Retardation Coefficient Research Articles

A three-scale model for ionic solute transport in swelling clays incorporating ion–ion correlation effects

A new three-scale model is proposed to describe the movement of ionic species of different valences in swelling clays characterized by three separate length scales (nano, micro, and macro) and two levels of porosity (nano- and micropores). At the finest (nano) scale the medium is treated as charged clay particles saturated by aqueous electrolyte solution containing monovalent and divalent ions forming the electrical double layer. A new constitutive law is constructed for the disjoining pressure based on the numerical resolution of non-local problem at the nanoscale which, in contrast to the Poisson–Boltzmann theory for point charge ions, is capable of capturing the short-range interactions between the ions due to their finite size. At the intermediate scale (microscale), the two-phase homogenized particle/electrolyte solution system is represented by swollen clay clusters (or aggregates) with the nanoscale disjoining pressure incorporated in a modified form of Terzaghi’s effective principle. At the macroscale, the electro-chemical–mechanical couplings within clay clusters is homogenized with the ion transport in the bulk fluid lying in the micro pores. The resultant macroscopic picture is governed by a three-scale model wherein ion transport takes place in the bulk solution strongly coupled with the mechanics of the clay clusters which play the role of sources/sinks of mass to the bulk fluid associated with ion adsorption/desorption in the electrical double layer at the nanoscale. Within the context of the quasi-steady version of the multiscale model, wherein the electrolyte solution in the nanopores is assumed at instantaneous thermodynamic equilibrium with the bulk fluid in the micropores, we build-up numerically the ion-adsorption isotherms along with the constitutive law of the retardation coefficients of monovalent and divalent ions. In addition, the constitutive law for the macroscopic swelling pressure is reconstructed numerically showing patterns of attractive forces between particles for bivalent ions for particular ranges of bulk concentrations. The three-scale model is applied to numerically simulate ion diffusion in a compacted clay liner underneath a sanitary landfill. Owing to the distinct constitutive behavior of the swelling pressure and partition coefficient for each ionic species, different compaction regimes and diffusion/adsorption patterns, with totally different characteristic time scales, are observed for sodium and calcium migration in the clay liner.

Fabrication of low-cost thermo-optic variable wave plate based on waveguides patterned on di-ureasil hybrids.

An integrated variable wave plate device based on a thermo-optic (TO) effect was fabricated by patterning a waveguide channel through direct UV laser writing on the surface of sol-gel derived organic-inorganic hybrid (di-ureasil) films. The di-ureasil layer is stable up to 250 °C and has a high TO coefficient calculated as -(4.9 ± 0.5) × 10(-4) °C(-1) at 1550 nm. The waveguide temperature was tuned, inducing optical phase retardation between the transverse electric and transverse magnetic modes, resulting in a controllable wave plate. A maximum phase retardation of 77 ° was achieved for a waveguide induced temperature increase of 5 °C above room temperature, with a power consumption of 0.4 W. The thermal linear retardation coefficient was calculated to be 19 ± 1 °/ °C.

Reactive Transport in Fractured Permeable Porous Media

AbstractThe transport of reactive solutes can be influenced by transport-related and sorption-related nonequilibrium processes. The reactive contaminant transport model for fracture and the multiprocess nonequilibrium (MPNE) model for porous formation is considered. Two coupled transport equations, one for the porous formation and the other for the fracture, were solved numerically using a hybrid finite-volume method. The numerical model employs a globally second-order accurate explicit finite-volume method for the advective transport and a finite-difference method for the dispersive transport and coupled reaction terms. An attempt is made to investigate the effects of various MPNE model parameters on the concentration profile in the fracture. It was found that the higher values of mass transfer coefficient, sorption coefficient, matrix diffusion coefficient, fracture retardation coefficient, and matrix porosity in the advective and nonadvective regions of the porous matrix leads to a decrease in the solu...

