar scaling behaviors also exist in the context of evaporation and are influenced by particle size, grain shape, and consequently by pore geometry. Fig. 6 displays the amplitude distributions for each particle type used in the present study. Following Moebius et al. (2012) a power law of the form N = a10bA[dB] was fitted to the data where N is the recorded number of AE hits, A is the waveform amplitude in dB, a is the constant of proportionality and b describes the exponent of power law. The curves fitted to these histograms exhibit power laws wherein the number of AEs observed decreases with amplitude for each particle. In all cases, fainter events are more abundant than louder events. Among particles with the same surface roughness, the magnitude of the exponent tends to increase with decreased particle size, indicating that small particles preferentially produce higher proportions of faint AEs relative to large particles. The converse also holds; higher proportions of loud AEs are generated during evaporation from the media with larger particle sizes. Comparing across grain shapes, we find that the smooth spherical glass beads with an average particle size of 0.53 mm exhibit a power law with a less negative value than the similarly sized but irregularly-shaped sand particles of average particle size 0.58 mm – the drying of smoother particles generates AEs with larger amplitudes. In other words, relative to smooth media, evaporation from pore spaces with rough, irregular surfaces produces more numerous AEs albeit at lower amplitudes. 3.4.3. Characteristics of AE hits as influenced by the particle size At a meniscus’ contact line, adhesive forces compete with gravitational, capillary, and viscous forces to stabilize the meniscus.
Fig. 6. The amplitude distributions of AEs observed during evaporation for each particle type. The data for (a) S 0.34 mm, S 0.58 mm, and S 0.89 mm are described by beta values of 0.11, 0.07, and 0.06 and for (b) GB 0.15 mm and GB 0.53 mm by 0.11 and 0.06 respectively. S and GB refer to sand and glass beads with the average particle sizes presented in the legend.
N. Grapsas, N. Shokri / International Journal of Multiphase Flow 62 (2014) 30–36
35
Fig. 7. Hit parameters averaged across all AEs recorded during stage-1 evaporation for each particle type. (a) Blue columns correspond to sand particles and red columns to glass beads. Results show that average hit energies trend upward with particle size and that AEs from glass beads exhibit higher energies than those from similarly sized sand grains. (b) Hit energy versus amplitude (A) in a double logarithmic scale. Hit energy (E) scale reasonably with the square of hit amplitudes in all cases. The solid line corresponds to the ideal case where E A2.
The amount of force needed to overcome adhesion depends on the properties of the liquid, the wettability of the surface, and pore geometry among other factors. When the meniscus destabilizes and undergoes a Haines jump, it releases energy in the form of an AE with features influenced by jump dynamics. It is reasonable to assume that hit energies may be imprinted with information about the nature of fluid interaction with the surface from which the meniscus detaches. Extending this logic, the geometry of the pore space (size and roughness) should affect individual AE waveforms either by controlling the nature of the de-pinning event or by modifying jump dynamics. Fig. 7a presents the mean energies observed for samples during stage-1 evaporation. Typical hit energies increase with particle size for both sand and glass beads, a trend aligned with the associated increases in pore size and jump displacement. Comparing the AEs from glass beads with average particle size of 0.53 mm to those from the sand with average particle size 0.58 mm reveals that evaporation from beads generates more energetic AEs on average than it does from sand. Fig. 7b plots hit energy as a function of amplitude in units of Pascal for each particle type in log–log space. Since the energy of an acoustic wave scales with the square of its amplitude (Nakamura et al., 1972), a power law of 2 would emerge in the presence of idealized sound propagation. As indicated in Fig. 7b, the exponents arising from these experiments deviate slightly from the ideal case, seemingly due to a combination of AE sensor detection accuracy and the 26 (dB) threshold used to filter out background noise. Since hit amplitude scales with the square root of hit energy, it follows that any patterns in hit energy will be reflected in hit amplitude. Accordingly, larger particle sizes and smoother surfaces correlate with increased AE amplitude. 4. Summary and conclusions Based on the findings of this paper, AE methods appear capable of non-destructively characterizing evaporation from porous media in real time while revealing information about the host medium and its resident fluid. There might be practical limitations to AE techniques at this stage, but this study illustrates the potential of AE methods in the context of drying – they may be used to noninvasively characterize evaporation rates from soil surfaces composed of varying particle sizes and grain shapes. This represents a crucial step toward developing a direct method for environmental flux measurements. Future work in this direction could focus on unambiguously delineating the source mechanism of AE generation; establishing a quantitative understanding of precisely how the acoustic signature generated during drying relates to pore geometry and pore-scale fluid dynamics; and determining whether the properties of AE waveforms can be used to deduce total evaporative mass loss.
