[1] We derive the equations of motion of a double-porosity medium based on Biot's theory of poroelasticity and on a generalization of Rayleigh's theory of fluid collapse to the porous case. Spherical inclusions are imbedded in an unbounded host medium having different porosity, permeability, and compressibility. Wave propagation induces local fluid flow between the inclusions and the host medium because of their dissimilar compressibilities. Following Biot's approach, Lagrange's equations are obtained on the basis of the strain and kinetic energies. In particular, the kinetic energy and the dissipation function associated with the local fluid flow motion are described by a generalization of Rayleigh's theory of liquid collapse of a spherical cavity. We obtain explicit expressions of the six stiffnesses and five density coefficients involved in the equations of motion by performing "gedanken" experiments. A plane wave analysis yields four wave modes, namely, the fast P and S waves and two slow P waves. As an example, we consider a sandstone and compute the phase velocity and quality factor as a function of frequency, which illustrate the effects of the mesoscopic loss mechanism due to wave-induced fluid flow.Citation: Ba, J., J. M. Carcione, and J. X. Nie (2011), Biot-Rayleigh theory of wave propagation in double-porosity media,

The photochemical formation and decay rates of superoxide radical ions (O 2•− ) in irradiated dissolved organic matter (DOM) solutions were directly determined by the chemiluminescent method. Under irradiation, uncatalyzed and catalyzed O 2dismutation account for ∼25% of the total O 2•− degradation in air-saturated DOM solutions. Light-induced O 2•− loss, which does not produce H 2 O 2 , was observed. Both the O 2•− photochemical formation and light-induced loss rates are positively correlated with the electron-donating capacities of the DOM, suggesting that phenolic moieties play a dual role in the photochemical behavior of O 2•− . In air-saturated conditions, the O 2 •− quantum yields of 12 DOM solutions varied in a narrow range, from 1.8 to 3.3‰, and the average was (2.4 ± 0.5)‰. The quantum yield of O 2•− nonlinearly increased with increasing dissolved oxygen concentration. Therefore, the quantum yield of one-electron reducing intermediates, the precursor of O 2•− , was calculated as (5.0 ± 0.4)‰. High-energy triplets ( 3 DOM*, E T > 200 kJ mol −1 ) and 1 O 2 quenching experiments indicate that 3 DOM* and 1 O 2 play minor roles in O 2•− production. These results are useful for predicting the photochemical formation and decay of O 2•− in sunlit surface waters.

Dissolved black carbon (DBC) is an important component of dissolved organic matter pool; however, its photochemical properties are not fully understood. In this study, we determined the excited triplet-state quantum yields of DBC (3DBC*) and 1O2 quantum yields (Φ 1O2 ) of six diverse DBCs using sorbic alcohol, 2,4,6-trimethylphenol (TMP), and furfuryl alcohol and compared the results with quantum yields of reference natural organic matters (NOMs). The average Φ 1O2 of six DBCs (4.2 ± 1.5%) was greater than that of terrestrial NOM (2.4 ± 0.3%) and comparable to autochthonous NOM (5.3 ± 0.2%). Using TMP as a probe for oxidizing triplets, DBC presented significantly higher apparent quantum yield coefficients for degrading TMP (f TMP) than the reference NOM, reflecting that the f TMP values of low-energy 3DBC* were approximately 12-fold greater than those of low-energy 3NOM*. The differences in the f TMP and Φ 1O2 trends among the DBCs indicated that the 3DBC* responsible for these reactions may be from different sources. In addition, DBC was much more effective than NOM, on a carbon-normalized basis, during photodegradation of pharmaceutically active compounds. This result confirms that the presence of DBC can accelerate the photodegradation of contaminants that are susceptible to one-electron oxidation by triplets.

Sulfate radical (SO 4•− )-mediated advanced oxidation processes via peroxymonosulfate (PMS) activation have been extensively investigated. However, the phototransformation of PMS in sunlit dissolved organic matter (DOM) solution has not been previously examined. For the first time, the photosensitized transformation of PMS in DOM-enriched solutions under simulated solar irradiation was observed. The generation of reactive species, including 1 O 2 , SO 4•− , and • OH, was confirmed by electron paramagnetic resonance and quantified by chemical probes. SO 4•− was the primary reactive species generated via the reaction of excited triplet DOM ( 3 DOM*) with PMS. 3 DOM* acted as a reactive reductant and was quickly oxidized by PMS, with an estimated reaction rate constant of (4.09 ± 0.21) × 10 8 M −1 s −1 . Compared to 3 DOM*, one-electron-reducing DOM (DOM •− ) was a minor contributor to the photosensitized transformation of PMS, and the contribution of DOM •− relied on the phenolic constituents. In addition, a series of different types of DOM, including terrestrial DOM, autochthonous DOM, and effluent organic matter and its fractions, were employed to examine the photosensitized transformation kinetics of PMS. Overall, the photosensitized transformation of PMS by irradiated DOM could be a useful and economical approach to generate SO 4•− under environmentally relevant conditions.

Hydroxyl radicals ( • OH) are important reactive species that are photochemically generated through solar irradiation of chromophoric dissolved organic matter (CDOM) in surface waters. However, the spatial distribution within the complex three-dimensional structure of CDOM has not been examined. In this study, we used a series of hydrophobic chlorinated paraffins as chemical probes to elucidate the microheterogeneous distribution of • OH in illuminated CDOM solutions. The steady-state concentration of • OH inside the CDOM microphase is 210 ± 31-fold higher than the concentration in the aqueous phase. Our results suggest that the most photochemically generated • OH are confined into the CDOM microphase. Thus, illuminated CDOM behaves as a natural microreactor for • OH-based oxidations. By including intra-CDOM • OH, the quantum yield of • OH for CDOM solutions was estimated to be 2.2 ± 0.5 × 10 −3 , which is 2 orders of magnitude greater than previously thought. The elevated concentrations of photogenerated • OH within the CDOM microphase may improve the understanding of hydrophobic pollutant degradation in aqueous environments. Moreover, our results also suggest that • OH oxidation may play more important roles in the phototransformation of CDOM than previously expected.