Thickness Of Electric Double Layer Research Articles

Cilia beating modulated radiating ternary nanofluids flow in a corrugated asymmetric channel with electromagnetohydrodynamic and momentum slip

AbstractA mathematical model is presented to study the cilia beating modulated radiated ternary nanofluid flow between two cilia‐carpeted walls propagating with an applicable phase difference to show the asymmetric nature of the pumping. To regulate further the cilia‐based pumping, electroosmosis, and magnetohydrodynamics mechanisms are considered in this model. Ternary nanofluid is considered with TiO2, SiO2, and Al2O3 nanoparticles dispersed in pure blood. The momentum slip condition is employed to derive the model solution. Thermal radiation and buoyancy effects are also taken into consideration. Mathematica NDSolve is utilized to simulate the numerical results for the velocity, temperature, and concentration profiles under the influence of the emerging parameters. Moreover, entropy generation and variation in Nusselt and Bejan numbers are computed for better thermal analysis. A comparative thermal analysis for unary, binary, and ternary nanofluids is also made. The results indicate that the trihybrid nanofluid offers an 8.5% increase in the heat transfer rate as compared to the conventional fluid. Furthermore, the Brownian motion is responsible for the enhancement in fluid temperature, while electric double layer thickness helps in increasing heat transfer irreversibility around the channel lower wall. It is found that the total entropy of the system at the channel upper and lower space is minimized in the case of ternary fluid rather than conventional fluid. The promising results of the present model reflect huge applications in biomedical engineering, particularly in designing thermal cilia‐based microfluidic devices.

Shielding behavior of electrokinetic properties of polystyrene latex particle by the adsorption of neutral poly(ethylene oxide)

To understand the shielding of electrokinetics of colloidal particles by polymer coating, we measured the electrophoretic mobility of negatively charged polystyrene sulfate latex (PSL) adsorbed with electrostatically neutral polyethylene oxide (PEO) chains with various molecular weights under different ionic strengths. We confirmed that substantial adsorbed neutral polymer on the particle surface would decrease the absolute value of electrophoretic mobility. Even though the polymer layer is sufficiently thicker compared to the thickness of electric double layer (EDL), the electrophoretic mobility (EPM) never vanishes, which indicates the incompleteness of electrokinetic shielding by an adsorbed neutral polymer. To relate such interesting phenomena, a simple mathematical model has been proposed to evaluate the electrophoretic mobility, assuming the presence of a scaling structure of adsorbed permeable polymer layer does not influence the Poisson–Boltzmann distribution of ions in the electric double layer (EDL). An analytical expression of electrophoretic mobility under Debye-Hu¨ckel approximation has been derived using the method of Ohshima-Kondo theory, which successfully justifies the experimentally obtained data.

Electro-osmotic peristaltic flow and heat transfer in an ionic viscoelastic fluid through a curved micro-channel with viscous dissipation.

Emerging systems in microfluidics are embracing bio-inspired designs in which boundaries are flexible and mimic peristaltic propulsion mechanisms encountered in nature. These devices utilize electro-kinetic body forces to manipulate very precisely ionic biofluids for a range of medical applications including. Motivated by exploring in more detail electro-hemorheological micro-pumping, in the current article, a mathematical model is developed for peristalsis propulsion of a viscoelastic biofluid in a curved microchannel with electro-osmotic effect and thermal transport under static axial electrical field and with viscous heating. The third grade Reiner-Rivlin model is deployed for blood rheology. The novelty of the current work is therefore the simultaneous consideration of electrokinetics, viscoelastic behavior with the third grade Reiner-Rivlin model and coupled flow and heat transport with viscous dissipation in peristaltic pumping in a curved micro-channel. A Poisson-Boltzmann formulation is adopted to simulate the charge number density associated with the electrical potential. Asymmetric zeta potential (25 mV) is prescribed and mobilizes an electric double layer (EDL). The governing conservation equations for mass, energy, momentum and electrical potential with associated boundary conditions are simplified using lubrication approximations and rendered dimensionless via appropriate scaling transformations. Analytical solutions are derived in the form of Bessel functions and numerical evaluations are conducted via the ND solver command in MATHEMATICA symbolic software. The simulations show that with stronger viscoelastic effect, boluses are eliminated and there is relaxation in streamlines in the core and peripheral regions of the micro-channel. Increasing Brinkman number (dissipation parameter) elevates temperatures. An increase in electrical double layer thickness initially produces a contraction in the upper bolus and an expansion (lateral) in the lower bolus in the micro-channel. With modification in zeta potential ratio parameter from positive to negative values, in the lower half of the micro-channel, axial flow deceleration is generated.

