In the computation of metal flux in aquatic systems, at consuming surfaces like organism membranes, diffusion processes of metal ions, ligands, and complex species, as well as the kinetic and thermodynamic aspects of their chemical interactions, must be considered. The properties of many natural ligands, however, are complicated (formation of successive complexes for simple ligands, polyelectrolytic properties and chemical heterogeneity for macromolecular ligands, large size distribution and fractal structure for suspended aggregates). These properties should be properly modeled to get the correct values of the chemical rate constants and diffusion coefficients required for flux computations. The selection of the most appropriate models and parameter values is far from straightforward. This series of papers discusses the various models and compiles the parameters needed for the three most important types of complexants found in aquatic systems: the small, simple ligands, the fulvic and humic compounds, and the colloidal "particles" or aggregates. In particular, new approaches are presented to compute the rate constants of metal complex formation, with both fulvics/humics and particles/aggregates. The method to include the site distribution of fulvics/humics and the size distribution of particles/aggregates in metal flux computation at consuming interfaces is also discussed in detail. These models and parameters are discussed critically and presented in the same framework, forthe computation of metal flux in presence of any of the above complexants or mixtures. Such parameters, largely spread in the literature, are gathered here and selected specifically for environmental applications. The focus in Part I of the series is on simple ligands and fulvic/humic compounds. Part II deals with particulate and aggregate complexants.

The computation of metal flux in aquatic systems at consuming surfaces like organism membranes must consider the diffusion processes of metal ions, ligands, and complex species, as well as the kinetic and thermodynamic aspects of their chemical interactions. Many natural ligands, however, have complicated properties (formation of successive complexes for simple ligands, polyelectrolytic properties and chemical heterogeneity for macromolecular ligands, large size distribution and fractal structure for suspended aggregates). These properties should be properly modeled to get the correct values of the chemical rate constants and diffusion coefficients required for flux computations. The selection of the most appropriate models and parameter values is far from straightforward. In this series of papers, models and compilations of parameters for application to the three most important types of complexants found in aquatic systems, the small, simple ligands, the fulvic and humic compounds, and the colloidal "particles" or aggregates, are discussed. In particular, new approaches are presented to compute the rate constants of metal complex formation for both fulvics/humics and particles/aggregates. A method to include the site distribution of fulvics/ humics and the size distribution of particles/aggregates in metal flux computation at consuming interfaces is also discussed in detail. These models and parameters are discussed critically and presented in a single consistent framework, applicable to the computation of metal flux in presence of any of the above complexants ortheir mixtures. Part I of the series focuses on simple ligands and fulvic/ humic compounds. Part II deals with particulate and aggregate complexants.

In biofilms, diffusion may limit the chemical activity of nutrients, toxic compounds, and medicines. This study provides direct, noninvasive insight into the factors that will most effectively limit the transport of antibiotics and biocides in biofilms. Self-diffusion coefficients have been determined for a number of fluorescent probes in biofilms of Streptococcus mutans using fluorescence correlation spectroscopy. The effects of probe size and charge and the roles of biofilm pH, ionic strength, and heterogeneity were studied systematically. The relative diffusion coefficients (D in the biofilm divided by that in water) decreased with increasing probe size (3,000-molecular-weight [3K], 10K, 40K, 70K, and 2,000K dextrans). Studies using variably charged substrates (tetramethylrhodamine, Oregon Green, rhodamine B, and rhodamine 6G) showed that the self-diffusion coefficients decreased with an increasing negative charge of the fluorescent probes. No significant effect was observed for changes to the ionic strength (10 ؊4 to 10 ؊1 M) or pH (4 to 9) of the biofilm. Biofilm heterogeneity was responsible for variations of ca. one order of magnitude in the diffusion coefficients.Biofilms are complex suprastructures in which bacterial microcolonies are dispersed in a matrix of extracellular polymeric substances (EPS; polysaccharides, proteins, and DNA), lipids, and other metabolites (3,6,11,14,21). Due to the functional groups on the EPS (e.g., carboxylate, pyruvate, sulfate, etc.), the biofilm generally has an overall negative charge and a high water content (21). The specific structure of biofilms is thought to provide them with a high level of resistance to antibiotics, disinfectants, and detergents (7,19,20). For example, it has been reported that the minimum antibiotic concentration to kill bacteria found in biofilms was about 100 to 1,000 times greater than what was observed for the planktonic organisms (19). A long-standing explanation for the observed increased tolerance to antibiotics is that the biofilm constitutes an effective barrier to the penetration of antimicrobial agents, which is related to a reduction in their diffusive flux with respect to that observed in water (18,19). To that end, it is vital to quantify diffusion in biofilms (23), preferably with noninvasive methods, such as fluorescence correlation spectroscopy (FCS) (4, 15) or attenuated total reflection-Fourier transform infrared spectroscopy (ATR-FTIR) (17). Unfortunately, no consensus yet exists on the role of biofilms in diffusion. Relative diffusion coefficients (defined as the diffusion coefficient, D, in a biofilm divided by that in water) vary greatly across the literature.In this paper, the effects of substrate size and charge and of biofilm pH and ionic strength were studied systematically for a biofilm of Streptococcus mutans. S. mutans is a main constituent of dental plaque, which can form dense biofilms both in vivo and in vitro (16). The diffusion coefficients of particle-size standards (dextrans of 3,000 molecular weight [3K], 10K...

