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.

Use of a State-Level Pharmaceutical Assistance Program Among Urban and Rural Elders

A number of state-level pharmaceutical assistance programs have been established as a result of the growing recognition of the role of pharmaceuticals in the long-term care of the elderly. However, existing research does not provide a coherent expectation for patterns of use by rural and urban elderly. The data for this analysis are drawn from a larger study of the Pennsylvania Pharmaceutical Assistance Contract for the Elderly (PACE). PACE provides prescription medicines for elderly who meet income requirements. The research project was designed to assess the characteristics of PACE program participants and non-participants on a wide range of issues. Chi-square analysis and regression models were used to assess the association between rural and urban residence and access to the PACE Program. The results indicate that rural/urban status of the elderly is not a significant predictor of the use of PACE. Other traditional variables (e.g., health self-rating and physician visits) did predict difference in the pattern of use.

State-Level Pharmaceutical Assistance Programs for the Elderly: A national survey.

In order to put Pennsylvania's Pharmaceutical Assistance Contract for the Elderly (PACE) Program in a national context, a nationwide mail survey and telephone follow-up to each of the 58 State Unit Directors on Aging in the United States and its territories identified 10 programs. The results reported in this article are specific to the seven state-level pharmaceutical assistance programs which were in operation during the fiscal year 1984-85. In general, the programs varied on select program characteristics and on their efforts to address major policy issues. Data from the non-program states indicated support, legislative efforts, and a high interest in fiscal concerns. The findings reflect a lack of program uniformity and have implications for program development and implementation. Suggestions on how to identify the "optimum" or best combination of program and policy options are discussed.

State Pharmaceutical Assisstance for the Elderly and Disabled: Planning Issues for Program and Non-Program States

The Medicare Catastrophic Coverage Act (MCCA) would have mandated federal assistance for Medicare beneficiaries who have high annual prescription medication costs, High national expenditures for such drugs have encouraged the development of private and state insurance programs to help with these costs. Ten state pharmaceutical assistance programs (SPAPs), designed to help certain elderly, low income, or disabled people, exist for those ineligible for Medicaid or unable to purchase coverage privately. Coordination of state and federal benefits was a consideration for established programs, and programs being planned needed to determine the feasibity of integration of federal assistance. But the enactment and subsequent appeal of the Act affected both planning and policy implications for these SPAPs. All U.S. states and territories were surveyed before the bill's repeal to collect data on the effects of MCCA for those with prescription drug programs and those without. The repeal of the federal program places pressure on the nonprogram states to proceed, perhaps more cautiously, to initiate program; for their own residents, given increasing out-of-pocket and insurance costs, and no federal program.