Diffuse Double Layer Theory Research Articles

Soil Permeability Controlled by Particle–Fluid Interaction

In this paper, Atterberg limits and hydraulic conductivity tests are performed in sand samples mixed with different amounts of silt, zeolite and bentonite. The testing liquids consist of kerosene, two paraffin oils with different viscosities, distilled water and 1, 10 and 1,000 mol/m³ calcium chloride solutions. Experimental results show that soils completely lost their plasticity when are in contact with light non-aqueous phase liquids, and that the liquid limit depends on the dynamic viscosity of the fluid surrounding the particles. Also, tested soils show different hydraulic conductivity with water before and after Ca2+ ions are introduced in the permeating fluid, in agreement with the change in the formation Gibbs free energy and diffuse double layer theory. Finally, the influence of viscosity ratio, specific surface of particles, soil fabric and PFI on hydraulic conductivity is discussed and related to the effective particle diameter and soil void ratio.

Advances on the knowledge of the buffer/backfill properties of heavily-compacted GMZ bentonite

GMZ bentonite has been selected as a potential material for the construction of engineered barrier in the Chinese program of geological nuclear waste disposal, for its high montmorillonite content, high cation exchange capacity (CEC) and large specific surface etc. Studies on mineralogy and chemical composition, mechanical properties, hydraulic behavior, swelling behavior, thermal conductivity, microstructure and volume change behavior of GMZ bentonite were performed from 1980s. Based on a review of the former studies, achievements on experimental and theoretic results obtained on compacted GMZ bentonite specimens including basic properties, thermal, hydraulic and mechanical behaviors are presented in this paper. Results show the thermal conductivity of GMZ bentonite and the bentonite-based mixtures influenced by its dry density, water content, mixture of other materials and degree of saturation etc. Water retention capacity of highly-compacted GMZ bentonite decreases as the temperature increases under confined and unconfined conditions. The hysteretic behavior in the water retention curves of the compacted GMZ bentonite is not so significant at 20 or 40 °C. The unsaturated hydraulic conductivity of compacted GMZ bentonite under unconfined conditions is higher than that of under confined conditions. This is possibly induced by the difference in the mechanism of microstructural changes during hydration under different confining conditions. The compaction curves for GMZ bentonite with different dry densities are clearly step-phased. And the optimum water content for GMZ bentonite is about 15%. An exponential relationship between swelling pressure and dry density of highly-compacted GMZ bentonite was determined for the prediction of swelling pressure. Furthermore, the void ratio after swelling for unconfined sample also can be predicted using diffuse double layer (DDL) theory.

The effect of surface–solute interactions on the transport of solutes through porous materials

SummaryWe have investigated the effect of differences in surface charge, valency of ion, solute concentration, solution flux and physical structure on the leaching and uptake of individual ions from simple solutions flowing through porous materials. We studied the miscible displacement of solutions of four salts (KBr, K2SO4, CaBr2 and CaSO4) having different cation : anion ratios separately through three inert materials (ballotini, pumice and ceramic) and two sizes of a reactive material (sepiolite) over several ranges of concentration (c) and at many pore‐water velocities (v) under steady vertical saturated flow. Breakthrough curves of individual effluent ions (K+, Br−, Ca2+ and SO42−) were analysed by CXTFIT 2.0 to optimize transport parameters (retardation factor, R; dispersion coefficient, K) assuming that transport was governed by the convective–dispersion equation. In the inert materials, R did not differ significantly from 1 irrespective of c. In sepiolite, R was < 1 for anions and > 1 for cations, and became more extreme as c decreased. R varied with the valency of the anions, as predicted by diffuse double layer theory, and with that of the cations by a simple charge balance. Freundlich isotherms, reconstructed from R values, described the sorption of the cations and exclusion of the anions. For the inert materials, K did not depend on the ion or c and increased monotonically with v. For sepiolite, K also increased with v and with small but non‐significant differences between ions and concentrations. The K(v) functions were consistent with Passioura’s theory of dispersion in aggregated media, and the transport was reversible as R and K values did not depend on whether the media were being leached or resalinized. The effective dispersion coefficient of an ion is K* = K/R so, although K(v) appears to be unaffected by ion or concentration of solute in sepiolite, K*(v) will be affected. Thus, the controlling factor of these surface–solute interactions is R.