Understanding the physical chemical behaviors of each metal species in a solution containing a mixture of ligands is a prerequisite, e.g., for studying metal bioavailability or making predictions on dynamic risk assessment in ecotoxicology. For many years, the reaction layer concept has been used fruitfully due to its simplicity for understanding and making predictions on diffusion/reaction processes. Until now, it has been applied mainly to solutions containing one ligand. Here, we reconsider the fundamentals of this approach and extend it to multiligand systems. It is shown that each metal complex has its own reaction layer (so-called composite reaction layer), which results from the interplay of this particular complex with all the other complexes. Moreover, it is shown that the overall metal flux can be computed by assuming the existence of one single fictitious equivalent reaction layer thickness for the whole of the complexes. This equivalent reaction layer is a mathematical combination of all the composite reaction layers. Simple analytical equations are obtained, which make it possible to readily interpret the role of the various types of metal species in a mixture. The revisited reaction layer approach, denoted as the reaction layer approximation (RLA), is validated by comparing the total metal flux, the individual fluxes of each metal species, and their concentration profiles computed by the RLA with those obtained by a rigorous mathematical approach. The examples of Pb(II) in a modified Aquil medium and of Cu(II) in solutions of nitrilotriacetic acid and N-(2-carboxyphenyl)glycine are treated in detail. In particular, an original result is obtained with the Cu/NTA/N-(2-carboxyphenyl)glycine system, namely an unexpected flux enhancement is observed, which is specific to solutions with ligand mixtures. The corresponding physicochemical mechanism is not readily understood by the rigorous mathematical (either numerical or analytical) solutions due to their involved combination of parameters. On the other hand, we show that, due to the simplicity of the RLA concept, the RLA facilitates elucidation of the physicochemical mechanism underlying complicated processes.

Metal flux at consuming interfaces (e.g., sensors or microorganisms) is simulated in environmental multiligand systems using a new numerical code, MHEDYN (Multispecies HEterogeneous DYNamics), based on the lattice Boltzmann method. The attention is focused on the computation of the maximum flux of Cu(II), that is, the flux controlled by diffusion-reaction in solution, irrespective of processes occurring at the interface. In parts III and IV of this series, three types of typical environmental complexants are studied: (a) simple ligands (OH- and C03(2-)), (b) fulvic or humic substances including many sites with broadly varying rate constants, and (c) aggregates including a broad range of sizes and diffusion coefficients. Part III focuses on computations in the presence of simple ligands and fulvic/humic substances separately, and part IV discusses the case of aggregate complexes alone and the mixtures of all ligands in typical natural waters. These papers describe the dynamic contribution of the various types of sites for fulvic and aggregate Cu(II) complexes for the first time. Whenever possible, the metal fluxes computed by MHEDYN are compared with those given by another code, FLUXY, based on a fully different mathematical approach, and very good agreement between these codes is obtained. In all cases, MHEDYN computes the concentration profile of each complex and its time evolution, as well as the steady-state flux and the corresponding contribution of each complex to the flux. The metal fluxes can be computed at a planar consuming surface such as an organism or a sensor surface, in presence of an unlimited number of complexation reactions of the metal M, and for any metal/ligand concentration ratio, with values of the physicochemical parameters ranging over many orders of magnitude.