Nonlinear Sorption Research Articles

Facilitating Effects of Metal Cations on Phenanthrene Sorption in Soils

Effects of metal cations (Na+, Ca2+, and Al3+) on phenanthrene sorption were investigated using two soils with contrasting organic carbon (OC) contents. The presence of the polyvalent cations (i.e., Ca2+ or Al3+) at a concentration of 0.01 mol/L significantly increased the capacity and nonlinearity of phenanthrene sorption to soils compared with the monovalent Na+. The effects were governed by the content of soil OC. Rubbery OC (i.e., soft, amorphous OC including dissolved organic carbon (DOC)) tended to become condensed on soil surfaces as evidenced by a decrease in the signals of the 1H NMR spectra of DOC and an increase in the glass transition temperature (Tg) of the soils when the polyvalent cations were present. Increasing Ca2+ concentration led initially to an effect similar to that of the polyvalent cations in the low cation concentration range, and the effect was gradually attenuated as Ca2+ concentration further increased. These findings lead us to propose that the modifications in the physical configuration and chemical characteristics of OC resulting from the presence of metal cations account for the increase in the capacity and nonlinearity of phenanthrene sorption to the soils. This study points to an important role of metal cations in the sorption and fate of phenanthrene in the soil environment.

Composition and dissolution kinetics of garnierite from the Loma de Hierro Ni-laterite deposit, Venezuela

The composition of a garnierite sample (Mg–Ni silicate) from the Loma de Hierro Ni-laterite deposit (Venezuela) has been determined by means of X-ray diffractometry (XRD), high-resolution transmission electron microscopy (HR-TEM) and electron microprobe (EM) analyses. This garnierite was collected from a vein in the parent rock of the laterite (serpentinized peridotite). XRD showed peaks at 7 Å and 10 Å, characteristic of the structures of serpentine and talc, respectively. HR-TEM revealed different areas characterized by either a 7 Å or 10 Å spacing. EM showed a homogeneous sample composition, with a (Mg + Ni)/Si ratio equal to 0.92. The stoichiometric formula for this garnierite is given by Mg 2.91Ni 0.09Si 3.27O 8.17(OH) 2.74, which corresponds to a mixture of Ni-containing serpentine (37 mol%) and talc (63 mol%). EM analyses were also performed on six additional samples from the main Ni enrichment zone of the laterite. The results show a clear correlation between Ni content and mole fraction of talc, indicating the affinity of Ni for the talc phase in the garnierite. Quantitative XRD fitting of one of these additional samples indicated that the talc belongs to the variety known as kerolite. Flow-through experiments were performed to measure far-from-equilibrium dissolution rates. At steady state, dissolution of garnierite was stoichiometric at pH greater than about 5 and non-stoichiometric at more acidic conditions. Since these solutions were undersaturated with respect to possible secondary precipitates, the results seem to indicate different contributions of Ni-containing serpentine and talc to the total rate. For pH below 5, the contribution from serpentine to the total rate increases with decreasing pH. The overall dissolution rate is proportional to a H+ 0.28, although pH dependence could also be described with a model based on non-linear sorption of H + on garnierite.

COMPETITIVE SORPTION-DESORPTION KINETICS OF ARSENATE AND PHOSPHATE IN SOILS

The competition between arsenate (AsO4-3) and phosphate (PO4-3) on mineral surfaces has the potential of increasing arsenic mobility and bioavailability in the soil and water environment. In this study, kinetics of competitive sorption of AsO4-3 and PO4-3 in three soils was investigated in batch systems by simultaneously introducing the ligands at different molar ratios. Adsorption was carried out at different retention times, and release was investigated using successive dilutions after adsorption. Nonlinear sorption isotherms of AsO4-3 and PO4-3 were observed for all soils. Rates and amounts of AsO4-3 adsorption were significantly reduced when PO4-3 concentrations in the soil solution increased. In addition, the relative sorption preference of AsO4-3 and PO4-3 did not exhibit changes with reaction time. Desorption and sequential extractions results indicated that a significant amount of AsO4-3 was irreversibly retained by all soils. Kinetic retention data of AsO4-3 and PO4-3 were successfully described using a mechanistic multireaction model that accounted for competitive retention. This study indicates that competition of AsO4-3 and PO4-3 for adsorption sites should be considered in models predicting arsenic release from soils receiving high phosphorus inputs.