Effects of solutes on clay–water interactions: Some comments

Schmitz [Schmitz, R.M., 2006. Can the diffuse double layer theory describe changes in the hydraulic conductivity of compacted clays? Geotechnical and Geological Engineering, 24, 1835–1844.] suggests that ‘unique interpretations and predictions of changes in hydraulic conductivity in clays’ follow appropriate interpretation of changes in double layer thickness. Existing data, however, suggest that reality is more complicated and that both the water content-water potential and hydraulic conductivity functions of clay–water systems must continue to be regarded as macroscopically measurable material properties and that double layer considerations provide only qualitative indications of general behaviour. At the same time, the composition of the equilibrium solution remains a necessary characteristic of the hydrostatic and dynamic properties of clay–water systems. Some experiments that might help our understanding of the hydrostatics and hydrodynamics of these systems are suggested.

Computation of hydraulic conductivity of montmorillonitic clays by diffuse double layer theory

Knowledge of hydraulic conductivity of clays is very important in many cases and in waste containment system in particular. Several investigations have been carried out on hydraulic conductivity in the past and it has been brought out that the hydraulic conductivity is strongly influenced by the pore fluid chemistry apart from the soil type and void ratio. Based on the theoretical considerations, the effect of dielectric constant of the pore fluid, valency and concentration of cations in the pore fluid, it is surmised that the hydraulic conductivity is significantly influenced by diffuse double layer thickness, which reduces the pore volume through which flow takes place. A study of Gouy-Chapman diffuse double layer theory show that the diffuse double layer thickness is negligible for non-polar fluid with very low dielectric constant (e.g. CCl4). Considering the thickness of diffuse double layer contributed by CCl4 as zero, the equivalent thickness of diffuse double layer as affected by dielectric constant, valency, concentration, hydrated radius of cation and specific surface has been estimated and presented for montmorillonitic clays. The effective void ratio has been evaluated and a unique relationship between effective void ratio and hydraulic conductivity has been brought out for montmorillonitic clays with different pore medium chemistry. The present study throws more light on the fundamental mechanisms controlling the hydraulic conductivity in clays.

Computation of hydraulic conductivity of montmorillonitic clays by diffuse double layer theory

AbstractKnowledge of hydraulic conductivity of clays is very important in many cases and in waste containment system in particular. Several investigations have been carried out on hydraulic conductivity in the past and it has been brought out that the hydraulic conductivity is strongly influenced by the pore fluid chemistry apart from the soil type and void ratio. Based on the theoretical considerations, the effect of dielectric constant of the pore fluid, valency and concentration of cations in the pore fluid, it is surmised that the hydraulic conductivity is significantly influenced by diffuse double layer thickness, which reduces the pore volume through which flow takes place. A study of Gouy-Chapman diffuse double layer theory show that the diffuse double layer thickness is negligible for non-polar fluid with very low dielectric constant (e.g. CCl4). Considering the thickness of diffuse double layer contributed by CCl4 as zero, the equivalent thickness of diffuse double layer as affected by dielectric...

Compressibility behaviour of clays at large pressures

In this study, a method is proposed on the basis of the diffuse double layer theory to determine the compressibility of clays for one-dimensional conditions for vertical pressures far greater than the testing range of conventional oeodometer tests. Experimental e–p curves of several reported bentonitic clays were considered to verify the proposed method. It is shown that the parameters required to use the diffuse double layer theory can be obtained from the experimental e–p data for a low range of pressure and those can in turn be used to compute void ratios at higher vertical pressures. The stepwise procedure to calculate the e–p relationships at high pressure is given. The results showed that the agreement between the calculated and experimental compression characteristics at large vertical pressures is very good for the clays considered in this study.Key words: clays, compressibility, consolidation, expansive soils.

Can the diffuse double layer theory describe changes in hydraulic conductivity of compacted clays?

Observations related to modifications of the hydraulic conductivity of compacted soils as a consequence of intentional compositional variation of the percolating fluid are often attributed vaguely to calculated changes in double layer thickness. The same calculated decrease or increase in double layer thickness is interpreted differently, depending on which (unconsciously held) boundary conditions authors take into account. The interpretations of different authors seem to be paradoxical only if the boundary conditions have not been mentioned. On the basis of a literature survey and own previously published test results the different boundary conditions have been grouped and divided into classes. With this division the interpretation of changes in double layer thickness will lead to unique interpretations and predictions of changes in hydraulic conductivity.