Numerical analysis of thermophoresis of charged colloidal particles in non-Newtonian concentrated electrolyte solutions.

Thermophoresis of colloidal particles in aqueous media is more frequently applied in biomedical analysis with processed fluids as biofluids. In this work, a numerical analysis of the thermophoresis of charged colloidal particles in non-Newtonian concentrated electrolyte solutions is presented. In a particle-fixed reference frame, the flow field of non-Newtonian fluids has been governed by the Cauchy momentum equation and the continuity equation, with the dynamic viscosity following the power-law fluid model. The numerical simulations reveal that the shear-thinning effect of pseudoplastic fluids is advantageous to the thermophoresis, and the shear-thickening effect of dilatant fluids slows down the thermophoresis. Both the shear-thinning and shear-thickening effects of non-Newtonian fluids on a thermodiffusion coefficient are pronounced for the case when the thickness of electric double layer (EDL) surrounding a particle is moderate or thin. Finally, the reciprocal of the dynamic velocity at the particle surface is calculated to approximately estimate the thermophoretic behavior of a charged particle with moderate or thin EDL thickness.

Unraveling the Molecular Interface and Boundary Problems in an Electrical Double Layer and Electroosmotic Flow.

In a nanofluidic system, the electroosmotic flow (EOF) is a complex fluid transport mechanism, where the formation of an electrical double layer (EDL) occurs ubiquitously at the dissimilar atomic interface. Several studies have suggested various interface boundaries to calculate the EDL thickness. However, the physical origin of the interface boundary and its effects on the flow properties is not yet clearly understood. Combining the theoretical framework and molecular dynamics (MD) simulations, we show the effects of different interfacial boundaries on the EDL thickness and EOF characteristics. Implemented interface boundaries exhibit the EDL thickness-boundary relation, i.e., the EDL thickness from MD simulations shows the tendency of converging toward the continuum approximation. Furthermore, inserting these values of EDL thicknesses into the continuum equation shows the convergence of flow transition of the molecular state to a neutral from an electrical violation phase, which takes a parabolic to plug-like shape in the velocity profile. Different interface boundaries also affect the hydrodynamic properties (viscosity and electroviscosity) of EOF, which varies from the bulk to interface region, as well as the fluid flow. Therefore, we can infer that, at the molecular level, the dissimilar atomic boundary and hydrodynamic properties dominate the electrokinetic flow. Our simulation results and theoretical model provide fundamental insightful information and guidelines for the EOF study based on the atomic interface and dynamic structure-based hydrodynamic property.

Exploring the polarization window during fluoride electrosorption in two activated carbons with significant differences in their pore-size distribution