THE INITIAL STATES OF WATER VAPOR ADSORPTION IN PILES OF GRANULES: A NEW APPROACH

In this work the wall effect during the initial states of water vapor adsorption was studied for different piles of granules held in a cylindrical container. A new diffusion model was developed for the description of the physical phenomenon whereby water vapor penetrates along the piles of cylindrical pores. The isotherm sorption equation was incorporated as a wall boundary condition of the cylindrical pore. Finally, the differential mass balance equation was solved numerically using a finite-difference method. A second-order central differencing scheme (CDS), in a general nonuniform grid, was adopted. A mathematical expression is proposed for linear sorption isotherm (given as Equation (28) here), and a numerical procedure is presented for the case of nonlinear moisture sorption isotherm. The numerical solutions were tested through the measurement of water vapor mass uptake for different piles of silica gel and breakfast cereals, and the experimental values obtained were in good agreement.

Distribution and partition of polycyclic aromatic hydrocarbon in surface water of the Pearl River Estuary, South China

Water samples were collected in the Pearl River Estuary in July 2002 and April 2003. The particulate and dissolved phase polycyclic aromatic hydrocarbons (PAHs) were determined. Total PAH concentrations in water samples were higher in April of 2003 (C (p): 4.0-39.1 ng/L or 445.1-1,089.9 ng/g; C (w): 15.9-184.2 ng/L) than in July of 2002 (C (p): 2.6-26.6 ng/L or 297.7-1,336.6 ng/g; C (w): 12.9-28.3 ng/L). It was found that 5, 6-ring PAHs enrich in the inner estuary samples and so did 3-ring PAHs in the July samples. Compositional differences in the suspended particulate matter (SPM) might be responsible for this observation. The partition coefficient (K (p)) increased with the increasing of the particular organic carbon content of suspended particles as well as the salinity of water, decreased with the increase of the total suspended particles content of samples. A linear correlation between logK (OC) and logK (OW) was found in two sampling periods. The observed values of logK (OC) exceed their predicted values derived form linear free energy relationship between logK (oc) and logK (ow), which could be attributed to the nonlinear sorption of soot-like carbons in suspended particles.

On the Use of Linearized Langmuir Equations

One of the most commonly used models for describing solute sorption to soils is the Langmuir model. Because the Langmuir model is nonlinear, fitting the model to sorption data requires that the model be solved iteratively using an optimization program. To avoid the use of optimization programs, a linearized version of the Langmuir model is often used so that model parameters can be obtained by linear regression. Although the linear and nonlinear Langmuir equations are mathematically equivalent, there are several limitations to using linearized Langmuir equations. We examined the limitations of using linearized Langmuir equations by fitting P sorption data collected on eight different soils with four linearized versions of the Langmuir equation and comparing goodness‐of‐fit measures and fitted parameter values with those obtained with the nonlinear Langmuir equation. We then fit the sorption data with two modified versions of the Langmuir model and assessed whether the fits were statistically superior to the original Langmuir equation. Our results demonstrate that the use of linearized Langmuir equations needlessly limits the ability to model sorption data with good accuracy. To encourage the testing of additional nonlinear sorption models, we have made available an easily used Microsoft Excel spreadsheet (ars.usda.gov/msa/awmru/bolster/Sorption_spreadsheets) capable of generating best‐fit parameters and their standard errors and confidence intervals, correlations between fitted parameters, and goodness‐of‐fit measures. The results of our study should promote more critical evaluation of model fits to sorption data and encourage the testing of more sophisticated sorption models.