Assessment of supporting electrolyte contributions in electrochemically modulated liquid chromatography

This paper reports the results of an investigation on the role of the supporting electrolyte in separations using electrochemically modulated liquid chromatography (EMLC) with a porous graphitic carbon stationary phase. With respect to the identity of the supporting electrolyte, the elution strength of the electrolyte anion increased as F − < OH − < BF 4 − < ClO 4 − < PF 6 − for injections of negatively charged aromatic molecules, whereas a 10-fold increase in electrolyte concentration induced a 60% change in retention for the same solutes. Furthermore, both the concentration and composition of the supporting electrolyte affected retention in a manner that varied with the charge of the analyte and applied potential. This behavior is explained using Gouy–Chapman diffuse double layer theory, coupled with comparisons of this theory with closely related models for ion-pair chromatography. Insights into the retention mechanism reveal that an ion-exchange mechanism controls the retention of negatively charged solutes at applied potentials removed from the potential of zero charge (PZC). At potentials close to the PZC, the electrostatic model is less effective with the predominant retention mechanism likely involving hydrophobic interactions with the carbonaceous stationary phase. The combined effects of these findings are demonstrated by using a temporal gradient in supporting electrolyte concentration to optimize an EMLC separation.

An upscaling method and a numerical analysis of swelling/shrinking processes in a compacted bentonite/sand mixture

AbstractThis paper presents an upscaling concept of swelling/shrinking processes of a compacted bentonite/sand mixture, which also applies to swelling of porous media in general. A constitutive approach for highly compacted bentonite/sand mixture is developed accordingly. The concept is based on the diffuse double layer theory and connects microstructural properties of the bentonite as well as chemical properties of the pore fluid with swelling potential. Main factors influencing the swelling potential of bentonite, i.e. variation of water content, dry density, chemical composition of pore fluid, as well as the microstructures and the amount of swelling minerals are taken into account. According to the proposed model, porosity is divided into interparticle and interlayer porosity. Swelling is the potential of interlayer porosity increase, which reveals itself as volume change in the case of free expansion, or turns to be swelling pressure in the case of constrained swelling. The constitutive equations for swelling/shrinking are implemented in the software GeoSys/RockFlow as a new chemo‐hydro‐mechanical model, which is able to simulate isothermal multiphase flow in bentonite. Details of the mathematical and numerical multiphase flow formulations, as well as the code implementation are described. The proposed model is verified using experimental data of tests on a highly compacted bentonite/sand mixture. Comparison of the 1D modelling results with the experimental data evidences the capability of the proposed model to satisfactorily predict free swelling of the material under investigation. Copyright © 2004 John Wiley &amp; Sons, Ltd.

An approach to the method for determination of surface potential on solid/liquid interface: theory

The electrochemical properties on solid particle surfaces in an aqueous system have found wide application in many fields. However, for some of them there are no reliable methods of determination. What is particularly worth mentioning is the surface potentials of solid particles. Though this is a most important property and a most basic parameter in colloid interface electrochemistry, no reliable method for its determination is available yet. In the present paper, based on the diffuse double-layer theory, mathematical relations are constructed between the average concentration of ions positively adsorbed in the diffuse double layer and the surface potential of solid particles, thus transforming the determination of surface potential of solid particles into that of the average concentration of ions in the diffuse double layer, and then by applying the standard relationships of Gouy–Chapman theory, the mathematical relations of the average concentration of ions in the diffuse double layer with surface charge density, electrical field strength at surface, and specific surface area of solid particles are constructed.

Swelling pressures of compacted bentonites from diffuse double layer theory

The swelling pressures of several compacted bentonites (MX80, Febex, and Montigel) proposed for use as barrier materials in storing high-level radioactive waste in many countries were determined from the Gouy–Chapman diffuse double layer theory. The swelling pressures thus determined were compared with the reported experimental swelling pressures. The study revealed that, in general, at low compaction dry densities of the bentonites, the experimental swelling pressures are less than their theoretical counterparts, with the reverse trend at high compaction dry densities. Based on the reported experimental results for the three bentonites, relationships between the nondimensional midplane potential function, u, and the nondimensional distance function, Kd, were established. New equations for the swelling pressure were proposed on the basis of the diffuse double layer theory and the reported experimental data to compute swelling pressures of compacted bentonites. The suitability of the new equations was also verified with additionally reported experimental swelling pressures from three other bentonites (Kunigel V1, Kunigel, and bentonite S-2) that have been also proposed for use as barrier materials. Very good agreement was found in all the cases between the experimental swelling pressures and the swelling pressures obtained using the proposed equations. The use of the proposed equations is based on the weighted average valency of the cations present in bentonites, since the valency of the cations present has a significant influence on the swelling pressure.Key words: clays, compressibility, swelling pressure, expansive soils, chemical properties, radioactive waste disposal.