This work reports the electrosorption of fluoride by two commercial activated carbons (coconut-shell and bituminous carbons) with significant differences in their pore-size distribution but with a similar surface area, surface chemistry and charging processes. The coconut-shell carbon is 95% microporous, while the bituminous carbon presents micro (75%) and mesoporosity (25%). Fluoride electrosorption was evaluated in sacrifice cells by polarizing at several potentials (Ecell = 0, 1.2, 1.6, 2 and 2.4 V). The fluoride removal capacity and rate without polarizing was really low and increased at different degrees as a function of increasing the applied potential for both carbons. At 2 Vcell, the bituminous and coconut-shell carbons increased their capacity from 0.073 to 0.431 mg g−1 and from 0.047 to 0.256 mg g−1, respectively, compared to conventional adsorption. On the other hand, the removal rate of the bituminous carbon was ∼ 4 times faster than that of the coconut-shell carbon at short times. This was associated to a higher presence of mesopores, as they enhance the mass-transport and the accessibility of the anion to the polarizable surface, and present less overlapping of the electrical double-layer (EDL). In this regard, a first approximation of the decrease of the EDL thickness was obtained from mathematical approximations and the obtained experimental results at 2 Vcell, in which the overlapping decreased by half, from a pore width of 18.67 nm to ∼ 9.5 nm. Parasitic faradaic reactions were induced at all the applied potentials, which decreased the charge efficiency of the process, although these reactions were more significant at 2.4 Vcell.

Geochemical investigation of electrical conductivity and electrical double layer based wettability alteration during engineered water injection in carbonates

The injection of engineered water to increase the oil recovery from carbonates is increasingly becoming popular due to its reduced environmental impact and low cost of operation. However, the related variation in electric properties of rock and fluid with this technique is still ambiguous and needs thorough investigation. This study explores the variation in electrical conductivity, ion mobility, electrical double layer thickness, and the related oil recovery with the change in water composition from a geochemical perspective. In this study, we implemented an improved wettability alteration model based on the variation in electrical conductivity with a Matlab-IPhreeqc coupled simulator, to model the electrical conductivity, ion mobility, and electrical double layer (EDL) thickness. The variation in concentration of the ionic species obtained from the geochemical model is used to determine the electrical conductivity. This electrical conductivity-based wettability modification is dynamically simulated in the transport model. The model is validated with experimental coreflood data conducted on carbonates by simulating the electrical conductivity measurements reported in the literature. From the findings, it is evident that the formation temperature, sulfate concentration, and dilution of injected seawater has a noticeable effect on electrical conductivity during engineered water injection. It is important to mention that the EDL thickness is the main parameter affected by the change in electrical conductivity. In consequence, it is suggested to inject high-temperature water in carbonate reservoirs because it will increase ion mobility. This increase in ion mobility will enhance the EDL thickness and water film will become stabilized. Moreover, seawater dilution decreases electrical conductivity while spiking of sulfate concentration increases the activity of sulfate ions. However, the concentration of sulfate ions must be controlled as a wettability alteration agent, as it can cause the formation and precipitation of calcium sulfate. Furthermore, the variation in electrical conductivity and EDL thickness caused by the injection of seawater and diluted seawater increased the recovery of oil by approximately 16–21% in the selected case study.

Diffusiophoresis of a moderately charged spherical colloidal particle.

An analytic expression is obtained for the diffusiophoretic mobility of a charged spherical colloidal particle in a symmetrical electrolyte solution. The obtained expression, which is expressed in terms of exponential integrals, is correct to the third order of the particle zeta potential so that it is applicable for colloidal particles with low and moderate zeta potentials at arbitrary values of the electrical double-layer thickness. This is an improvement of the mobility formula derived by Keh and Wei, which is correct to the second order of the particle zeta potential. This correction, which is related to the electrophoresis component of diffusiophoresis, becomes more significant as the difference between the ionic drag coefficients of electrolyte cations and anions becomes larger and vanishes in the limit of thin or thick double layer. A simpler approximate mobility expression is further obtained that does not involve exponential integrals.