Effect of sorption intensities on dispersivity and macro-dispersion coefficient in a single fracture with matrix diffusion

Matrix diffusion and sorption are among the key processes impacting the efficiency of natural attenuation in the subsurface. While these processes have been studied extensively in fractured media, limited information exists on the sorption nonlinearity. To address this shortfall, a numerical model has been developed that couples matrix diffusion and nonlinear sorption at the scale of a single fracture using the dual-porosity concept. The study is limited to a constant continuous-solute-source boundary condition. The influence of sorption intensities on dispersivity and macro-dispersion coefficient is investigated using a method of spatial moments. Results suggest that mixing of solutes is significantly lowered by nonlinear sorptive behavior, with respect to the mixing caused by matrix diffusion for linearly sorbing solutes. Also, the magnitude of time dependent dispersivity during the pre-asymptotic regime is lower for nonlinearly sorbing solutes with respect to the linearly sorbing solutes. Reduced mixing is also observed for nonlinearly sorbing solutes under combined mechanisms of matrix diffusion and decay.

Influences of preparative methods of humic acids on the sorption of 2,4,6-trichlorophenol

Humic acids (HAs) are a major component of soil organic matter which strongly affects the sorption behavior of organic contaminants in soils. To assess the sorption–desorption characteristics of organic compounds on HAs, the organic adsorbent is usually isolated using an acid-base extraction method followed by air-drying or freeze-drying. In this study, a peat soil from the Yangming mountain area of Taiwan was sampled and repeatedly extracted followed by either air-drying or a non-drying treatment (denoted DHAs and NDHAs, respectively). The sorption of 2,4,6-TCP on HAs was evaluated using the batch method. Kinetic sorption results indicated that DHAs exhibited a two-step first-order sorption behavior, involving a rapid sorption followed by a slow sorption. The slow sorption may be attributed to the diffusion of 2,4,6-TCP through the condensed aromatic domains of HAs. On the contrary, the sorption of 2,4,6-TCP on NDHAs was extremely rapid, and the sorption data did not fit existing kinetic models. Each HA sample exhibited a nonlinear sorption isotherm. Sorption nonlinearity (represented by Freundlich N values) and K oc had a positive relationship with aliphaticity for DHAs; however, nonlinearity and K oc correlated positively with aromaticity when NDHAs adsorbents were used. We conclude that the air-drying technique may artificially create a more condensed area, which strongly affects the sorption characteristics of HAs. Thus, an incorrect evaluation of the sorption capacity and its relationship with the chemical composition of HAs would arise following use of the air-drying method.

Clarification of nonlinear retardation factors for colloid-enhanced transport in porous media

There have been a couple of contaminant retardation factors reported for the three-phase (aqueous, solid, and colloid) groundwater system. However, the retardation factor has often been presented by itself and not incorporated into the relevant transport equation, particularly when derived from the mass fraction approach. This may cause a misunderstanding of the retardation factor especially for the systems where multi-phases exist due to the presence of colloids and/or nonlinear sorption processes are involved. It is, therefore, necessary to clarify the form of the nonlinear retardation factor along with the relevant transport equation in the multi-phase system. Alternative forms of the retardation factor and relevant transport equation for specific conditions are presented in various combinations of the nonlinearity of involved sorption mechanisms. The retardation factors for specific conditions are compared with the ones available in the literature. The results indicate that more caution should be given in applying the retardation factor in order to explore contaminant transport in the multi-phase system where any nonlinear sorption is involved. Finally, presentation of the retardation factor along with the relevant transport equation in this study would help prevent possible misuse of the retardation factor in investigating contaminant transport in the multi-phase system.

