Extraction of Phenol and Chlorophenols Using Ionic Liquid [Bmim]+[BF4]− Dissolved in Tributyl Phosphate

In the present work, experiments have been carried out with a focus to reduce the volume requirement of solvent by mixing with imidazolium based ionic liquids (ILs) for the solvent extraction of phenol, p‐chlorophenol, 2,4‐dichlorophenol, 2,4,6‐trichlorophenol, and pentachlorophenol from aqueous solutions. The effect of aqueous phase pH (2–12), agitation speed (100–450 rpm), solute concentration in feed (2–50 mg/L), temperature (303–333 K), treat ratio (1–11), and 1‐butyl‐3‐methyl imidazolium tetrafluoroborate [Bmim]⁺[BF₄]^? volume in tributyl phosphate (TBP; 0–0.7% v/v) on extraction of phenols has been studied and optimized. Parameters like strip phase pH (3–13) and stripping agent concentration (0.001–0.009 N) have also been studied for stripping of phenols from solvent phase. It has been found that 0.5% v/v of ionic liquid [Bmim]⁺[BF₄]^? in solvent TBP extracts more than 97.5% of phenol and chlorophenols from aqueous solutions with a treat ratio (aqueous to solvent phase ratio) of 5. Transport mechanism for extraction and stripping of phenol and chlorophenols using ionic liquid [Bmim]⁺[BF₄]^? has been discussed. The results show that by appropriate selection of extraction and stripping conditions, it is possible to remove nearly all phenols with a treat ratio of 5.     

Sorption of ortho‐Phenylphenol to Soils

Conflicting sorption coefficients for ortho‐phenylphenol (OPP) have been reported in the literatures, which resulted in the conflicting assessments on OPP mobility in soil. To ascertain the sorption coefficient of OPP, batch experiments were performed based on OECD guideline 106, using three types of soils. Headspace solid‐phase microextraction (HS‐SPME) and GC‐MS were applied to the determination of OPP concentration in the liquid phase. The sorption isotherms obtained for all three soils under equilibrium conditions were described well, assuming linear sorption. The organic carbon normalized distribution coefficients (K_oc) ranged from 894 to 1703 L kg^?1, which suggested that OPP is moderately mobile in soil. The results also showed that the K_oc value of OPP can be predicted precisely from K_ow, whereas it was underestimated by one order of magnitude when water solubility is used.     

Separation and Preconcentration of Boron with a Glucamine Modified Novel Magnetic Sorbent

A novel, simple method based on magnetic separation was developed for analytical purposes. In this method, N‐methyl‐D‐glucamine (NMDG) modified magnetic microparticles that were synthesized by using the sol‐gel method were used for the selective extraction and preconcentration of boron from aqueous solutions. This method combines the simplicity and selectivity of solvent extraction with the easy separation of magnetic microparticles from a solution with a magnet without any preliminary filtration step. The structure of the prepared γ‐Fe₂O₃‐SiO₂‐NMDG (magnetic sorbent) composites were characterized by using X‐ray diffraction (XRD), Transmission Electron Microscopy (TEM), and Fourier Transform Infrared Spectroscopy (FTIR). The influence of different parameters on the sorbent capacity, such as the sorption/desorption of boron, magnetic sorbent dosage, pH, equilibrium time, type, and amount of stripping solution, were evaluated by using the magnetic sorbent. Any equilibrium pH greater than 6 can be used for sorption. Desorption from the sorbent was carried out by using 1.0 M HCl. The sorption and desorption efficiency of the γ‐Fe₂O₃‐SiO₂‐NMDG was found as 92.5 ± 0.5% and 99.8 ± 6%, respectively.     

