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.

An Investigation On The Use Of Microalgae For Biogas Enrichment

There is a need for biomethane capture and carbon dioxide sequestration to mitigate evident global climate change. This research work investigated the potential for microalgae to remove CO2 from biogas as a biotechnical method for upgrading the thermal value for subsequent compression, liquification, or introduction to natural gas pipelines. Because biogas is largely methane, the effect of high methane environments on mixed microalgae was explored and found that specific carbon utilization rates were not statistically different when microalgae were exposed to biogas environments (70% v/v CH4) , relative to high CO2 environment. The uses of conventional bubbled column photobioreactors (PBR) were assessed for CO2 removal and subsequent CH4 enrichment. A continuously-bubbled biogas PBR (cB-PBR5) and intermittently-bubbled biogas PBR (iB-PBR) experienced CO2 loading rates of about 1664 and 832 mg C/L*day and showed 30.0 and 60.1 % carbon removal, respectively. However, a lack of biogas enrichment and issues associated growth inhibition due to high CO2 environments as well as stripping the dissolved gases, namely oxygen and nitrogen, from the bulk liquid and introduction to the outlet gas prompted the consideration for gas/liquid separation using nonporous hollow-fiber (HF) membranes for CO2 transfer. The potential for two non-porous HF membrane materials [polydimethylsiloxane (PDMS) and composite polyurethane (PU)] were modeled along fiber length using a mechanistic model based on polymeric material transport properties (Gilmore et al., 2009). Based on a high CO2:CH4 permeability selectivity for PU of 76.2 the model predicted gas enrichment along an 8.5 cm fiber length. Because PDMS permeability selectivity is low (3.5), evident gas transfer was not predicated along a 34.3 cm length. Both of these HF materials were implemented in hollow-fiber membrane-carbonated biofilm (HFMcB) PBRs for microalgal-mediated biogas enrichment. Phototrophic biofilm colonization occurred on the membrane, where CO2 concentration was greatest. The presence of a biofilm demonstrated greater resiliency to high CO2 environments, compared to the conventional PBRs. However, as the PDMS model predicted, the PDMS HFMcBs did not demonstrate gas enrichment. These reactors received CO2 loading rates of 200 mg C/L*day based on PDMS permeability flux and showed approximately 65% removal of the total C transferred across the membrane. Thus, the HFMcBs demonstrated controlled carbonation of the bulk liquid via a nonporous HF membrane. Likewise, the experimental PU HFMcB did not show gas enrichment yet this result should be further explored due to the high permeability selectivity of the polymeric material. Chemical stratifications, namely pH and dissolved O2, present in a PDMS membrane-carbonated biofilm were analyzed using electrochemical microsensors. Results indicated that high DO (20 mg L-1) exists at surface of the biofilm where light availability is greatest and low pH microenvironments (pH=5.40) exist deep in the biofilm where the diffusive flux of CO2 drives transfer through the biofilm. The presence of a 400-600 ¿m liquid phase boundary layer was evident from microsensor profiles. Cryosectioning of the biofilm samples showed the biofilm to be approximately 1.17 ± 0.07 mm thick, suggesting that the high localized concentration of biomass associated with the phototrophic biofilm aided in overcoming inhibition in a microenvironment dominated by CO2(aq). Challenges of biofilm detachment and PBR fouling as well as microalgal growth inhibition in the presence of high CO2 content remain for applications of microalgae for biogas enrichment.

Continuous, Passive Liquid-Liquid Extraction and Emulsion Separation Within Microfluidic and Millifluidic Devices

Liquid-liquid extraction (LLE) is a method used to separate compounds based on their relative activity in two immiscible phases. By significantly reducing the scale of liquid-liquid extraction to the micro- and milli-fluidic levels, this separation process can bemade suitable for low volume, high value materials.

Efficient Liquid Liquid Extraction By Emulsion Formation and Separation in Robust Milli-Fluidic Devices

Conventional liquid liquid extraction (LLE) methods require large volumes of fluids to achieve the desired mass transfer of a solute, which is unsuitable for systems dealing with a low volume or high value product. An alternative to these methods is to scale down the process. Millifluidic devices share many of the benefits of microfluidic systems, including low fluid volumes, increased interfacial area-to-volume ratio, and predictability. A robust millifluidic device was created from acrylic, glass, and aluminum. The channel is lined with a hydrogel cured in the bottom half of the device channel. This hydrogel stabilizes co-current laminar flow of immiscible organic and aqueous phases. Mass transfer of the solute occurs across the interface of these contacting phases. Using a y-junction, an aqueous emulsion is created in an organic phase. The emulsion travels through a length of tubing and then enters the co-current laminar flow device, where the emulsion is broken and each phase can be collected separately. The inclusion of this emulsion formation and separation increases the contact area between the organic and aqueous phases, therefore increasing the area over which mass transfer can occur. Using this design, 95% extraction efficiency was obtained, where 100% is represented by equilibrium. By continuing to explore this LLE process, the process can be optimized and with better understanding may be more accurately modeled. This system has the potential to scale up to the industrial level and provide the efficient extraction required with low fluid volumes and a well-behaved system.