Bartlett-Lewis of rectangular pulse modified model: estimate of parameters for simulation of precipitation in sub-hourly duration

The Bartlett-Lewis Rectangular Pulse Modified (BLPRM) model simulates the precipitous slide in the hourly and sub-hourly and has six parameters for each of the twelve months of the year. This study aimed to evaluate the behavior of precipitation series in the duration of 15 min, obtained by simulation using the model BLPRM in situations: (a) where the parameters are estimated from a combination of statistics, creating five different sets; (b) suitability of the model to generate rain. To adjust the parameters were used rain gauge records of Pelotas/RS/Brazil, which statistics were estimated - mean, variance, covariance, autocorrelation coefficient of lag 1, the proportion of dry days in the period considered. The results showed that the parameters related to the time of onset of precipitation (λ) and intensities (μx) were the most stable and the most unstable were ν parameter, related to rain duration. The BLPRM model adequately represented the mean, variance, and proportion of the dry period of the series of precipitation lasting 15 min and, the time dependence of the heights of rain, represented autocorrelation coefficient of the first retardation was statistically less simulated series suitability for the duration of 15 min.

Removal of Cadmium(II) from Aqueous Solutions by Calcium Alginate Beads

Sorption of Cd(II) ions from dilute aqueous solutions by alginate beads has been studied. The measurements were run at 25°C at a fixed pH of 5.0. Equilibrium sorption isotherms have been determined over a wide cadmium concentration range of 0.3-3 mmol/dm3. The Langmuir equation has been found to adequately describe experimental results, and the equilibrium constants depended on the alginate content in the beads. The values of the maximum sorption capacity of Cd(II) ions have been found to decrease with increasing alginate content in the beads. Effective diffusivity (De) of the cadmium compounds was also calculated in the beads. The study was carried out using two methods: a shrinking core model (SCM) method and a newly developed method named conductometric. The conductometric method turned out to be a simple and effective one for calculation of effective diffusivity of Cd(II) in alginate sorbents. The De values obtained by the two methods depended on the alginate content in the beads. However, the SCM method, in contrast to the conductometric one, gave the De values increasing with increasing alginate level in the beads and higher than the molecular diffusivity of Cd(II), this being inconsistent with the mechanism of diffusion in porous carriers. For this reason, the conductometric method can be considered as one giving more reliable results than the SCM method. Moreover, the retardation coefficients of the diffusion in the alginate beads were calculated. Enhanced content of the biopolymer in the beads caused retardation of Cd(II) diffusion in the beads owing to decreasing of calculated retardation coefficients with increasing alginate contents in the beads.

Transport parameters of I− and IO3 − determined in crushed granitic rock columns and groundwater system under dynamic flow conditions

Transport of two principal inorganic iodine anions separately in two crushed crystalline granitic rocks, gabbro and tonalite, have been investigated. The rocks were crushed and sieved, and finally a fraction between 0.25 and 0.80 mm was filled in 5 cm3 PET columns (medical syringes) of 5.40 cm length and 1.24 cm in inner diameter. NaI and NaIO3 were dissolved in synthetic groundwater (SGW) in a concentration as low as 10−4 mol/dm3. The SGW was pumped into the columns at a seepage velocity of 0.031 ± 0.001 cm/min using a multi-head peristaltic pump. Iodine concentration in the outflow SGW from the columns was determined by UV–Vis spectrophotometry at 510 nm absorption maximum in CHCl3 using redox reactions. By the use of a dependence of concentration on the number of pore volumes from the outflow and the linear isotherm model, based on erfc-function, breakthrough curves were constructed and the principal transport parameters were calculated. The values of sorption and desorption retardation coefficients of about 1 for both iodide and iodate have been obtained, which show evidence of practically non-sorption behavior of these chemical forms of iodine in the tested granitic rocks. The values of hydrodynamic dispersion coefficients and corresponding Peclet numbers were about 0.0077 ± 0.0006 and 21.6 ± 1.8 cm2/min, respectively, for both anions and rocks under given conditions.

Analytic solution of biparameter axial dispersion model

A linear axial dispersion model involving two parameters, Peclet number (Pe) and retardation coefficient (Rd) has been presented. Model equations have been solved analytically, using Laplace transform. Solution has been obtained in terms of complementary error function. Two limiting cases of perfect mixing and perfect displacement have also been discussed. Verification of model is carried out by using the experimental data of a washing cell.