Subsurface contaminant transport in the presence of colloids: Effect of nonlinear and nonequilibrium interactions

The effect of kinetic nonlinear sorption of contaminants in the presence of colloids is the focus of this study. Different sorption isotherms are considered where contaminant sorption and colloid deposition are assumed to be linear or nonlinear (Freundlich), and contaminant attachment to mobile and immobile colloids is assumed to follow either linear or Langmuir isotherms. Varying combinations accounting for different possibilities are used to investigate effects of different isotherms on contaminant transport. Two‐dimensional numerical simulations in homogenous media show that the effect of colloids on nonlinearly sorbing contaminant is altered from facilitation to retardation depending on the Freundlich exponent and concentration value. One finding from the study indicates that incorporating the colloid effect on contaminant transport does not necessarily represent a conservative assumption. The study shows that ignoring the fact that colloids have limited sites and describing contaminant attachment to colloids by linear isotherms may lead to inaccurate results. In addition, it is found that assuming colloids are linearly deposited on the solid matrix is a conservative assumption in the applications that focus on peak concentration arrival. However, when small contaminant concentrations are of concern (i.e., early arrival is the quantity of interest), assuming nonlinear colloidal deposition becomes the critical scenario.

Physical origin for the nonlinear sorption of very hydrophobic organic chemicals in a membrane-like polymer film

Bioconcentration factor (BCF) is often assumed to be linearly associated with the octanol–water partition coefficient K ow for hydrophobic organic chemicals (HOCs). However, a large amount of data has suggested that the correlation between the log BCF and log K ow is curvilinear for HOCs. Similar curvilinear relationship has also been noticed for sorption of HOCs into poly(dimethyl)siloxane (PDMS), a polymer with cross-linked interior structures. So far no satisfactory explanation has been given to account for the deviation. In this study, we acquired additional experimental data to show that the curvilinear relationship between the log-based PDMS-coated fiber–water partition coefficient (log K f) and log K ow for polychlorinated biphenyls (PCBs) was indeed a reflection of the sorption process occurring in PDMS film other than experimental defects. The physical origin of the nonlinearity was pinpointed based on the theory of phase partitioning for HOCs. The linear relationship is observed if the solute molecule is considerably smaller than the size of a monomer unit of PDMS in that the Gibbs free energy required for cavity formation in PDMS is comparable to that in octanol. Higher free energy of cavity formation is needed to create sufficient free volume if the PCB molecular size is comparable to or larger than the monomer unit of PDMS. On the other hand, the free energy of cavity formation in octanol remains almost constant when this occurs, resulting in the observed curvilinear relationship. The proposed model adequately explains the observed data, as well as sheds lights into the physical origin of the steric interactions of large molecular size solute with the PDMS polymer network.

Direct and split operator approaches with ELLAM for reactive transport equations

AbstractNumerical models for solving reactive solute transport in groundwater are often based on standard Eulerian methods, such as finite elements (FE). In this work, we combine the moving mesh Eulerian Lagrangian Localized Adjoint Method (ELLAM) with the direct substitution approach (DSA) and the sequential non‐iterative approach (SNIA) to accurately solve advection dominated problems including chemical reactions. Performances of ELLAM are evaluated in comparing SNIA_ELLAM and DSA_ELLAM to SNIA_FE and DSA_FE for (1) kinetic reactions with first‐order decay, Monod biodegradation, and interphase mass transfer problems and (2) equilibrium reactions with linear and nonlinear sorption problems. DSA_ELLAM (respectively SNIA_ELLAM) is shown to be more efficient and accurate than DSA_FE (respectively SNIA_FE). For the test cases with kinetics, SNIA_ELLAM is highly accurate and efficient. However, for equilibrium reactions, it induces numerical diffusion and DSA_ELLAM reveals the more efficient and accurate method. © 2007 American Institute of Chemical Engineers AIChE J, 2007

Modeling reactive transport in heterogeneous saturated porous media. Effects of nonlinear sorption

Modeling reactive transport in heterogeneous saturated porous media. Effects of nonlinear sorption

Modeling Cadmium Transport in Soils Using Sequential Extraction, Batch, and Miscible Displacement Experiments