Behavior and Fate of PFOA and PFOS in Sandy Aquifer Sediment

Microcosms were constructed with sediment from beneath a landfill that received waste containing PFOA (perfluorooctanoic acid) and PFOS (perfluorooctane sulfonate). The microcosms were amended with PFOA and PFOS, and sampled after 91, 210, 343, 463, 574, and 740 d of incubation. After 740 d, selected microcosms were extracted to determine the mass of PFOA and PFOS remaining. There was no evidence for degradation of PFOA or PFOS. Over time, the aqueous concentrations of PFOA and PFOS increased in the microcosms, indicating that PFOA and PFOS that had originally sorbed to the sediment was desorbing. At the beginning of the experiment, the adsorption coefficient, K_d, averaged 0.27 L/kg for PFOA and 1.2 L/kg for PFOS. After 740 d of incubation, sorption of PFOA was not detectable and the K_d of PFOS was undetectable in two microcosms and was 0.08 L/kg in a third microcosm. During incubation, the pH of the pore water in the microcosms increased from pH 7.2 to pH ranging from 8.1 to 8.8. The zeta potential of the sediment decreased with increasing pH. These observations suggest that the sorption of PFOA and PFOS at near neutral pH was controlled by the electrostatic sorption on ferric oxide minerals, and not by the sorption to organic carbon. Accurate predictions of PFOA and PFOS mobility in ground water should be based on empirical estimates of sorption using affected aquifer sediment.     

A Practical Measurement Strategy to Estimate Nonlinear Chlorinated Solvent Sorption in Low foc Sediments

In this study, we tested a practical strategy useful for accurate chlorinated volatile organic compound (cVOC) sorption prediction. Corresponding to the feature of the superposition of adsorption due to thermally altered carbonaceous matter (TACM) with organic carbon‐water partitioning, a nonlinear Freundlich sorption isotherm covering a wide range of aqueous concentrations was defined by equilibrium sorption measurement at one or a few low concentration points with extrapolation to the empirical organic carbon‐water partition coefficient (K_oc,e) near compound solubility. We applied this approach to obtain perchloroethene equilibrium sorption isotherm parameters for TACM‐containing glacial sand and gravel subsoil samples from a field site in New York. Sorption and associated K_oc,c applicable to low (5–500 µg/L) and high (>100,000 µg/L) aqueous concentrations were determined in batch experiments. (The K_oc,c is the organic carbon‐normalized sorption partition coefficient corresponding to aqueous concentration C_w.) The K_oc,c measurements at low concentration (~5 µg/L) were 6 to 34 times greater than the K_oc,e. The importance of this type of data is illustrated through presentation of its substantial impact on the site remedy. In so doing, we provide an approach that is broadly applicable to cVOC field sites with similar circumstances (low carbon content glacial sand and gravel with TACM).     

Partitioning of Fluoroquinolones on Wastewater Sludge

Laboratory‐scale batch experiments were conducted to investigate the adsorption behavior of eight fluoroquinolones (FQs) on aerobic, anoxic, and anaerobic sludge, under different adsorpiton time, pH, and temperature conditions. Results indicated that adsorption of FQs onto all sludge was a physical sorption process. The relationship of the partitioning coefficient (K_d) and the octanol/water partition coefficient (K_ow) for each FQ was established. The adsorbed fraction of FQs on sludge could then be predicted with the K_d. It was calculated that about 50–72% of the FQs were adsorbed on the sludge. Therefore, the adsorption effect must be considered when studying the fate and occurrence of FQs in wastewater treatment systems.     

Influence of pH on the Toxicity of Phenol and its Two Derivatives Pentachlorophenol and Dinitrophenol to Some Fresh Water Teleosts

— The fish Colisa fasciatus, Saccobranchus fossilis and Notopterus notopterus were exposed to phenol, pentachlorophenol and dinitrophenol at four pH levels, i. e. 4.6 + 0.12, 6.0±0.14, 7.3 ±0.10 and 8.8 ±0.13, to evaluate the effect of pH on the toxicity of these chemicals. — A change in pH from 7.3 ± 0.10 to 6.0 ± 0.14 increased toxicity to a certain degree while a change from 7.3 ± 0.10 to 4.6 ± 0.12 potentiated the toxicity of phenol, pentachlorophenol and dinitrophenol 5.05, 19.30 and 22.33 times, respectively for Notopterus notopterus, 3.59, 4.39 and 4.73 times, tespectively for Colisa fasciatus and 3.04, 4.68 and 5.85 times, respectively for Saccobranchus fossilis. — A change in pH from 7.3 ± 0.10 to 8.8 ± 0.13 has a protective effect on the toxicities.     