Influence of cellulose ether on hydration and carbonation kinetics of mortars

The hydration process of Portland cement and retarding effect of cellulose ether (CE) on hydration and carbonation were studied. The degree of CE-substitution is a major parameter which plays an important role in terms of retardation of both hydration and carbonation. For the hydration process, this CE-effect was highlighted through the results of an experimental campaign based on thermogravimetric analysis (TGA) performed on mortar samples conserved in an ambient air in which the atmospheric CO2 was absorbed by whitewash solution. This type of conservation is chosen in order to make precise the measurement of dehydration rate by TGA tests. While for the carbonation mechanism, the CE-effect was identified by the measurement of carbonation depth with phenolphthalein spraying.This paper aims to determinate a coefficient of retardation of hydration according to the CE-rate used in the manufacturing of mortars. This coefficient may be taken into account in the calculation of the reaction rate of anhydrous constituents of cement in order to determine a precise hydration degree of mortars. Consequently, this delay in cement hydration delays the carbonation processes because of the lack of hydrates to react with CO2.

Simulation and prediction of ion transport in the reclamation of sodic soils with gypsum based on the support vector machine.

The effect of gypsum on the physical and chemical characteristics of sodic soils is nonlinear and controlled by multiple factors. The support vector machine (SVM) is able to solve practical problems such as small samples, nonlinearity, high dimensions, and local minima points. This paper reports the use of the SVM regression method to predict changes in the chemical properties of sodic soils under different gypsum application rates in a soil column experiment and to evaluate the effect of gypsum reclamation on sodic soils. The research results show that (1) the SVM soil solute transport model using the Matlab toolbox represents the change in Ca2+ and Na+ in the soil solution and leachate well, with a high prediction accuracy. (2) Using the SVM model to predict the spatial and temporal variations in the soil solute content is feasible and does not require a specific mathematical model. The SVM model can take full advantage of the distribution characteristics of the training sample. (3) The workload of the soil solute transport prediction model based on the SVM is greatly reduced by not having to determine the hydrodynamic dispersion coefficient and retardation coefficient, and the model is thus highly practical.

Thin-layer chromatography in the investigation of polystyrene macromolecule interaction with nanoporous silica

The behavior of polystyrene macromolecules in nanopores of silica (silica gel, silochrome, MPS porous glass) is studied by a method of thin-layer chromatography. Tetrahydrofuran (THF) and a mixture of benzene with cyclohexane are used as solvents in this work. The relative coefficient of retardation (capacity coefficient) k′ and the distribution coefficient of polystyrene macromolecules between two phases K p are calculated from R f values. THF elution is characterized by a negative adsorption of polystyrenes because of preferential adsorption of solvent molecules and different availability of sorbent pore volume for macromolecular coils of polystyrenes. The calculated values R f > 1, k′ < 0, and K p < 1 reflect the mode of negative sieve chromatography and formation of monolayer of THF molecules adsorbed on the sorbent surface. The ratios between the retardation parameters in thin-layer and column chromatography are considered. The influence of the sorbent pore sizes and polystyrene molecular weights on the parameters of thin-layer chromatography is discussed.

Interaction of 3H+ (as HTO) and 36Cl- (as Na36Cl) with crushed granite and corresponding fracture infill material investigated in column experiments.

The transport of 3H+ (as HTO) and 36Cl− (as Na36Cl) was investigated in the dynamic system, i.e., in the columns filled with crushed pure granite and fracture infill of various grain sizes. The aim of column experiments was to determine important transport parameter, such as the retardation, respectively distribution coefficients, Peclet numbers and hydrodynamic dispersion coefficients. Furthermore, the research was focused to quantification of the effect of grain size on migration of studied radionuclides. The experimental breakthrough curves were fitted by a model based on the erfc-function, assuming a linear reversible equilibrium sorption/desorption isotherm, and the above mentioned transport parameters were determined. The results showed that influence of grain size on sorption of 3H+ and 36Cl− was negligible. Retardation and distribution coefficients of both tracers converged to one and zero, respectively, in case of all fractions of crushed granite and infill material. Generally, the presumed ion exclusion of 36Cl in anionic form was proved under given conditions, only very weak one seems to exist in a case of infill material. In principal, both radionuclides behaved as non-sorbing, conservative tracers. On the other hand, the influence of grain size on Peclet numbers value and on dispersion coefficient was observed for both crystalline materials, namely in agreement with theoretical suppositions that the values of Peclet numbers decrease with increasing grain size and values of dispersion coefficient increase.

