Progress 09/01/07 to 08/31/11
Outputs
OUTPUTS: To gain insight into the mechanism behind the retention of pathogens in unsaturated soils, we quantified the contribution to retention of the air-water-solid (or more generally, the non wetting-wetting-solid) contact line in simple geometries and granular materials. Comparing contact line length and air/water interfacial area enables predictions about where colloidal particles are trapped when compared with experimental visualizations conducted in this project and reported in the literature. We used a novel computational, level set method based, progressive quasi-static algorithm (LSMPQS) to determine the configuration of AWS contact lines. LSMPQS tracks the pore scale motion of interfaces assuming capillary forces are dominant. It has been implemented to compute the location of an interface between two immiscible fluids (e.g. air and water) confined by arbitrary solid surfaces (e.g. soil grains). Thus the method implicitly determines the location of contact lines as the intersection of two pairs of interfaces (e.g., the air-water interface with the water-solid interface) as a function of applied capillary pressure or of moisture content. The resulting contact line is a collection of digitized links and nodes, and subsequent length measurement is straightforward. This procedure was written in a C code and added as a new functionality to the LSMPQS software package publicly available from the Level Set Method Library (LSMLIB). A large number of experiments were conducted with pore-scale micromodels and columns packed with glass beads as porous media, using two-phase flow with water and low-viscosity silicone oil as wetting and non-wetting phase, respectively. The micromodels were made from rectangular micro-slide (Ibidi, 400 x 3800 micron) with uncoated and coated inner wall to provide hydrophilic and hydrophobic surfaces, and the columns (diameter 2.5 cm and height 8 cm) were packed with either hydrophilic or hydrophobic glass beads. Visualization from the micromodel experiments show that colloids are retained at the oil-water- interface in both hydrophilic and hydrophobic cells, and that moving interface can mobilize colloids previously attached to the walls on the hydrophobic cell but not on the hydrophilic one. These observations suggest that stability of colloid retention on the interfaces is controlled by the local balance of colloidal, drag, and surface tension forces. Regarding contact lines, the micromodel visualizations suggest that colloids are more likely to be trapped at contact lines associated with immobile wetting phase. The breakthrough time and the concentration of colloids at steady state during both infiltration and drainage, again using the silicon oil as non-wetting phase, were recorded for the column experiments. While the same general trends were found on the role of AWI and contact line on colloid retention and mobilization, the larger scale experiments show additional effects by preferential flow due to non-uniform wetting. PARTICIPANTS: Steven Bryant, PI. Yan Jin, co-PI. Dr. Masa Prodanovic, research scientist (computational research). Drs. Yuni Zevi and Volha Lazouskaya, post-doctoral researcher (experiments). Elena Rodriguez: Ph.D. student (computational research). TARGET AUDIENCES: Target audiences are scientists and engineers working on groundwater contamination, especially contamination caused by movement of certain bacteria and viruses associated with agricultural operations. PROJECT MODIFICATIONS: Nothing significant to report during this reporting period.
Impacts
The method for quantifying the length of AWS contact line was applied to a small, computer-generated packing of equal spheres. Drainage and imbibition displacements were simulated with LSMPQS, and at each step the fluid configurations were analyzed for contact line length. An important outcome was the role of pendular rings of wetting phase at grain contacts. These rings make the main contribution to contact line length for water saturations below about 40%. Each ring creates two separate contact lines, one on each grain at the contact. A remarkable result is that the AWS contact line length for granular material plotted versus water saturation shows little hysteresis between drainage and imbibition. (In contrast the interfacial area between air and water shows substantial hysteresis.) The reason is the competition between growth of pendular rings (which increases contact line length) and destruction of pendular rings (which creates menisci in pore throats with smaller contact line length) during imbibition. This is the first quantification of contact line length ever reported for porous media. These results thus form the basis for new understanding of a variety of phenomena in unsaturated soils. The experiments in Ibidi channels provided direct visualization of drainage and imbibition fronts and their roles in colloid mobilization. Both theoretical analysis and experiments demonstrate that substrate contact angle is the key parameter controlling colloid mobilization because it determines front and surface tension force configurations and affects film thickness and flow pattern. Colloid entrapment within disconnected pendular rings during drainage makes colloid mobilization by AWI ineffective. Consequently, we have also computed with the level set method the fraction of contact lines associated with the trapped phase. This provides important insight into the dynamic, local nature of colloid retention: any model that treats all air-water-solid contact lines as functionally equivalent (in terms of their ability to retain colloids) will never be predictive of field behavior. Additional research should seek to improve understanding and quantification of contact length and morphology taking into account the transient nature of imbibition/drainage fronts in order to accurately assess colloid behavior in unsaturated porous media.