Acknowledgements The authors would like to thank Prof. Dani Or for helpful discussions. We would like to thank Prof. Jonathan D. Woodruff and his graduate student Christine Brandon at University of Massachusetts, Amherst for allowing us to use their CAMSIZER Digital Image Processing (from HORIBA) to analyze the particle size distribution of the materials used in our experiments. References Aker, E., Måløy, K.J., Hansen, A., Basak, S., 2000. Burst dynamics during drainage displacements in porous media: simulations and experiments. Europhys. Lett. 51 (1), 55–61. Aminzadeh, M., Or, D., 2013. Temperature dynamics during nonisothermal evaporation from drying porous surfaces. Water Resour. Res. 49, 7339–7349. http://dx.doi.org/10.1002/2013WR014384. Blunt, M.J., Scher, H., 1995. Pore-level modeling of wetting. Phys. Rev. E 52 (6), 6387–6403. Chapuis, O., Prat, M., 2007. Influence of wettability conditions on slow evaporation in two-dimensional porous media. Phys. Rev. E 75 (4), 046311. Chotard, T., Quet, A., Ersen, A., Smith, A., 2006. Application of the acoustic emission technique to characterise liquid transfer in a porous ceramic during drying. J. Eur. Ceram. Soc. 26 (7), 1075–1084. Crandall, D., Ahmadi, G., Ferer, M., Smith, D.H., 2009. Distribution and occurrence of localized-bursts in two-phase flow through porous media. Physica A 388 (5), 574–584. DiCarlo, D.A., Cidoncha, J.I., Hickey, C., 2003. Acoustic measurements of pore-scale displacements. Geophys. Res. Lett. 30 (17), 1901. Doel, P., Heitman, J., Amoozegar, A., Ren, T., Horton, R., 2012. Quantifying nonisothermal subsurface soil water evaporation. Water Resour. Res. 48, W11503. http://dx.doi.org/10.1029/2012WR012516. Faure, P., Coussot, P., 2010. Drying of a model soil. Phys. Rev. E 82 (3), 036303. Furuberg, L., Måløy, K.J., Feder, J., 1996. Intermittent behavior in slow drainage. Phys. Rev. E 53, 966–977. Gauglitz, P.A., Radke, C.J., 1989. Dynamics of Haines jumps for compressible bubbles in constricted capillaries. AIChE J. 35 (2), 230–240. Gauglitz, P.A., Radke, C.J., 1990. The dynamics of liquid-film breakup in constricted cylindrical capillaries. J. Colloid Interface Sci. 134 (1), 14–40. Haghighi, E., Shahraeeni, E., Lehmann, P., Or, D., 2013. Evaporation rates across a convective air boundary layer are dominated by diffusion. Water Resour. Res. 49, 1602–1610. Haines, W.B., 1930. Studies in the physical properties of soil. V. The hysteresis effect in capillary properties, and the modes of moisture distribution associated therewith. J. Agric. Sci. 20, 97–116. Jia, X., 2004. Codalike multiple scattering of elastic waves in dense granular media. Phys. Rev. Lett. 93 (15), 154303. Joekar-Niasar, V., Hassanizadeh, S.M., Leijnse, A., 2008. Insights into the relationships among capillary pressure, saturation, interfacial area and relative permeability using pore-network modelling. Trans. Porous Media 74 (2), 201–219. Kovscek, A.R., Radke, C.J., 1996. Gas bubble snap-off under pressure-driven flow in constricted noncircular capillaries. Colloids Surf., A 117 (1–2), 55–76. Laurindo, J.B., Prat, M., 1998. Numerical and experimental network study of evaporation in capillary porous media. Drying rates. Chem. Eng. Sci. 53 (12), 2257–2269. Lehmann, P., Assouline, S., Or, D., 2008. Characteristic lengths affecting evaporative drying of porous media. Phys. Rev. E 77 (5), 056309. Lu, T.X., Biggar, J.W., Nielsen, D.R., 1994. Water movement in glass bead porous media: 1. Experiments of capillary rise and hysteresis. Water Resour. Res. 30 (12), 3275–3281.