Simulation study on the flow behaviors of weak electrolyte solutions in nano-sized and micron-sized pores considering electric double layer interactions

ABSTRACT The interactions between the ions in the weak electrolyte solutions and the charged solid wall result in the formation of an electric double layer (EDL) in nano-sized and micron-sized pores. However, in nano-sized pores, EDLs may be overlapping. Herein, a widely applicable Poisson-Nernst-Planck equation combined with the Navier–Stokes equation was adopted for the flow of weak electrolyte solutions under pressure-driven conditions. Meanwhile, the finite element method was utilized to solve the governing equations and investigate the influence of EDL interactions on flow behaviors in different pore radii (25 nm~5 μm). The results showed that as the pore radius increased, the influence of EDL interactions on fluid flow behaviors first increased and then decreased. The influence of EDL interactions on fluid flow behaviors was the most noticeable when the pore radius was close to the EDL thickness. Furthermore, the influence of EDL interactions appeared to be negligible in the pore radius greater than 5 μm. When EDL interactions were ignored, the volume flow in the pores of the circular, square, and equilateral triangle was increased by about 13%. This study provides new insights into the flow behaviors of weak electrolyte solutions in nano-sized and micron-sized pores.

Mathematical modeling of electrothermal couple stress nanofluid flow and entropy in a porous microchannel under injection process

We examine the effects of ion diffusion coefficient on steady electroosmotic couple stress nanofluid flow and heat transfer in a porous microchannel bounded by two permeable beds. The study considers the nanofluid injection process through porous beds. The combined effects of ion diffusivity and injected nanofluid velocity on EDL (Electric double layer) thickness are analytically expressed. The differential transform method (DTM) is used to solve the flow equations. The DTM solution is then compared with the exact analytical solution of velocity, Zeta potential function and a square averaged residual analysis is conducted. These comparisons show excellent matching. We observe that the enhancement of ion diffusion coefficient increases nanofluid velocity at the edge of EDL but diminishes with intrinsic couple stress. The bulk nanofluid flow rate is found to follow a quadratic like relationship with the couple stress parameter. We have investigated the nanofluid temperature and nanoparticle concentration distribution in microchannel for variations of the diffusive Reynolds number, porous permeability parameter and couple stress parameter. The nanofluid temperature is found to increase with an enhancement of ion diffusion coefficient, which is related with experimental results observed by Kong et al. (Phys. Chem. Chem. Phys. 19 (2017) 7678) for NaCl electrolyte solution confined in a graphene nanochannel. Moreover, the nanofluid temperature decreases with enhancement of both porous permeability of the medium and couple stress parameter.

Impact of polymer on electro-kinetic properties of crude oil, brine and rock interfaces

In recent years, there has been a growing interest in the petroleum industry to improve the ultimate oil recovery method by using low-salinity polymer flooding (LSPF) with the synergistic effect by combining polymer and low-salinity water injection. Although numerous research studies have focused on the technical and economic benefits of low salinity polymer (LSP), to the best of our knowledge, crude oil/brine/rock (COBR) interactions in LSP did not receive enough attention due to the complexity of the interactions between brine, polymer, crude oil, and the rock surface. Therefore, this study aimed to investigate the impact of polymer on COBR interactions with different brine chemistry and improve the understanding of active mechanisms of LSPF. Partially hydrolyzed polyacrylamide (HPAM) polymer, Boise rock, a crude oil sample from an Omani oil field, and several brine solutions were used in the study. Zeta potential and pH measurements were performed to examine the role of polymer on electrical properties of brine/rock and oil/brine interfaces. In addition, rheological properties of the polymer were investigated at different salinity and brine compositions. Changes in Boise rock surface charge through zeta potential measurements were investigated in the absence and presence of polymer. pH and rheology measurements for equilibrated brines with and without polymer and zeta potential of crude oil/equilibrated brine were performed. The results revealed that the addition of polymer to the brine not only increased the viscosity, but also affected the electrical charge at crude oil/brine/rock (COBR) interfaces and triggered pH increase of the brine. The impact of polymer on COBR interactions is mainly controlled by the water chemistry. In the absence of ions, polymer molecules did not affect the charge of COBR interfaces, while in the presence of ions, at different compositions and concentrations, the charge of COBR interfaces changed to become more negative. Thus, the presence of polymer in brine increases the electrostatic repulsion between crude oil/brine and brine/rock interfaces, increases electrical double layer (EDL) thickness, and makes the water film more stable. A direct relationship between the viscosity and zeta potential of the polymer solutions was observed at different brine chemistry. Moreover, the presence of polymer at different brine chemistry resulted in an increase in pH of the aqueous phase. This could in turn reduce the adsorption of polar organic acids from crude oil. Therefore, in addition to the reduction of the water-oil mobility ratio, polymer molecules could contribute to an increase in the repulsion forces between COBR interfaces and an increase in the pH of the aqueous solution.