Publications
- E. Rodriquez, M. Prodanović and S. L. Bryant, 2012, Contact Line Extraction and Length Measurements in Model Sediments and Sedimentary Rocks, Journal of Colloid and Interface Science 368 (1), 2012, pp 558-577, doi: 10.1016/j.jcis.2011.10.059
- Lazouskaya, V., L-P. Wang, H. Gao, G. X. Shi, K. Czymmek, Y. Jin. 2011. Pore-scale investigation of colloid transport and retention in the presence of dynamic air-water interface. Vadose Zone J. 3:434-443
- Lazouskaya, V., Y. Zevi, G. Wang, D. Or, J. L. Caplan, and Y. Jin. 2012. Colloid mobilization by fluid displacement fronts in channels and porous media. Vadose Zone J. (to be submitted)
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Progress 09/01/09 to 08/31/10
Outputs
OUTPUTS: This year we have focused upon the quantification of the air-water-solid (AWS) contact line in simple geometries and granular materials. Comparing contact line length and air/water interfacial area enables predictions about where colloidal particles are trapped when compared with experimental visualizations conducted in this project and reported in the literature. We used a novel computational, level set method based, progressive quasi-static algorithm (LSMPQS) to determine the configuration of AWS contact lines. LSMPQS tracks the pore scale motion of interfaces assuming capillary forces are dominant. It has been implemented to compute the location of an interface between two immiscible fluids (e.g. air and water) confined by arbitrary solid surfaces (e.g. soil grains). Thus the method implicitly determines the location of contact lines as the intersection of two pairs of interfaces (e.g., the air-water interface with the water-solid interface) as a function of applied capillary pressure or of moisture content. In the level set method the fluid locations are defined by a function whose value is zero at the interface between the two fluids, less than zero for the non-wetting phase and larger than zero for the wetting phase. Another level set function is defined for the solid. This function is equal to zero on the interface between solid and pore space and negative in the pore space. The region where the fluid and solid level set functions are zero corresponds to the interface between solid and non-wetting phases. Similarly, the locus of points where the fluid function is positive and the solid function is zero corresponds to the interface between solid and wetting phases. To identify triple contact points conveniently, we introduce an auxiliary level set function for the wetting phase that will be less than zero where the fluid function is positive and the solid function is negative and larger than zero elsewhere. As a result the triple contact points will be the locations where all three level set functions are equal to zero. While the contact line position and identification in the porous media is conceptually simple, due to discretization (in simulation) and finite resolution (in imaging), its extraction and precise length measurement are not trivial. We thus first identify rather thick regions of voxels around triple contact lines where the value of the level set function is within a specified tolerance of zero. We "thin" these thick regions of voxels using medial axis approach implemented in publicly available 3DMA-Rock package. The medial axis of an object can be seen as its skeleton. Thus the medial axis of the thick region of voxels should be a very good representation of the contact line, which is a one-dimensional object. The resulting contact line is a collection of digitized links and nodes, and subsequent length measurement is straightforward. This procedure was written in a C code and added as a new functionality to the LSMPQS software package publicly available from the Level Set Method Library (LSMLIB). PARTICIPANTS: Steven Bryant, PI. Yan Jin, co-PI. Dr. Masa Prodanovic, research scientist (computational research). Dr. Yuni Zevi, post-doctoral researcher (experiments). Elena Rodriguez: Ph.D. student (computational research). TARGET AUDIENCES: Target audiences are scientists and engineers working on groundwater contamination, especially contamination caused by movement of certain bacteria and viruses associated with agricultural operations. PROJECT MODIFICATIONS: Not relevant to this project.