Study of the Interaction Mechanism in the Biosorption of Copper(II) Ions onto Posidonia oceanica and Peat

A systematic approach was used to characterize the biosorption of copper(II) onto two biosorbents, Posidonia oceanica and peat, focusing on the interaction mechanisms, the copper(II) sorption–desorption process and the thermal behavior of the biosorbents. Sorption isotherms at pH 4–6 were obtained and the experimental data were fitted to the Langmuir model with a maximum uptake (q_max) at pH 6 of 85.78 and 49.69 mg g^?1, for P. oceanica and peat, respectively. A sequential desorption (SD) with water, Ca(NO₃)₂, and EDTA was applied to copper‐saturated biosorbents. Around 65–70% copper(II) were desorbed with EDTA, indicating that this heavy metal was strongly bound. The reversibility of copper(II) sorption was obtained by desorption with HCl and SD. Fourier transform IR spectroscopy (FTIR) analysis detected the presence of peaks associated with OH groups in aromatic and aliphatic structures, CH, CH₂, and CH₃ in aliphatic structures, COO^? and COOH groups and unsaturated aromatic structures on the surface of both biosorbents, as well as peaks corresponding to Si? O groups on the surface of peat. The results of SEM‐EDX and FTIR analysis of copper‐saturated samples demonstrated that ion exchange was one of the mechanisms involved in copper(II) retention. Thermal analysis of biosorbent samples showed that copper(II) sorption–desorption processes affected the thermal stability of the biosorbents.     

Atmospheric Concentrations and Phase Partitioning of Polycyclic Aromatic Hydrocarbons in Izmir,Turkey

Ambient air polycyclic aromatic hydrocarbon (PAH) samples were collected at a suburban (n = 63) and at an urban site (n = 14) in Izmir, Turkey. Average gas‐phase total PAH (∑₁₄PAH) concentrations were 23.5 ng m^?3 for suburban and 109.7 ng m^?3 for urban sites while average particle‐phase total PAH concentrations were 12.3 and 34.5 ng m^?3 for suburban and urban sites, respectively. Higher ambient PAH concentrations were measured in the gas‐phase and ∑₁₄PAH concentrations were dominated by lower molecular weight PAHs. Multiple linear regression analysis indicated that the meteorological parameters were effective on ambient PAH concentrations. Emission sources of particle‐phase PAHs were investigated using a diagnostic plot of fluorene (FLN)/(fluorine + pyrene; PY) versus indeno[1,2,3‐cd]PY/(indeno[1,2,3‐cd]PY + benzo[g,h,i]perylene) and several diagnostic ratios. These approaches have indicated that traffic emissions (petroleum combustion) were the dominant PAH sources at both sites for summer and winter seasons. Experimental gas–particle partition coefficients (K_P) were compared to the predictions of octanol–air (K_OA) and soot–air (K_SA) partition coefficient models. The correlations between experimental and modeled K_P values were significant (r² = 0.79 and 0.94 for suburban and urban sites, respectively, p < 0.01). Octanol‐based absorptive partitioning model predicted lower partition coefficients especially for relatively volatile PAHs. However, overall there was a relatively good agreement between the measured K_P and soot‐based model predictions.     

Runoff modelling at two field slopes: use of in situ measurements of air permeability to characterize spatial variability of saturated hydraulic conductivity

The time required at a field site to obtain a few measurements of saturated hydraulic conductivity (K_s) will allow for many measurements of soil air permeability (k_a). This study investigates if k_a measured in situ (k_{a, in situ}) can be a substitute for measurement of K_s in relation to infiltration and surface runoff modelling. Measurements of k_{a, in situ} were carried out in two small agricultural catchments. A spatial correlation of the log‐transformed values existed having a range of approximately 100 m. A predictive relationship between K_s and k_a measured on 100‐cm³ soil samples in the laboratory was derived for one of the field slopes and showed good agreement with an earlier suggested predictive K_s–k_a relationship. In situ measurements of K_s and k_a suggested that the predictive relationships also could be used at larger scale. The K_s–k_a relationships together with the k_{a, in situ} data were applied in a distributed surface runoff (DSR) model, simulating a high‐intensity rainfall event. The DSR simulation results were highly dependent on whether the geometric average of k_{a, in situ} or kriged values of k_{a, in situ} was used as model input. When increasing the resolution of K_s in the DSR model, a limit of 30–40 m was found for both field slopes. Below this limit, the simulated runoff and hydrograph peaks were independent of resolution scale. If only a few randomly chosen values of K_s were used to represent the spatial variation within the field slope, very large deviations in repeated DSR simulation results were obtained, both with respect to peak height and hydrograph shape. In contrast, when using many predicted K_s values based on a K_s–k_a relationship and measured k_{a, in situ} data, the DSR model generally captured the correct hydrograph shape although simulations were sensitive to the chosen K_s–k_a relationship. As massive measurement efforts normally will be required to obtain a satisfactory representation of the spatial variability in K_s, the use of k_{a, in situ} to assess spatial variability in K_s appears a promising alternative. Copyright © 2004 John Wiley & Sons, Ltd.     

