Critical review of coupled flux formulations for clay membranes based on nonequilibrium thermodynamics

Extensive research conducted over the past several decades has indicated that semipermeable membrane behavior (i.e., the ability of a porous medium to restrict the passage of solutes) may have a significant influence on solute migration through a wide variety of clay-rich soils, including both natural clay formations (aquitards, aquicludes) and engineered clay barriers (e.g., landfill liners and vertical cutoff walls). Restricted solute migration through clay membranes generally has been described using coupled flux formulations based on nonequilibrium (irreversible) thermodynamics. However, these formulations have differed depending on the assumptions inherent in the theoretical development, resulting in some confusion regarding the applicability of the formulations. Accordingly, a critical review of coupled flux formulations for liquid, current, and solutes through a semipermeable clay membrane under isothermal conditions is undertaken with the goals of explicitly resolving differences among the formulations and illustrating the significance of the differences from theoretical and practical perspectives. Formulations based on single-solute systems (i.e., uncharged solute), single-salt systems, and general systems containing multiple cations or anions are presented. Also, expressions relating the phenomenological coefficients in the coupled flux equations to relevant soil properties (e.g., hydraulic conductivity and effective diffusion coefficient) are summarized for each system. A major difference in the formulations is shown to exist depending on whether counter diffusion or salt diffusion is assumed. This difference between counter and salt diffusion is shown to affect the interpretation of values for the effective diffusion coefficient in a clay membrane based on previously published experimental data. Solute transport theories based on both counter and salt diffusion then are used to re-evaluate previously published column test data for the same clay membrane. The results indicate that, despite the theoretical inconsistency between the counter-diffusion assumption and the salt-diffusion conditions of the experiments, the predictive ability of solute transport theory based on the assumption of counter diffusion is not significantly different from that based on the assumption of salt diffusion, provided that the input parameters used in each theory are derived under the same assumption inherent in the theory. Nonetheless, salt-diffusion theory is fundamentally correct and, therefore, is more appropriate for problems involving salt diffusion in clay membranes. Finally, the fact that solute diffusion cannot occur in an ideal or perfect membrane is not explicitly captured in any of the theoretical expressions for total solute flux in clay membranes, but rather is generally accounted for via inclusion of an effective porosity, n(e), or a restrictive tortuosity factor, tau(r), in the formulation of Fick's first law for diffusion. Both n(e) and tau(r) have been correlated as a linear function of membrane efficiency. This linear correlation is supported theoretically by pore-scale modeling of solid-liquid interactions, but experimental support is limited. Additional data are needed to bolster the validity of the linear correlation for clay membranes. Copyright 2012 Elsevier B.V. All rights reserved.

Critical Review of Coupled Flux Formulations for Clay Membranes Based on Nonequilibrium Thermodynamics

Extensive research conducted over the past several decades has indicated that semipermeable membrane behavior (i.e., the ability of a porous medium to restrict the passage of solutes) may have a significant influence on solute migration through a wide variety of clay-rich soils, including both natural clay formations (aquitards, aquicludes) and engineered clay barriers (e.g., landfill liners and vertical cutoff walls). Restricted solute migration through clay membranes generally has been described using coupled flux formulations based on nonequilibrium (irreversible) thermodynamics. However, these formulations have differed depending on the assumptions inherent in the theoretical development, resulting in some confusion regarding the applicability of the formulations. Accordingly, a critical review of coupled flux formulations for liquid, current, and solutes through a semipermeable clay membrane under isothermal conditions is undertaken with the goals of explicitly resolving differences among the formulations and illustrating the significance of the differences from theoretical and practical perspectives. Formulations based on single-solute systems (i.e., uncharged solute), single-salt systems, and general systems containing multiple cations or anions are presented. Also, expressions relating the phenomenological coefficients in the coupled flux equations to relevant soil properties (e.g., hydraulic conductivity and effective diffusion coefficient) are summarized for each system. A major difference in the formulations is shown to exist depending on whether counter diffusion or salt diffusion is assumed. This difference between counter and salt diffusion is shown to affect the interpretation of values for the effective diffusion coefficient in a clay membrane based on previously published experimental data. Solute transport theories based on both counter and salt diffusion then are used to re-evaluate previously published column test data for the same clay membrane. The results indicate that, despite the theoretical inconsistency between the counter-diffusion assumption and the salt-diffusion conditions of the experiments, the predictive ability of solute transport theory based on the assumption of counter diffusion is not significantly different from that based on the assumption of salt diffusion, provided that the input parameters used in each theory are derived under the same assumption inherent in the theory. Nonetheless, salt-diffusion theory is fundamentally correct and, therefore, is more appropriate for problems involving salt diffusion in clay membranes. Finally, the fact that solute diffusion cannot occur in an ideal or perfect membrane is not explicitly captured in any of the theoretical expressions for total solute flux in clay membranes, but rather is generally accounted for via inclusion of an effective porosity, ne, or a restrictive tortuosity factor, tr, in the formulation of Fick's first law for diffusion. Both ne and tr have been correlated as a linear function of membrane efficiency. This linear correlation is supported theoretically by pore-scale modeling of solid-liquid interactions, but experimental support is limited. Additional data are needed to bolster the validity of the linear correlation for clay membranes.