Experimental investigation of solute transport in stratified porous media

In this study, an attempt is made to investigate the behaviour of solute transport through stratified porous media using laboratory experiments. A physical model is constructed to represent stratified porous media consisting of an advective region sandwiched between two non-advective regions. Pulse of tracer was injected at the inlet of the sand layer situated in between the clay matrix of the experimental model, and samples of tracer were collected at the other end of the model. An implicit finite-difference numerical technique is used to solve advective dispersive transport equations, including equilibrium sorption and first-order degradation constant for reactive transport through stratified porous media. A numerical model is used to simulate the breakthrough curves of experimental data of chloride and fluoride. It is seen that the peak of breakthrough curves is higher for the non-reactive solute compared to that of the reactive solute. The observed breakthrough curves were also found to be skewed in shape for solutes in stratified porous media. The numerical model was also found to be more sensitive to the value of transverse diffusion during simulation of experimental breakthrough curves. Finally, the values of effective diffusion coefficient and retardation coefficient are estimated by simulation of experimental breakthrough curves.

Failure Probability Evaluation of a Near-Surface Radioactive Waste Repository Due to Water Infiltration

This paper aims to determine, for the period of institutional control (300 yr), the probability of occurrence of the net release scenario of radioactive waste from a near-surface repository. The radioactive waste focused on in this work is that of low and medium activity generated by a pressurized water reactor plant. The repository is divided into eight modules, each of which consists of six barriers (top cover, upper layer, packages, base, walls, and geosphere). The repository is a system where the modules work in series and the module barriers work in active parallel. The module failure probability for radioactive elements is obtained from a Markov model because of shared loads assumed for the different barriers. Lack of field failure data led to the necessity of performing sensitivity analyses to assess the failure rate impact on module and barrier failure probabilities. Module failure probabilities have been found to be lower for those radioactive elements with higher retardation coefficients. The geosphere mean time to failure is the most important parameter for calculating module failure probabilities for each radioactive element. The repository module has presented higher failure probabilities for iodine, technetium, and strontium. For iodine, the estimated probability is 16% for 300 yr and 96% for 1000 yr. The basis for performance evaluation of the deposition system is the understanding of its gradual evolution. There are many uncertainty sources in this modeling, and efforts in this direction are strongly recommended.

Use of raw or incubated organic wastes as amendments in reducing pesticide leaching through soil columns

Soil amendment with organic wastes is becoming a widespread management practice since it can effectively solve the problems of uncontrolled waste accumulation and improve soil quality. However, when simultaneously applied with pesticides, organic wastes can significantly modify the environmental behaviour of these compounds. This study evaluated the effect of sewage sludges (SS), grape marc (GM) and spent mushroom substrates (SMS) on the leaching of linuron, diazinon and myclobutanil in packed columns of a sandy soil with low organic matter (OM) content (<1%). Soil plus amendments had been incubated for one month (1m) or 12months (12m). Data from the experimental breakthrough curves (BTCs) were fitted to the one-dimensional transport model CXTFIT 2.1. All three amendments reduced leaching of linuron and myclobutanil relative to unamended soil. SMS was the most effective in reducing leaching of these two compounds independent of whether soil was incubated for 1m or 12m. Soil amendments increased retardation coefficients (Rexp) by factors of 3 to 5 for linuron, 2 to 4 for diazinon and 3 to 5 for myclobutanil relative to unamended soil. Leaching of diazinon was relatively little affected by soil amendment compared to the other two compounds and both SS and SMS amendment with 1m incubation resulted in enhanced leaching of diazinon. The leaching data for linuron and myclobutanil were well described by CXTFIT (mean square error, MSE<4.9·10−7 and MSE<7.0·10−7, respectively) whereas those of diazinon were less well fitted (MSE<2.1·10−6). The BTCs for pesticides were similar in soils incubated for one month or one year, indicating that the effect of amendment on leaching persists over relatively long periods of time.

