Cation Diffusion in Compacted Clay: A Pore-Scale View

Adsorption of Diffusing Tracers, Apparent Tortuosity, and Application to Mesoporous Silica

The apparent tortuosity due to adsorption of diffusing tracers in a porous material is determined by a scaling approach and is used to analyze recent data on LiCl and alkane diffusion in mesoporous silica. The slope of the adsorption isotherm at small loadings is written as β = qA/qG, where qA is the adsorption-desorption ratio and qG = ϵ/(as) - 1 is a geometrical factor depending on the range a of the tracer-wall interaction, the porosity ϵ, and the specific surface area s. The adsorption leads to a decrease of effective diffusion coefficient, which is quantified by multiplying the geometrical tortuosity factor τgeom by an apparent tortuosity factor τapp. In wide pores or when the adsorption barrier is high, τapp = β + 1, as obtained in previous works, but in narrow pores there is an additional contribution from frequent adsorption-desorption transitions. These results are obtained in media with parallel pores of constant cross sections, where the ratio between the effective pore width ϵ/s and the actual width is ≈0.25. Applications to mesoporous silica samples are justified by the small deviations from this ideal ratio. In the analysis of alkane self-diffusion data, the fractions of adsorbed molecules predicted in a recent theoretical work are used to estimate τgeom of the silica samples, which is ≫1 only in the sample with the narrowest pores (nominal 3 nm). The application of the model to Li+ ion diffusion leads to similar values of τgeom and to a difference of energy barriers of desorption and adsorption for those ions of ∼0.06 eV. Comparatively, alkane self-diffusion provides the correct order of magnitude of τgeom, with adsorption playing a less important role, whereas adsorption effects on Li+ diffusion are much more important.

A Lab on a Chip Experiment for Upscaling Diffusivity of Evolving Porous Media

Reactive transport modelling is a powerful tool to assess subsurface evolution in various energy-related applications. Upscaling, i.e., accounting for pore scale heterogeneities into larger scale analyses, remains one of the biggest challenges of reactive transport modelling. Pore scale simulations capturing the evolutions of the porous media over a wide range of Peclet and Damköhler number in combination with machine learning are foreseen as an efficient methodology for upscaling. However, the accuracy of these pore scale models needs to be tested against experiments. In this work, we developed a lab on a chip experiment with a novel micromodel design combined with operando confocal Raman spectroscopy, to monitor the evolution of porous media undergoing coupled mineral dissolution and precipitation processes due to diffusive reactive fluxes. The 3D-imaging of the porous media combined with pore scale modelling enabled the derivation of upscaled transport parameters. The chemical reaction tested involved the replacement of celestine by strontianite, whereby a net porosity increase is expected because of the smaller molar volume of strontianite. However, under our experimental conditions, the accessible porosity and consequently diffusivity decreased. We propose a transferability of the concepts behind the Verma and Pruess relationship to be applied to also describe changes of diffusivity for evolving porous media. Our results highlight the importance of calibrating pore scale models with quantitative experiments prior to simulations over a wide range of Peclet and Damköhler numbers of which results can be further used for the derivation of upscaled parameters.

How the Solid/Liquid Ratio Affects the Cation Exchange Process and Porosity in the Case of Dioctahedral Smectite: Structural Analysis?

The performance of a clay mineral geomembrane used in the context of a geological barrier for industrial and radioactive waste confinement must pass through the understanding of its hydrous response as well as the limits of the cation exchange process which are closely related to the solid/liquid ratio constraint. The Na-rich montmorillonite is used, as starting material, to evaluate the link between the applied external constraint (variable solid/liquid ratio) and the structural response of the material. The geochemical constraint is realized at the laboratory scale, and the possible effects are investigated in the cases of Ba2+ and Ni2+ heavy metal cations. The structural analysis is achieved using the XRD profile modeling approach to quantify the interlayer space (IS) deformation. The quantitative XRD analysis, which consists of the comparison of experimental 001 reflections with the calculated ones deduced from structural models, allowed us to determine the optimal structural parameters describing IS configuration along the $c\ast$ axis. The obtained result showed an interstratified hydration character, for both studied exchangeable cations, regardless of the solid/liquid ratio being described probably by a partial cation exchange process. The theoretical mixed layer structure (MLS) suggests the coexistence of more one cristallite species saturated by more than one exchangeable cations, indicating a partial saturation of all exchangeable sites. The optimum structural parameter values, from the theoretical model, allowed us to follow the evolution of several intrinsic properties versus the applied constraint strength. The variable solid/liquid ratio effect on the material porosity is examined by the BET-specific surface area and BJH pore size distribution (PSD) analyses. The adsorption measurement outcomes confirm XRD results concerning mainly the link between several intrinsic clay properties and the constraint strength.