A study of the thickening process for fine tailings of gold-bearing ores

Refractory low-grade gold-bearing ores require deep processing with finer preliminary grinding. As a result, finely dispersed products are formed, including fine tailings, which raise particular environmental concerns. The article presents the results of experimental thickening studies for the concentration tailings of gold-bearing ores from the Yuzhno-Nevyanskoe and Panovskoe deposits. The material studied is distinguished by the presence of fine clay inclusions, which reduce the sedimentation rate of slurry solids. The main processing methods are gravity separation in centrifugal concentrators and flotation. Electrokinetic properties of the particle surface, in particular, the x-potential, in the tailings slurries entering the thickening process may be used to predict thickening performance with sufficient accuracy and significantly reduce the number of laboratory experiments. Measured values of the x-potential, electric double layer thickness, and other dielectric properties of the particle surface were used to establish that the most effective sedimentation of the tailings was achieved at a mass fraction of solids in the slurry of up to 25 % and a pH value of at least 10.5. The optimal flocculant feed amount required to increase the slurry sedimentation rate was also established. It is therefore recommended to use the following flocculants for the ore processing tailings of the Yuzhno-Nevyanskoe deposit: Praestol 2510 at more than 10 g/t and Magnaflok 10 at over 20 g/t. Flocculants are not required for thickening the ore processing tailings of the Panovskoe deposit.

Understanding the electrosteric dispersion of α-alumina particles using a sulfonated tannin of natural origin

This work explores the stabilization effect of a sulfonated tannin (black wattle extract) on water-suspended α-alumina particles. Results showed that first additions lead to particle agglomeration. A minimum of 0.5 wt% tannin (relative to the alumina content) is required to cover the whole particle surface. Suspensions regain stability at ca. 1.0 wt% tannin (ca.1 mg tannin/m2 alumina surface area), due to a high negative ζ-potential (−60 mV, pH = 8.0). Both ζ-potential and particle hydrodynamic diameter are then close to those in electrostatically dispersed alumina particles. Changes in ionic strength cause changes in ζ-potential and hydrodynamic diameter but hardly affect the tannin adsorption. The electrosteric stabilization results from the repulsion provided by the ~15 nm thick adsorbed tannin layer (steric effect) and the enveloping electric double layer, which remains sensitive to the suspension ionic strength (electrostatic effect). Changes in hydrodynamic diameter can be used to infer the electric double layer thickness.

Inclusion of DLVO forces in simulations of non-Brownian solid suspensions: Rheology and structure

The understanding of the rheological behaviour of suspensions in aqueous electrolytes is necessary for the optimal design of hydraulic transport lines. In these applications, particle size is at least 10 micron, and the particle Reynolds number, Rep, is finite: O(10−1). Although there are some experimental and numerical data on the rheology of such suspensions, the number of detailed analyses is limited. Therefore, 3-D direct numerical simulations of dense suspensions in aqueous electrolytes are conducted to assess the dynamics of the relative apparent viscosity and particle structures. The solid–liquid interfaces are resolved, and the flow is simulated, employing an in-house immersed boundary-lattice Boltzmann method code. In addition to the hydrodynamics resolved in the computational grid, our simulations include unresolved sub-grid scale lubrication corrections and non-contact electric double layer (EDL) and Van der Waals forces for a wide range of particle volume fractions, ϕv, at a single Rep=0.1. Under these conditions, the contribution of the Van der Waals force was found to be weak. With an increase in ϕv, the effect of EDL forces decreased the relative apparent viscosity. Particle layering and structural arrangements were analysed for ϕv=43 and 52%. As the Debye length (i.e., the thickness of EDL) decreases, the particle layers near the walls weakened. The analyses reveal how at these high volume fractions, chain-like assemblies are transformed into hexagonal arrangements.