Impacts
The method for quantifying the length of AWS contact line was applied to a small, computer-generated packing of equal spheres. Drainage and imbibition displacements were simulated with LSMPQS, and at each step the fluid configurations were analyzed for contact line length. An important outcome was the role of pendular rings of wetting phase at grain contacts. These rings make the main contribution to contact line length for water saturations below about 40%. Each ring creates two separate contact lines, one on each grain at the contact. Resolving individual rings is impossible with coarse grids, and estimates of contact line length will be too small by nearly a factor of two. Simulations suggest that the grid refinement of 0.04 grain radius or smaller is necessary. A remarkable result is that the AWS contact line length for granular material plotted versus water saturation shows little hysteresis between drainage and imbibition. (In contrast the interfacial area between air and water shows substantial hysteresis.) The reason is the competition between growth of pendular rings (which increases contact line length) and destruction of pendular rings (which creates menisci in pore throats with smaller contact line length) during imbibition. The new method was also applied to high-resolution X-ray computed tomography images of several sediments and sedimentary rocks. Simulations of drainage and imbibition in the images of rocks showed significant hysteresis in the contact line length, which is consistent with the much smaller number of pendular rings that formed. The computed dimensionless specific contact line length during showed little variation from simple model sediments (sphere packings) to sedimentary rocks, suggesting that a single curve might describe a wide range of natural materials for drainage. The specific contact line length during imbibition was also similar for the sedimentary rocks, the difference in curves being attributable to the difference in residual air saturation. This suggests that contact line length for natural materials could be correlated with a simple family of curves. The predictions of specific contact line length were validated using high-resolution images of the same materials when partially saturated. The images were acquired only at endpoints of drainage and imbibition. Excellent agreement was found at the imbibition endpoint in a bead pack when the simulation used the same coarse resolution as the image. Good agreement was also found at imbibition endpoint in a sandstone. The contact line measured at drainage endpoint in a dolomite is dominated by spurious contribution from wetting films held in roughness on the grain surfaces. Additional research is needed to distinguish this contribution from that of AWS, which is more relevant to colloid retention. This is the first quantification of contact line length ever reported for porous media. These results thus form the basis for new understanding of a variety of phenomena in unsaturated soils.
Publications
- Prodanović, M., Wildenschild, D., Rodriguez-Pin, E., and Bryant, S. "Interfacial areas and triple contact lines at drainage and imbibition: theory, experiments and simulation", 2010 Interpore Conference and Annual Meeting, Texas A&M University, College Station, TX, March 14-17, 2010.
- Prodanović, M., Wildenschild, D., Rodriguez-Pin, E., and Bryant, S. "Pore scale study of interfacial areas at drainage and imbibition in granular media" American Geophysical Union Fall Meeting, San Francisco, 14-18 Dec. 2009.
