Approximation of a radial diffusion model with a multiple-rate model for hetero-disperse particle mixtures.

An innovative method is proposed for approximation of the set of radial diffusion equations governing mass exchange between aqueous bulk phase and intra-particle phase for a hetero-disperse mixture of particles such as those occurring in suspension in surface water, in riverine/estuarine sediment beds, in soils and in aquifer materials. For this purpose the temporal variation of concentration at several uniformly distributed points within a normalized representative particle with spherical, cylindrical or planar shape is fitted with a 2-domain linear reversible mass exchange model. The approximation method is then superposed in order to generalize the model to a hetero-disperse mixture of particles. The method can reduce the computational effort needed in solving the intra-particle mass exchange of a hetero-disperse mixture of particles significantly and also the error due to the approximation is shown to be relatively small. The method is applied to describe desorption batch experiment of 1,2-dichlorobenzene from four different soils with known particle size distributions and it could produce good agreement with experimental data.

The influence of the rigidity of geosorbent organic matter on non-ideal sorption behaviors of chlorinated benzenes.

This study focused on evaluating the influence of the rigidity of natural organic matter (NOM) associated with four natural geosorbents in controlling the non-ideal sorption behaviors of five chlorinated benzenes. Single solute sorption isotherms for each sorbate/sorbent combination were modeled and interpreted by the Freundlich sorption isotherm and the adsorption-partitioning model based on Polanyi-Manes theory (PM model). "Rigid" organic matter was operationally quantified as the fraction of carbon resistant to wet chemical oxidation (hard carbon) or thermal oxidation (soot carbon); atomic H/O ratios indicated a close correlation between the degree of reduction of the NOM and its rigidity. Sorbents with larger rigid carbon fractions had more non-linear sorption isotherms and higher organic carbon (OC) normalized sorption affinities. The size of the PM hole filling domain for a given sorbent was closely correlated with the extent to which the sorbent's affinity for chlorobenzenes exceeded predictions from a linear free energy relationship. Loss of some portions of the rigid character of the NOM domain due to the penetration of sorbate molecules (plasticization) was discussed as a possible contributor to the non-ideal sorption behaviors observed in this study. The existence of a permanently rigid NOM domain, not subject to plasticization under environmental conditions, was postulated as an additional factor determining the observed sorption behavior.

The influence of natural organic matter rigidity on the sorption, desorption, and competitive displacement rates of 1,2-dichlorobenzene.

The influence of natural organic matter (NOM) rigidity on the sorption, desorption, and competitive displacement rates of 1,2-Dichlorobenzene (1,2-DCB) was evaluated using batch reactor experiments with two surface soils (Yolo and Forbes) and a shale (Ohio). Previous characterization suggests that the shale NOM is the most reduced and condensed, the Yolo soil is the most oxidized and amorphous, and Forbes soil has an intermediate NOM structure. The rate study for each sorbent was conducted under the same reactor parameters, and 1,2-DCB mass-transfer rates were determined using the distributed first-order mass-transfer rate model based on the gamma probability density function. To measure competitive displacement rates, 1,2,4-trichlorobenzene (1,2,4-TCB) was delivered as a competitor after 34 days pre-equilibration. Higher fractions of contaminant subject to instantaneous mass transfer and much faster rates of approach to apparent sorption equilibrium are found in Yolo soil when compared with Forbes soil and the shale. The size of the instantaneously desorbing fraction thus appears inversely related to the hard carbon fraction. In the NOM compartment where mass transfer is rate-limited, rate coefficient distributions are shifted toward lower rates for desorption and competitive displacement of 1,2-DCB in Ohio shale, followed by Forbes soil. Sorption and desorption rate distributions are almost the same for the shale, while desorption rates are a few times greater than sorption rates in Yolo and Forbes soils. Mass-transfer coefficients for competitive displacement are considerably slower than those for desorption in Forbes soil and the shale. However, the mass-transfer rates for the two processes seem to be similar in Yolo soil, which has a NOM matrix comprising a relatively larger soft organic carbon fraction. The concept of "solute induced softening" is discussed as a mechanistic rationale for the experimental observations.

Effects of competitor and natural organic matter characteristics on the equilibrium sorption of 1,2-dichlorobenzene in soil and shale.

The competitive sorption behaviors of 1,2-DCB in binary solute systems in four natural sorbents having natural organic matter (NOM) matrixes of different physicochemical characters were investigated in batch reactors. Specifically, the study focused on investigating how the extent of 1,2-DCB competitive sorption depends on (i) the rigidity of NOM matrixes as assessed by the efficiency of chemical oxidation and (ii) the closeness of competitor structure to that of the primary solute. The chemical oxidation and elemental composition results suggest that the shale NOM is the most reduced and condensed, the peat was the most oxidized and amorphous, and two surface soils had intermediate NOM structures. Four chlorinated benzenes and phenanthrene were used as competing solutes. All five chemicals exhibited competition against 1,2-DCB in all sorbents, including the peat, but the extent of competition varied significantly. Little difference in the extent of competition with 1,2-DCB was observed for the various chlorinated benzenes even though some were liquids and some were solids at the experimental temperature. All of the chlorobenzenes were more effective competitors than phenanthrene. The shale showed markedly different competition features from the other sorbents, with a much smaller competitive effect at a given sorbed volume of competitor. However, normalizing sorbed competitor volumes by the capacity of the adsorption domain in the Polanyi-Manes single-solute partition-adsorption model (V0) produced qualitatively similar competitive behavior for each solute; displacement of 1,2-DCB increased with increasing sorbed competitor volumes up to V0, and little additional competition occurred beyond that point. The extent of competition was positively correlated with the maximum adsorption capacity and the fraction of "hard" and "soot" carbon contents as assessed by chemical and thermal oxidation methods. These findings indicate that competition is associated with voids in the NOM structure, that these voids are likely present within the condensed ("hard" plus "soot") carbon domain, and therefore that diagenetic alteration of NOM plays a central role in determining competitive sorption characteristics for hydrophobic contaminants.