Fully developed opposing mixed convection in inclined microchannel with electric double layer effects

In this paper, the mixed convection flow driven in an inclined microchannel by pressure gradient and buoyancy in the presence of electrical double layer is considered. Analytical solutions for electrostatic potential, velocity and temperature distribution are given to the governing equations ruled by the buoyancy parameter, the pressure parameter, and the electrostatic and stream potential parameters after dimensionless transformation. The influences of various physical parameters on velocity and temperature distribution are illustrated and discussed. The onset of flow reversal is examined in detail. In addition to the pressure gradient and buoyancy, it is found that the electrostatic force is significant to affect the flow reversal regime, and the thickness of the electrical double layer has little effect on it. It is also found that the stream potential increases with zeta potential and the thickness of electrical double layer.

Similarity principle based multi-physical parameter unification and comparison in salinity-gradient osmotic energy conversion

Nanofluidic osmotic energy conversion has the potential of directly converting renewable salinity-gradient energy into electricity. Existing research mainly focuses on the ion selectivity and robustness of nanoporous membranes. However, the multi-physical governing parameters of salinity-gradient osmotic energy conversion have never been unified and compared. In the current study, a similarity principle is constructed for ion selective transport in nanofluidic channel through dimensionless analysis, which lays a theoretical foundation for experimental design and data analysis to develop engineering correlations in osmotic energy conversion under a salinity-gradient. The derived dimensionless governing parameters are grouped into four categories with different physical meanings including ion driving source, ion selectivity, ion transport characteristics, and nanoporous membrane configuration. Particularly, a key dimensionless governing parameter named “IonS” is developed for ion selectivity of nanofluidic channel, indicating that the ion selectivity has a positive linear correlation with the nanochannel surface charge density and a negative linear correlation with ion concentration and nanofluidic channel radius. Considering the similarity phenomena in salinity-gradient osmotic energy conversion, future experimental burden is dramatically alleviated. In addition, a sensitivity analysis using Taguchi method is carried out to evaluate the dominance order of multi-physical parameters in salinity-gradient osmotic energy conversion. The ion concentration and nanofluidic channel radius are found to be dominant for maximum output power and energy conversion efficiency because of their significant influences on the thickness of electric double layer and its overlapping degree. The current dimensionless analysis based similarity principle and sensitivity analysis of multi-physical parameters offer an intrinsic insight for ion selective transport in nanofluidic channels, contributing to the development of salinity-gradient osmotic energy conversion for practical applications.

Effect of skimming layer in an electroosmotically driven viscoelastic fluid flow over charge modulated walls

We report a numerical study on the effect of the skimming layer in an EOF of Oldroyd-B fluid over charge modulated walls. Three types of flow conditions were identified on the basis of the relative thickness of the skimming layer and the electrical double layer. We observe maximum slip velocity magnitude when the skimming layer thickness is very less than the thickness of the electrical double layer. For higher skimming layer thickness compared to the thickness of electrical double layer, slip velocity magnitude attenuates, and the polymeric stress inside the skimming layer becomes zero. Enhanced fluid elasticity generates asymmetric flow structures inside the microchannel, which can also be achieved by imposing an asymmetric surface charge along the channel walls. Our present analysis highlights the complex flow dynamics of the EOF of biofluids/polymeric fluids with a near-wall region depleted of macro-molecules.