Asymmetric transport behavior of Cd in soils can result from sorption nonlinearity or rate-limited sorption, of which the relative significance is difficult to be discerned by transport modeling alone. Multiple approaches incorporating batch, sequential extraction, and miscible displacement experiments were therefore used in this study. Batch isotherm was used to indicate the range of Cd concentration where sorption became nonlinear. It is noteworthy that batch kinetics illustrated a shorter apparent equilibrium time of sorption at a higher Cd concentration, which presumably correlates with the significance of rate-limited sorption. In addition, sequential extraction results indicated that the relative contribution of rate-limited specific sorption to total sorption became negligible with increasing Cd concentration. Since the rate-limited specific sorption appears to be of low capacity, it is only important for sorption at low concentration. In miscible displacement experiments, Cd transport at 10 -5 M could only be simulated using a nonequilibrium model, whereas a nonlinear model was necessary for describing Cd transport at 10 -3 M. Therefore, this study demonstrated that transport behavior is predominantly influenced by rate-limited sorption at sufficiently low concentration, while by sorption nonlinearity at sufficiently high concentration. Additionally, sequential extraction can be a useful tool to illustrate the significance of rate-limited specific sorption and the corresponding chemical nonequilibrium transport behavior.

Nonlinear Sorption of Three Alcohol Ethoxylates to Marine Sediment: a Combined Langmuir and Linear Sorption Process?

Alcohol ethoxylates (AE) are nonionic surfactants mainly used in laundry cleaning products. The relation between particle bound and freely dissolved concentrations is an important entity in risk assessment. The mechanistic understanding of AE sorption is still poor, hampering extrapolations from laboratory studies to the field. We studied the sorption of three AE with 8 EO units but with increasing alkyl chains (C10, C12, and C14) to a marine sediment. Solid-phase microextraction, using polyacrylate as the extraction phase, was applied to measure freely dissolved concentrations in pore water. A model that combines a Langmuir and a linear sorption term fitted the nonlinear sorption data to sediment well. At low aqueous concentrations, adsorption dominates over absorption leading to higher distribution coefficients for AE at low field concentrations. This dual-mode model offers the possibility to extrapolate to other AE homologues and other marine sediments and also from high to low field concentrations.

Diffusion anomaly and blind pore character in carbon molecular sieve membrane

The structure of a carbon molecular sieve (CMS) membrane is characterized by the through pores and blind pores with non-linear sorption isotherms inside. Time-lag analysis was conducted for gas permeation in such a structure and mathematical formulations were derived for two cases. It is found that the pressure dependence of the time lag is dominated by the ratio of sorption affinities in the two types of pores. The experimental permeation data of pure component CO 2 and N 2 measured on a CMS membrane were used to validate the model. It is found that, for the adsorbing species ( CO 2 ) , the model is able to well describe the diffusion anomalies over a wide range of permeation pressure, while for the weakly adsorbing species ( N 2 ) , the model is inadequate to cope with the anomalies at the low end of permeation pressure.

Phenanthrene Sorption to Soil Humic Acid and Different Humin Fractions

This study was undertaken to provide an insight into the effect of heterogeneous soil organic matter (SOM) on the sorption of phenanthrene. Humic acid (HA) and humin were extracted from a peat soil. Humin was further fractionated into bound-humic acid (BHA), lipid, and insoluble residue (IR) fractions. Heterogeneous natures of these fractions were characterized by elemental analysis, ultraviolet-visible spectroscopy, Fourier transform infrared spectroscopy, and solid-state 13C NMR. Aliphaticity of the fractions followed the order lipid >BHA > HA > IR, while the polarity order was IR > BHA> HA > lipid. Sorption of phenanthrene on these fractions fitted the Freundlich equation, suggesting that phenanthrene sorption isotherms of lipid were almost linear (N = 0.993), while those of HA, BHA, and IR were nonlinear, with N values ranging from 0.723 to 0.910. The N values followed the order lipid > HA > BHA > IR and were significantly correlated inversely with their polarities (p < 0.05). Organic carbon-normalized sorption coefficients (K(FOC)) were independent of aliphatic or aromatic contents of the SOM fractions. The results suggested that SOM, especially for the humin fractions, was highly heterogeneous in terms of elemental composition, structure, and polarity. Such heterogeneity was considered to be responsible forthe nonlinear sorption of phenanthrene.