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Progress 09/01/08 to 08/31/09
Outputs
OUTPUTS: To gain insight into the mechanism behind the retention of pathogens in unsaturated soils, we quantified the contribution to retention of the air-water-solid (or more generally, the non wetting-wetting-solid) contact line in simple geometries and granular materials. We have used a computational tool based on the level set method to reveal the configuration of these three phase (triple) contact lines. This tool was previously used to compute interfacial areas (wetting/non-wetting, wetting/solid, non-wetting/solid) and since the interfaces are confined by solid surfaces, i.e. the grains in the porous medium, the contact lines were computed straight away as the intersection of the interfaces with grain surfaces. We have computed contact lines in thin channels (less than two bead diameters in aperture) packed with beads; this geometry corresponds to the experimental apparatus (see below). We have also computed the contact lines in subsets of model sediments (random packs of spheres). By recording contact lines at increasing/decreasing applied capillary pressure, corresponding to a drainage/imbibition cycle, we have been able to identify their canonical shape. For example, the contact line associated with a pendular ring is made of a pair of isolated circles. The computational resolution needed in order to resolve contact lines in small constrictions has also been tested. To date, the computation of the contact lines has been performed only in systems having strongly water-wet surfaces (contact angle of 0). Theoretical calculations in pair of spheres revealed that the length of the contact line decreases with the increase of the contact angle, but the implementation of the calculation for larger systems is yet to be done. The results are being compared with experiments conducted using pore-scale micromodels and column packed with glass beads as porous media, using two-phase flow with water and low-viscosity silicone oil as wetting and non-wetting phase, respectively. The micromodels are made from rectangular -slide (Ibidi, 400 x 3800 micron) with uncoated and coated inner wall to provide hydrophilic and hydrophobic surfaces, and the columns (diameter 2.5 cm and height 8 cm) are packed with either hydrophilic or hydrophobic glass beads. The computer generated domains and these experimental media have the same pore-scale geometry. PARTICIPANTS: Dr. Steven Bryant, The University of Texas at Austin. Principal investigator. Dr. Yan Jin, U. of Delaware. Co-principal investigator. Dr. Masa Prodanovic. Research associate, UT-Austin. Carries out research in developing and applying the level set method, including the extension to handling nonzero contact angle. Dr. Yuniati Zevi. Post-doctoral researcher, U. Delaware. Carries out experiments and images the air/water interface and retained colloids in 3D micromodel. Elena Rodriguez. Graduate research assistant at UT-Austin. Carries out research in application of the level set method to determine air/water interface geometry and characteristics (total meniscus area, contact line length) TARGET AUDIENCES: Not relevant to this project. PROJECT MODIFICATIONS: Nothing significant to report during this reporting period.
Impacts
Visualization of the micromodel experiments show that colloids are retained at the oil-water- interface in both hydrophilic and hydrophobic cells. That moving interface can mobilize colloids previously attached to the walls on the hydrophobic cell but not on the hydrophilic one. These observations suggest that stability of colloid retention on the interfaces is controlled by the local balance of colloidal, drag, and surface tension forces. Regarding contact lines, the micromodel visualizations suggest that colloids are more likely to be trapped at contact lines associated with immobile wetting phase. Consequently we have also computed with the level set method the fraction of contact lines associated with the trapped phase. This provides important insight into the dynamic, local nature of colloid retention: any model that treats all air-water-solid contact lines as functionally equivalent (in terms of their ability to retain colloids) will never be predictive of field behavior. The breakthrough time and the concentration of colloids at steady state during both infiltration and drainage, again using the silicon oil as non-wetting phase, are recorded for the column experiments. This information combined with the computed length of contact line and interfacial areas for the analogous geometry is helping us to identify which is the controlling mechanism for pathogen retention (contact line vs. interfaces). The length of the contact line has been calculated by means of computing its "medial axis" or skeleton, since the result of the level set method is actually three dimensional. The contact line length is not a monotonic function of saturation: during drainage it increases until the wetting phase saturation is about 20%, then decreases. The contact line length as a function of wetting phase saturation exhibits little hysteresis, the length for imbibition being slightly larger than the length for drainage at a given water saturation. This is understandable since the decrease in capillary pressure during imbibition may be causing the rings to expand.