Effective removal of ammonium nitrogen using titanate adsorbent: Capacity evaluation focusing on cation exchange

Cation exchange is one of the dominant mechanisms in the adsorption of cationic ammonium nitrogen (NH₄⁺) from water. In this study, we focus on the role of counter cations in cation exchange process of NH₄⁺ to enhance the adsorption capacity. Five amorphous titanates namely lithium titanate (LiT), sodium titanate (NaT), potassium titanate (KT), strontium titanate (SrT) and barium titanate (BaT) with different counter cation were facilely synthesized. The adsorption performance for NH₄⁺ by these samples is in the order of LiT> NaT > KT> > SrT > BaT. The maximum adsorption capacity of LiT calculated by Langmuir is as high as 50.31 mg·g^-1. According to the experimental results and theoretical analysis, the electrostatic interaction between counter ions (cations in framework or eternal solution) and charged framework (fixed ions) is the main influence factor during cation exchange process in general. The cation valence and the hydrated ionic radius of the counter ions can inversely affect the ion exchange equilibrium and the affinity of counter ions to titanates. Therefore, a definition of a brief parameter, affinity coefficient K_f (relating to ion valence and distance between opposite charged ions), is introduced and used to explain the difference in adsorption performance of five titanates for NH₄⁺. The conclusion about cation exchange and ions affinity may provide possible strategies for enhancement of cationic contaminant adsorption from water or wastewater.

Electrokinetic Delivery of Reactants: Pore Water Chemistry Controls Transport, Mixing, and Degradation

Electrokinetics in porous media entails complex transport processes occurring upon the establishment of electric potential gradients, with a wide spectrum of environmental applications ranging from remediation of contaminated sites to biotechnology. The resulting electric forces cause the movement of pore water ions in opposite directions, leading to charge interactions that can affect the distribution of charged species in the domain. Here, we demonstrate that changes in chemical conditions, such as the concentration of a background electrolyte in the pore water of a saturated porous medium, exert a key control on the macroscopic transport of charged tracers and reactants. The difference in concentration between the background electrolyte and an injected solute can limit or enhance the reactant delivery, cause nonintuitive patterns of concentration distribution, and ultimately control mixing and degradation kinetics. With nonreactive and reactive electrokinetic transport experiments combined with process-based modeling, we show that microscopic charge interactions in the pore water play a crucial role on the transport of injected plumes and on the mechanisms and rate of both physical and chemical processes at larger, macroscopic scales. Our results have important implications on electrokinetic transport in porous media and may greatly impact injection and delivery strategies in a wide range of applications, including in situ remediation of soil and groundwater.

Temperature effects on electrical double layer at solid-aqueous solution interface

Despite the significant influence of solution temperature on the structure of electrical double layer, the lack of theoretical model intercepts us to explain and predict the interesting experimental observations. In this work, we study the structure of electrical double layer as a function of thermochemical properties of the solution by proposing a phenomenological temperature dependent surface complexation model. We found that by introducing a buffer layer between the diffuse layer and stern layer, one can explain the sensitivity of zeta potential to temperature for different bulk ion concentrations. Calculation of the electrical conductance as function of thermochemical properties of solution reveals the electrical conductance not only is a function of bulk ion concentration and channel height but also the solution temperature. The present work model can provide deep understanding of micro- and nanofluidic devices functionality at different temperatures.