Competitive adsorption and transport of phthalate esters in the clay layer of JiangHan plain, China

This study aimed to investigate the adsorption behavior of phthalate esters (PAEs) in the clay layer of JiangHan Plain, China, so as to make better understanding about the source and control of PAEs in groundwater. Adsorption kinetics, isotherms, and miscible displacement experiments were conducted, and different models were used to simulate the experiment data. Results showed that the adsorption kinetics followed pseudo-second-order model. The kinetic parameters showed quantitative relationships with straight and branched chain carbon numbers of PAEs. These relationships were simulated and carefully discussed. The adsorption isotherms followed linear model better. And partition coefficient (Kd) increased with the carbon chain length of PAEs. Miscible displacement experiments showed that DEHP could not flow out of the column in 100d. HYDRUS-1D and two-site sorption model (linear, first order nonequilibrium adsorption) were used for the simulation of the breakthrough and transport curves of DMP, DEP, DBP, and DiBP. Results showed that the dispersion coefficients (D) and partition coefficient (Kd′) increased with the carbon chain length. About 10% DBP and DiBP and 1% DMP and DEP were absorbed on the type-1 sites. DMP and DEP were much easier to transfer into the type-2 sites than DBP and DiBP. DBP and DiBP might aggregate in micro-pores of the sorbent. Retardation coefficient and Damkohler number were also calculated and discussed. It was proved that clay layer is an important retarder for PAEs downward transport. However, it can be passed through if the time is sufficient.

Effect of grain size on the sorption and desorption of SeO4 2− and SeO3 2− in columns of crushed granite and fracture infill from granitic water under dynamic conditions

The sorption of 2 × 10−5 mol/dm3 Na2SeO4 and Na2SeO3 dissolved in synthetic granitic water (SGW) were investigated in columns of crushed granite and fracture infill (clay minerals) of various grain sizes. Desorption was studied using pure SGW. The goal of study was the quantification of the effect of grain size on the retardation and distribution coefficients of SeO42− and SeO32−, as well as on the other transport parameters (Peclet number and hydrodynamic dispersion coefficient). A model based on the erfc-function, assuming a non-linear reversible equilibrium sorption/desorption isotherm, was used for evaluation of sorption/desorption and transport parameters. The determination of selenium was performed using an ICP-MS technique. The experimental breakthrough curves were fitted using non-linear regression procedure, in the course of which the parameters mentioned were sought. Summing up, no sorption was recorded in the case of SeO42− under these conditions. The values of retardation coefficients were practically one for all studied grain sizes. On the other hand, significant sorption was found for SeO32−: depending on the grain size, the retardation coefficients varied between 1.6–8.7 in pure granite and 1.8–37.2 in infill materials. These values correspond to distribution coefficients of 0.2–2.5 and 0.2–12.7 cm3/g, respectively. The both parameters have similar values in a case of desorption which reflects the reversible character of sorption process. It was found that retardation and distribution coefficients and sorption capacity for SeO32− also increase with decreasing grain size.

Effect of grain size on the 85Sr2+ sorption and desorption in columns of crushed granite and infill materials from granitic water under dynamic conditions

The sorption of 85Sr2+ in the form of 10−6 M Sr(NO3)2 in synthetic granitic water (SGW), and its desorption using the same radiotracer-free solution, were investigated under dynamic conditions in columns loaded with crushed granitic materials. The goal of study was to evaluate the influence of grain size on the retardation (R) and distribution (Kd) coefficients of the soluble 85Sr2+, as well as on the other transport parameters type of Peclet number (Pe) and hydrodynamic dispersion coefficient (Dd). Pure granitic sample and granitic fissure infill samples were used, crushed and sieved into 4 different grain size from 0.063 to1.25 mm were used. In order to determine migration parameters, the model based on erfc-function was used, assuming reversible equilibrium linear or non-linear (Freundlich) sorption/desorption isotherms. By means of both model approaches, the experimental breakthrough curves were fitted using non-linear regression procedure according to Newton–Raphson method. The obtained results also validated the applicability of the linear equilibrium isotherms of the 85Sr2+ sorption/desorption in the studied systems. It was found that in the case of linear isotherm approach, both retardation and distribution coefficients increased with decreasing grain size. Moreover, their values for fracture infill samples are higher than comparing to granite. Depending on the grain size, the retardation coefficient R varied between 11 and 25 for pure granite and 33–58 between for fissure infill material. These values correspond to distribution coefficients Kd of 2–7 and 9–24 cm3/g, respectively. Consequently, the sorption capacity of crushed rocks also increases with decreasing grain size and are about 2.5-times higher for fracture infill than in pure granite. The values of Dd increase with increasing grain size. Due to inverse proportion, values of Pe number are decreasing.