Effect of physical forms of soil organic matter on phenanthrene sorption

The sorption coefficient, K(OC), of phenanthrene (PHE) has been reported to vary with different types of organic matter, leading to uncertainties in predicting the environmental behavior of PHE. Among the studies that relate organic matter properties to their sorption characteristics, physical conformation of organic matter is often neglected. In this work, organic matter samples of different physical forms were examined for their sorption characteristics. Dissolved humic acids (DHA) showed significantly higher K(OC) than the corresponding solid humic acids (SHA) from which the DHAs were made. The K(OC) of DHAs was found to be related to polarity, whereas K(OC) of SHAs increased with aliphatic carbon content. Soil particles were treated with H(2)O(2) to remove organic matter, and humic acid was coated on H(2)O(2)-treated soil particles to make organo-mineral complexes at pH 4, 7 and 10. Although the nonlinear sorption was apparent for SHAs and H(2)O(2)-treated soil particles, the organo-mineral complexes formed using these two components at pH 4, 7 and 10 exhibited relatively linear sorption at organic carbon content, f(OC)>0.5%. These results indicate that organic matter of the same composition may have different sorption properties due to different physical forms (or conformations). Nonlinear sorption for the complexes formed at pH 4 with lower f(OC) (<0.5%) was also discussed.

Modeling Contaminant Transport in a Three-Phase Groundwater System with the Freundlich-Type Retardation Factor

Colloid-facilitated contaminant transport was simulated in this study for the three-phase groundwater system where one or more sorption processes can be described with nonlinear sorption isotherm (Freundlich isotherm). A concise form of contaminant transport equation was derived from the mass balance equation of the contaminant. The developed model was numerically solved by the finite difference method along with the Picard iteration. The simulation results were used to quantitatively analyze the previously reported column data showing nonlinear sorption behavior. The analysis led to the following observations: (i) increases of the distribution coefficient of contaminant between the aqueous and solid phases (Ks c) and the one between the dissolved natural organic matters and solid phase (Ks OM) generate less facilitation (i.e., late arrival of contaminant breakthrough curves (BTCs), and the distribution coefficient of contaminant between the aqueous and the solid phases (KOM c) gives the opposite result; (ii) the increase of the Freundlich constant for the sorption isotherm between the aqueous and the solid phases (Ns c) yields the late arrival of BTC, and the other two Freundlich constants produce the opposite results; (iii) the Freundlich constants generally yield a sharper front as the BTC arrives at later pore volumes, while the distribution coefficients generally yield a more spread of the BTC as it arrives at later volumes. This modeling study shows that transport modeling provides a more efficient analyzing tool than the retardation factor alone concerning the colloid-facilitated contaminant transport with nonlinear sorption processes.

Sorption of male hormones by soils and sediments

This paper reports the sorption of two male hormones, testosterone and androstenedione, by four soil and sediment samples at both equilibrium and rate-limiting conditions. Unlike prior studies, androstenedione was studied independently of testosterone. Apparent sorption equilibrium is achieved in one to two weeks when the initial aqueous hormone concentrations (C0) at 10,000 microg/L (approximately 30% of their solubility limits [S(w)]) and two to three weeks when the C(0) is 300 microg/L (less than 1% of S(w)). The Freundlich model parameter n ranged from 0.698 to 0.899 for all soil-solute systems indicating nonlinear sorption isotherms. Isotherm nonlinearity leads to an inverse correlation between single-point organic carbon-normalized sorption distribution coefficients (K(oc)) and equilibrium androgen concentration (C(e)). When C(e)S(w) = 0.012, the log K(oc) values for testosterone and androstenedione on the various sorbents ranged from 6.18 to 6.75 and 6.83 to 6.04, respectively, compared to 6.30 to 6.80 and 6.16 to 6.92 when C(e)/S(w) = 0.004. This study suggests that male hormones may exhibit slow rates of sorption over 14 d or longer and that soils and sediments may have greater sorption distribution coefficients when concentrations fall into the ng/L range.