Publications
- No publications reported this period
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Progress 09/01/07 to 08/31/08
Outputs
OUTPUTS: In the past year our experimental focus has been on addressing the first question in the proposal: "What are the relative contributions of the air-water interface (AWI) and air-water-solid contact line to retention of colloids such as pathogenic microorganisms" On the experimental front, Jin's group has been conducting pore-scale visualization experiments using a fast confocal microscopy (Zeiss LSM-510 Meta) to observe a partially saturated 3D microchannel (0.4 x 3.8 x 17 mm) packed with several layers of glass beads (180 - 200 micron diameter). We are using two types of model colloids in the study: fluorescent carboxylated-modified polystyrene (hydrophilic) and sulfate latex microspheres (hydrophobic), both have mean diameter of 1.0 um and a density of 1.05 g/cm3. Packed micromodels were prepared to have two moisture levels: high where air phase in the channel is mostly discontinuous as insular bubbles and low where air phase is continuous along the channel walls or as thin films around glass beads. Colloid retention on air bubbles or contact line were observed under the two scenarios at different solution ionic strength (1.0, 10, and 50 mM) at pH 8.5. Our modeling focus has been on developing the capability of handling nonzero contact angles in our level-set-method approach for predicting the configuration of air/water phases within the experimental apparatus. This will enable us to predict air/water meniscus areas (AWI) and air/water/solid contact line lengths (AWS). These quantities are difficult to extract directly from the experiment, so the simulations will greatly enhance the interpretation of the colloid retention in the experiments. We implemented a method for handling prescribed contact angle on any part of the grain surface and are currently validating its predictions. Because it proved difficult to determine the geometric arrangement of beads within the 3D microchannel from experiment, we also developed an algorithm to simulate a dense, disordered packing of beads confined within a slit. Simulation of drainage and imbibition into this model medium produces configurations very similar to those observed in the experiments. We conclude that the AWI and AWS obtained from simulations within the model can be reasonably compared to observations. PARTICIPANTS: Dr. Steven Bryant, The University of Texas at Austin. Principal investigator. Dr. Yan Jin, U. of Delaware. Co-principal investigator. Dr. Masa Prodanovic. Research associate, UT-Austin. Carries out research in developing and applying the level set method, including the extension to handling nonzero contact angle. Dr. Yuniati Zevi. Post-doctoral researcher, U. Delaware. Carries out experiments and images the air/water interface and retained colloids in 3D micromodel. Elena Rodriguez. Graduate research assistant at UT-Austin. Carries out research in application of the level set method to determine air/water interface geometry and characteristics (total meniscus area, contact line length) TARGET AUDIENCES: Not relevant to this project. PROJECT MODIFICATIONS: Nothing significant to report during this reporting period.
Impacts
Our main findings so far: 1) the AWI on insular air bubbles is an unlikely site of colloid retention; 2) the contact line (where air, water and solid phases meet) is a preferred retention site over AWI for both hydrophilic carboxylated and hydrophobic sulfate latex microspheres; and 3) sulfate particles are retained more than carboxylated particles under the same solution chemistry. We are in the process of analyzing these observations using DLVO theory and approaches used in flotation literature. These pore-scale observations provide insight into colloid retention in unsaturated porous media at 1) relatively high water content where insular sir bubbles contribute mainly to the total AWI area and 2) relatively low water content where AWI mainly exists on contact line. The results suggest that the configuration of AWI rather the total interfacial area controls colloid retention. Colloids such as pathogenic microorganisms are a primary cause of the contamination of water resources by agricultural operations. The impact of these results is that they contribute to better understanding of the fundamental mechanisms involved in colloid retention in unsaturated porous media.
Publications
- Zevi, Y., M. Prodanovic, S.L. Bryant, and Y. Jin. The effect of air and water phase configuration on colloid retention in partially saturated porous media. Presented at 1) 82nd Colloid & Surface Science Symposium, American Chemical Society, June 15-18. North Carolina State University, Raleigh, NC. 2) 2008 GSA-SSSA-ASA-CSSA Joint meeting, October 5-8, Houston, TX
- Prodanović, M. and Bryant, S. Investigating matrix-fracture transfer via a level set method for drainage and imbibition. SPE116110, Proceedings of the 2008 SPE Annual Technical Conference and Exhibition Denver, Colorado, U.S.A., 21-24 September 2008.
- M. Prodanović and S. L. Bryant. A level set method for non-zero contact angle drainage and imbibition in realistic porous media. Presentation at Computational Methods in Water Resources 2008, San Francisco, CA, July 6-10, 2008
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