Chemical compatibility of soil-bentonite cutoff wall backfills containing modified bentonites

This study examined the chemical compatibility of several model soil-bentonite(SB) backfills with an inorganic salt solution (CaCl2). First, bentonite-water slurry was created using a natural sodium-bentonite, as well as two modified bentonites –multiswellable bentonite (MSB) and a “salt-resistant” bentonite (SW101). Once slurries that met typical construction specifications had been created using the various bentonites,the model SB backfills were prepared for each type of bentonite. These backfills werealso designed to meet conventional construction and design requirements. The SB backfills were then subjected to permeation with tap water and/or CaCl2 solutions of various concentrations in order to evaluate the compatibility of the SB backfills with inorganic chemicals. The results indicate that SB backfill experiences only minor compatibility issues (i.e., no large differences between the hydraulic conductivity of the SB backfill to tap water and CaCl2) compared to many other types of clay barriers. In addition, SB backfills show no major change in final hydraulic conductivity to CaCl2 when permeated with tap water before CaCl2 versus being permeated with CaCl2 directly. These results may be due to the ability of the bentonite in the SB backfills to undergo osmotic swelling before permeation begins, and the inability of the CaCl2 solutions to undo the osmotic swelling. Similar results were obtained for all three clays tested, and while MSB did show less compatibility issues than the natural bentonite and SW101, it appears that the differences in performance may generally be negligible. Overall, thisstudy makes a significant addition to the understanding of SB cutoff wall compatibility.

Investigating The Fate Of Positively Charged Nanoparticles In A Soil Environment

The recent increase in the amount of nanoparticles incorporated into commercial products is accompanied by a rising concern of the fate of these nanoparticles. Once released into the environment, it is inevitable that the nanoparticles will come into contact with the soil, introducing them to various routes of environmental contamination. One route that was explored in this research was the interaction between nanoparticles and clay minerals. In order to better define the interactions between clay minerals and positively charged nanoparticles, in situ atomic force microscopy (AFM) was utilized. In situ AFM experiments allowed interactions between clay minerals and positively charged nanoparticles to be observed in real time. The preliminary results demonstrated that in situ AFM was a reliable technique for studying the interactions between clay minerals and positively charged nanoparticles and showed that the nanoparticles affected the swelling (height) of the clay quasi-crystals upon exposure. The preliminary AFM data were complemented by batch study experiments which measured the absorbance of the nanoparticle filtrate after introduction to clay minerals in an effort to better determine the mobility of the positively charged nanoparticles in an environment with significant clay contribution. The results of the batch study indicated that the interactions between clay minerals and positively charged nanoparticles were size dependent and that the interactions of the different size nanoparticles with the clay may be occurring to different degrees. The degree to which the different size nanoparticles were interacting with the clay was further probed using FTIR (Fourier transform infrared) spectroscopy experiments. The results of these experiments showed that interactions between clay minerals and positively charged nanoparticles were size dependent as indicated by a change in the FTIR spectra of the nanoparticles upon introduction to clay.