An approach to the method for determination of surface potential on solid/liquid interface: theory

The electrochemical properties on solid particle surfaces in an aqueous system have found wide application in many fields. However, for some of them there are no reliable methods of determination. What is particularly worth mentioning is the surface potentials of solid particles. Though this is a most important property and a most basic parameter in colloid interface electrochemistry, no reliable method for its determination is available yet. In the present paper, based on the diffuse double-layer theory, mathematical relations are constructed between the average concentration of ions positively adsorbed in the diffuse double layer and the surface potential of solid particles, thus transforming the determination of surface potential of solid particles into that of the average concentration of ions in the diffuse double layer, and then by applying the standard relationships of Gouy–Chapman theory, the mathematical relations of the average concentration of ions in the diffuse double layer with surface charge density, electrical field strength at surface, and specific surface area of solid particles are constructed.

New equations for swelling characteristics of bentonite-based buffer materials

Compacted bentonite and sand–bentonite mixtures are attracting greater attention as buffer material for repositories of high-level nuclear waste. This buffer material is expected to fill up the space between the canisters containing the waste and the surrounding ground by swelling. To produce the specifications, such as dry density, sand–bentonite mass ratio, and dimensions, of the buffer material, the swelling characteristics of compacted bentonite and sand–bentonite mixtures must be evaluated quantitatively. New equations for evaluating the swelling behavior of compacted bentonite and sand–bentonite mixtures are presented that can accommodate the influences of the sand–bentonite mass ratio and the exchangeable-cation composition of bentonite. The new method for predicting swelling characteristics is presented by combining the new equations with the theoretical equations of the Gouy–Chapman diffuse double layer theory and of the van der Waals force, which can evaluate the repulsive and attractive forces of montmorillonite mineral (i.e., the swelling clay mineral in bentonite). Furthermore, the applicability of the new prediction method has been confirmed by comparing the predicted results with laboratory test results on the swelling deformation and swelling pressure of compacted bentonites and sand–bentonite mixtures.Key words: bentonite, diffuse double layer theory, van der Waals force, nuclear waste disposal, swelling deformation, swelling pressure.

Influence of physicochemical properties of soil on pH of pore water

pH of soil pore water is the important factor in heavy metal retention and migration in soil. Buffer capacity of clays such as kaolinite, hectorite, attapulgite, and Na-bentonite were determined. The magnitude of buffer capacity is in the order of hectorite>Na-bentonite>attapulgite>kaolinite. Carbonate content and CEC of soil affect most on the magnitude of buffer capacity while effects of organic content and surface area were negligible. Attempts were made to simulate buffer capacity experimental results in this research. In order to model the buffer capacity of soil, chemical interactions between proton and surface functional group were modeled using the diffuse double layer theory. An empirical model as functions of carbonate content and CEC were proposed as well. Predictions made by the diffuse double layer model agreed with experimental results well.

Consolidation Behavior of Bentonite in Electrolyte Solutions

Abstract Volume change behavior of clays in different pore fluids is very important in their use as compacted clay liners for landfills. The present study brings out the variations in the consolidation behavior of bentonite compacted at Proctor's optimum conditions in different electrolyte solutions. Qualitatively the behavior can be explained using diffuse double layer theory. Existing methods to calculate theoretically e-log p curves based on this theory have been referred to the theoretical curves that agree closely with experimental curves. Clay properties, which are critical in the theoretical prediction of the curves, have been identified. However, the effect of potassium ions, which link bentonite clay particles, cannot be assessed by diffuse double layer theory.