Fate and transport of ethanol-blended dissolved BTEX hydrocarbons: a quantitative tracing study of a sand tank experiment

To estimate the behavior of ethanol-blended dissolved BTEX hydrocarbons in groundwater, a quantitative tracing study instead of qualitative analysis was carried out by using a large sand tank, into which 2-L solution including bromide, ethanol and dissolved BTEX was injected under a controlled hydraulic condition. Mean residence time (MRT), pore volume swept by solute (Vp), retardation coefficient (R) and biodegradation rate constant (k) of injected solutes were estimated. Compared with bromide that was used as a conservative tracer, ethanol and BTEX had shorter MRT and smaller Vp with the sequence of EtOH T > E > m/p-X > o-X > B was just opposite to the sequences of MRT and Vp. The relationship among above sequences implies that MRT and Vp can be used as indicators to assess in situ biodegradability of a solute. Biodegradation of a reactive solute can make its MRT shortened and Vp shrunk. In addition, the sorption of ethanol could be neglected (R = 1.0), whereas BTEX compounds were adsorbed (R = 1.04–1.15). It should be noted that biodegradation of a solute can affect the estimation of its retardation coefficient. To our knowledge, this paper provides an available route to quantitatively estimate biodegradability of a solute in groundwater.

Sorption of 125I−, 137Cs+, 85Sr2+ and 152,154Eu3+ during their transport in undisturbed vertical and horizontal soil cores under dynamic flow conditions

Transport and sorption of 125I−, 137Cs+, 85Sr2+ and 152,154Eu3+ in undisturbed soil cores have been studied under dynamic conditions. Radionuclides were dissolved in synthetic groundwater (SGW) of 0.015 mol/dm3 ionic strength, pH 8.4 and redox potential Eh = 145 mV. The soil samples were taken vertically and horizontally from the river bed at 5–100 cm depths, about 120 m southward of the Dukovany Low and Medium Level Radioactive Waste Repository. The respective water-soluble carriers in the 10−6 mol/dm3 concentration were added into the SGW prior to the experiments. The soil cores of 9 cm height and 3.8 cm in diameter were placed into columns made of 150 cm3 PE injection syringes of suitable dimensions. The SGW was introduced into columns from the Mariotte’s bottle through a glass manifolds to supply the soil columns by gravity flow at a constant flow-rate about 1.2 cm3/h. Into the water stream, radioactive nuclides were added individually in a form of a short pulse in 0.1 cm3 of demineralized water. In the case of 125I− transport, retardation and hydrodynamic dispersion coefficients were determined, using an integral form of a simple advection-dispersion equation. For each radionuclides, sorption and desorption data have been obtained, evaluated and the results were compared mutually. Residual distributions of the sorbed cationic radionuclides along the soil columns were also presented.

Erratum to: Effect of grain size on the sorption and desorption of 137Cs in crushed granite columns and groundwater system under dynamic conditions

In this work, the sorption of 137Cs+ dissolved as 137CsNO3 in the solution of 10−6 M CsNO3 in SWG, and its desorption by solution mentioned, were investigated under dynamic conditions in columns with crushed granitic materials of various grain sizes, namely, of pure granite and, of corresponding filling materials. It aims at the quantification of the influence of grain size on the retardation and distribution coefficients of 137Cs, as well as on the other transport parameters (Peclet numbers and dispersion coefficients). For their determination, model based on erfc-function was used, assuming reversible equilibrium linear or non-linear sorption/desorption isotherms. By means of both model approaches, the experimental BTC S were fitted using non-linear regression procedure, in the course of which the parameters mentioned were sought. The obtained results also validated the applicability of the linear equilibrium isotherms of the 137Cs+ sorption/desorption in the studied transport processes and systems. Depending on the grain size, the retardation coefficients were between 40–93 in pure granite and 140–200 in filling materials. These values correspond to distribution coefficients of 11–34 cm3/g and 40–69 cm3/g, respectively. It was found that both retardation and distribution coefficients increase with decreasing grain size.