Electroosmotic flow of viscoelastic fluid through a microchannel with slip-dependent zeta potential

We investigate flow characteristics for an electroosmotic flow of viscoelastic fluids through a hydrophobic plane microchannel, considering the coupled effect of interfacial slip and zeta potential. We employ a simplified Phan–Thien–Tanner model to describe the constitutive behavior of the fluid. The governing equations are solved analytically to obtain electric double layer (EDL) potential distribution, flow velocity, flow rate, stresses, and viscosity. We have compared the obtained analytical flow field with the established theoretical and experimental works at the limiting cases. We demonstrate that ignoring the effect of the interfacial slip on zeta potential will lead to underprediction of the flow rate, and this underprediction is amplified with the increase in the Deborah number, decrease in the EDL thickness, and increase in the slip coefficient. Moreover, the relative flow rate augmentation by the rheological behavior strictly depends on the range of slip coefficients with the change in the EDL thickness. Accordingly, we have identified three regions of the slip coefficient. In addition, the viscosity near the wall decreases with the slip coefficient for the slip dependent zeta potential model. In contrast, the normal and shear stresses are augmented with the slip coefficient. Outcomes of the present investigation may help one to understand the enhanced flow behavior for the transport of complex fluids through a hydrophobic microchannel.

A novel mechanistic anion exclusion model to investigate partially water‐saturated transport in soils and shales: A case study of nitrate solution flow

AbstractAnion exclusion is an important phenomenon in agricultural, environmental and engineering fields which still needs suitable quantitative models. In this work, a novel model is proposed which considers the porous media as parallel capillaries with negatively charged walls that cause total anion exclusion at a distance from the walls. By defining the ‘anion velocity coefficient’, , as the ratio of anion velocity to pore fluid velocity, equations to estimate the value of at the injection inlet have been derived by three different methods, namely from the profiles' data, , from the concentration ratio at the inlet, , and from the electrical double layer thickness model, . Finally, a simple sensitivity analysis for the third method has been presented. The estimates of presented in this paper were examined versus 22 data points for nitrate solution flow in initially dry soil columns for various soil and salt types and solution concentrations. The coefficient of determination between and for the whole dataset was 0.7755. Also, the estimate could predict the value estimated from the breakthrough anion concentration curve for available data of an advective injection test in a clayey rock. As a result, when anion exclusion dominates, the anion flux decreases but the anion velocity increases. In the case of using nitrate fertilisers, this point may be used to regulate the amount of optimal irrigation and also to explain the extent of contamination of a distant groundwater body.Highlights Modelling the anion exclusion phenomena in soils and shales. A mechanistic capillary model is developed to extract the anion velocity coefficient from data. Anion exclusion explains the anion concentration peaks in the unsaturated soil column test results. The derived estimates for anion velocity coefficient are shown to be reliable and promising.

Radial basis function interpolation supplemented lattice Boltzmann method for electroosmotic flows in microchannel.

Large gradients of physical variables near the channel walls are characteristic of EOF. The previous numerical simulations of EOFs with the lattice Boltzmann method (LBM) utilize uniform lattice and are not efficient, especially when the electric double layer (EDL) thickness is significantly smaller than the channel height. The efficient LBM simulation of EOF in microchannel calls for a nonuniform mesh which is dense in the EDL region and sparse in the bulk region. In this article, we formulate a radial basis function (RBF)-based interpolation supplemented LBM (ISLBM) to solve the governing equations of EOF, that is, the Poisson, Nernst-Planck, and Navier-Stokes equations, in a nonuniform mesh system. Unlike the conventional ISLBM, the RBF-ISLBM determines the prestreaming distribution functions by using the local RBF-based interpolation over circular supporting regions and is particularly suitable for nonuniform meshes. The RBF-ISLBM is validated by the EOFs in infinitely long and finitely long microchannels. The results show that the RBF-ISLBM possesses excellent robustness and accuracy. Finally, we use the RBF-ISLBM to simulate the EOFs with the hitherto highest electrokinetic parameter, κa, defined by the ratio of channel height a to EDL thickness κ-1 , in LBM simulations of EOF.