Boundary layer and the stability of hydrophilic dispersions

This article presents the results of an experimental study of the influence of different factors on the structure and extent of the hydration boundary layers (BL) of oxidised synthetic diamond (OSD) and oxidised graphite (OG). The experimental technique allows changes in the hydrodynamically immobile BL thickness to be recorded by means of an electrokinetic method. It also provides independent information about the surface charge ( σ), ζ potential and sol stability over a wide range of pH and concentration of the inert electrolyte (KCl). To check the correctness and the reliability of the technique we studied the influence of the four different factors on the BL thickness: (1) hydrophilization of the graphite and diamond surface (by means of an increase in the degree of oxidation); (2) preliminary thermotreatment of the OSD micropowder in an inert gas flow or in a vacuum; (3) introduction into aqueous dispersions of OSD and OG of the non-ionogenic compounds, promoting the destruction of the BL structure; (4) influence of temperature on the electrophoretic mobility and the dispersion stability. On the basis of the influence of each of these factors on the BL, it is established that the sign of the ζ potential change correlates strictly with the direction of the shift in the slip-plane boundary, supporting the basic concept of the method. On the basis of the dependences obtained, ζ( C el) for constant σ(pH), and ζ( σ) for constant ionic strength, we estimated the thickness h of the hydrodynamically immobile hydration layer on the surfaces of OSD and OG, applying the diffuse double electric layer theory. Using the different approaches we found that h varied in the range h=1.0–3.0 nm. The values obtained for h on average correspond to the BL thickness of 5–7 molecular water layers. These results are in quantitative agreement with experimental data on the stability of the dispersions under consideration and with the results of a calculation of the pair interaction potential curves for OSD and OG particles in the framework of the generalised DLVO theory taking into account the structural forces.

Two components of boundary potentials at the lipid membrane surface: electrokinetic and complementary methods studies

Bilayer lipid membranes (BLM) are commonly used as models for cell membranes to study their interactions with inorganic ions and molecules of biological importance. In this work the principal electrostatic effects at the BLM surface are demonstrated by two methods: by the inner membrane field compensation (IFC) which is applied to planar BLM and sensitive to changes in the total boundary potential; and by electrokinetic measurements in liposome suspensions, sensitive to diffuse (surface) component of this potential. The difference in these two potentials allows us to conclude on changes in the dipole component of the boundary potential caused by structural changes at the membrane–water interface. No difference in the experimental data of both methods was observed for Be 2+ and other divalent cation adsorption to unchanged phosphatidyl choline (PC) membranes. These data are in a good agreement with the Gouy–Champan–Stern (GCS) theory of diffuse double layer. This theory gives the value of binding constants for Be 2+ about 400 M −1 and 10 4 M −1 for DPPC liposomes in the liquid and solid states of the lipids, respectively. Clear isotope effects for normal and heavy water solutions of Be 2+ were observed both by the electrostatic measurements and by differential scanning calorimetry. In contrast to PC, the electrostatic potentials induced by Be 2+ and Gd 3+ adsorption to membranes from phosphatidyiserine (PS) show the difference between the data of mentioned methods — total boundary potential changes are much higher in comparison to the surface potential. Dipole potential changes (about 150 mV) caused by changes in PS head group orientation may be more important in this specific case.

Prediction for swelling characteristics of compacted bentonite: Discussion

The paper by H. Komine and N. Ogata is a welcome addition to the existing literature. The discusser would like to draw the attention of the authors to some major limitations of the various equations pertaining to the diffuse double-layer theory used by them for the prediction. In the Langmuir equation (eq. [1] of the authors’ paper), the parameter u refers to the nondimensional mid-plane potential (all notations are the same as those of the authors unless specified):

A Critique of Diffuse Double Layer Models Applied to Colloid and Surface Chemistry

AbstractThe use of Derjaguin-Landau-Verwey-Overbeek (DLVO) theory in colloid science has continued to the present day in spite of the inability of this theory to explain, even qualitatively, numerous phenomena exhibited by clays and other colloidal materials. An alternative description of the fundamental forces involved in the formation of dispersions and gels was presented in 1938 by Langmuir, but was never widely accepted among colloid scientists. Recent experimental and theoretical work, particularly in Japan, has revived this alternative view, in which a long-range Coulombic attraction force appears to explain several phenomena, particularly transitions among ordered and disordered phases of colloidal particles in dilute salt solutions.Examples are given from surface chemistry where rather complex models based on diffuse double layer theory are used to explain chemical adsorption behavior that often has a simpler explanation. It is argued that the rule of parsimony (Ockham's Razor) should be applied to complex models that appear to explain the data at hand before such models are taken to be generally valid. A satisfactory fit of model predictions to experimental data obtained under a very limited range of conditions does not prove the validity of the model. Thus, it is concluded that the DLVO theory and its modifications fail to meet the 2 criteria necessary to the acceptance of a theory: agreement with observations and simplicity.