36
N. Grapsas, N. Shokri / International Journal of Multiphase Flow 62 (2014) 30–36
Måløy, K.J., Furuberg, L., Feder, J., Jossang, T., 1992. Dynamics of slow drainage in porous media. Phys. Rev. Lett. 68 (14), 2161–2164. Manasseh, R., Riboux, G., Risso, F., 2008. Sound generation on bubble coalescence following detachment. Int. J. Multiphase Flow 34 (10), 938–949. Michlmayr, G., Cohen, D., Or, D., 2012. Sources and characteristics of acoustic emissions from mechanically stressed geologic granular media – a review. Earth Sci. Rev. 112 (3–4), 97–114. Moebius, F., Canone, D., Or, D., 2012. Characteristics of acoustic emissions induced by fluid front displacement in porous media. Water Resour. Res. 48 (12), 11507–11519. Nair, A., Cai, C.S., 2010. Acoustic emission monitoring of bridges: review and case studies. Eng. Struct. 32 (6), 1704–1714. Nakamura, Y., Veach, C.L., McCauley, B.O., 1972. Amplitude distribution of acoustic emission signals. Acous. Emiss., ASTM STP 505, 164–186. Or, D., Lehmann, P., Shahraeeni, E., Shokri, N., 2013. Advances in soil evaporation physics – a review. Vadose Zone J. 12 (4), 1–16. http://dx.doi.org/10.2136/ vzj2012.0163. Orr, F.M., Scriven, L.E., Rivas, A.P., 1975. Pendular rings between solids—meniscus properties and capillary force. J. Fluid Mech. 67, 723–742. Peysson, Y., Fleury, M., Blazquez-Pascual, V., 2011. Drying rate measurements in convection- and diffusion-driven conditions on a shaly sandstone using Nuclear Magnetic Resonance. Trans. Porous Media 90 (3), 1001–1016. Quere, D., 1997. Inertial capillarity. Europhys. Lett. 39 (5), 533–538. Ransohoff, T.C., Gauglitz, P.A., Radke, C.J., 1987. Snap-off of gas bubbles in smoothly constricted noncircular capillaries. AIChE J. 33 (5), 753–765. Sahimi, M., 2011. Flow and Transport in Porous Media and Fractured Rock: From Classical Methods to Modern Approaches. Wiley-VCH Publishers, Weinheim, Germany (773 pp.). Saravanapavan, T., Salvucci, G.D., 2000. Analysis of rate-limiting processes in soil evaporation with implications for soil resistance models. Adv. Water Resour. 23, 493–502. http://dx.doi.org/10.1016/S0309-1708(99)00045-7.
Scherer, G.W., 1990. Theory of drying. J. Am. Ceram. Soc. 73, 3–14. Shahraeeni, E., Or, D., 2010. Pore-scale analysis of evaporation and condensation dynamics in porous media. Langmuir 26 (17), 13924–13936. Shaw, T.M., 1987. Drying as an immiscible displacement process with fluid counterflow. Phys. Rev. Lett. 59 (15), 1671–1674. Shokri, N., Or, D., 2011. What determines drying rates at the onset of diffusion controlled stage-2 evaporation from porous media? Water Resour. Res. 47, W09513. http://dx.doi.org/10.1029/2010WR010284. Shokri, N., Or, D., 2013. Drying patterns of porous media containing wettability contrasts. J. Colloid Interface Sci. 391, 135–141. Shokri, N., Sahimi, M., 2012. The structure of drying fronts in three-dimensional porous media. Phys. Rev. E 85, 066312. Shokri, N., Salvucci, G., 2011. Evaporation from porous media in the presence of a water table. Vadose Zone J. 10, 1309–1318. http://dx.doi.org/10.2136/ vzj2011.0027. Shokri, N., Sahimi, M., Or, D., 2012. Morphology, propagation, dynamics and scaling characteristics of drying fronts in porous media. Geophys. Res. Lett. 39, L09401. http://dx.doi.org/10.1029/2012GL051506. Simons, S.J.R., Seville, J.P.K., Adams, M.J., 1994. An analysis of the rupture energy of pendular liquid bridges. Chem. Eng. Sci. 49 (14), 2331–2339. Yiotis, A.G., Tsimpanogiannis, I.N., Stubos, A.K., Yortsos, Y.C., 2006. Pore-network study of the characteristic periods in the drying of porous materials. J. Colloid Interf. Sci. 297, 738–748. Yiotis, A.G., Salin, D., Tajer, E.S., Yortsos, Y.C., 2012a. Analytical solutions of drying in porous media for gravity-stabilized fronts. Phys. Rev. E 85, 046308. Yiotis, A.G., Salin, D., Tajer, E.S., Yortsos, Y.C., 2012b. Drying in porous media with gravity-stabilized fronts: experimental results. Phys. Rev. E 86, 026310.