Adsorption Characteristics of Reactive Black 5 from Aqueous Solution onto Chitosan

Adsorption of reactive black 5 (RB5) from aqueous solution onto chitosan was investigated in a batch system. The effects of solution pH, initial dye concentration, and temperature were studied. Adsorption data obtained from different batch experiments were modeled using both pseudo first‐ and second‐order kinetic equations. The equilibrium adsorption data were fitted to the Freundlich, Tempkin, and Langmuir isotherms over a dye concentration range of 45–100 µmol/L. The best results were achieved with the pseudo second‐order kinetic and Langmuir isotherm equilibrium models, respectively. The equilibrium adsorption capacity (q_e) was increased with increasing the initial dye concentration and solution temperature, and decreasing solution pH. The chitosan flakes for the adsorption of the dye was regenerated efficiently through the alkaline solution and was then reused for dye removal. The activation energy (E_a) of sorption kinetics was estimated to be 13.88 kJ/mol. Thermodynamic parameters such as changes in free energy (ΔG), enthalpy (ΔH), and entropy (ΔS) were evaluated by applying the van't Hoff equation. The thermodynamics of reactive dye adsorption by chitosan indicates its spontaneous and endothermic nature.     

Using a transient infiltrometric technique for intensively sampling field‐saturated hydraulic conductivity of a clay soil in two runoff plots

The point measurement of soil properties allows to explain and simulate plot scale hydrological processes. An intensive sampling was carried out at the surface of an unsaturated clay soil to measure, on two adjacent plots of 4 × 11 m² and two different dates (May 2007 and February–March 2008), dry soil bulk density, ρ_b, and antecedent soil water content, θ_i, at 88 points. Field‐saturated soil hydraulic conductivity, K_fs, was also measured at 176 points by the transient Simplified Falling Head technique to determine the soil water permeability characteristics at the beginning of a possible rainfall event yielding measurable runoff. The ρ_b values did not differ significantly between the two dates, but wetter soil conditions (by 31%) and lower conductivities (1.95 times) were detected on the second date as compared with the first one. Significantly higher (by a factor of 1.8) K_fs values were obtained with the 0.30‐m‐diameter ring compared with the 0.15‐m‐diameter ring. A high K_fs (> 100 mm h^?1) was generally obtained for low θ_i values (< 0.3 m³m^?3), whereas a high θ_i yielded an increased percentage of low K_fs data (1–100 mm h^?1). The median of K_fs for each plot/sampling date combination was not lower than 600 mm h^?1, and rainfall intensities rarely exceeded 100 mm h^?1 at the site. The occurrence of runoff at the base of the plot needs a substantial reduction of the surface soil permeability characteristics during the event, probably promoted by a higher water content than the one of this investigation (saturation degree = 0.44–0.62) and some soil compaction due to rainfall impact. An intensive soil sampling reduces the risk of an erroneous interpretation of hydrological processes. In an unstable clay soil, changes in K_fs during the event seem to have a noticeable effect on runoff generation, and they should be considered for modeling hydrological processes. Copyright © 2012 John Wiley & Sons, Ltd.     

Adsorption of Au(III) and Au(I) complexes on δ-MnO2

The sorption of AuCl₄ ⁻,AuCl₂ ⁻ and Au(S₂O₃)^3- on δ-MnO₂ was investigated at pH2–11.6, 0.01 mol/L and 0.1 mol/L NaNO₃ solutions. At pH 4 in two electrolyte strength solutions, Au sorption densities on δ-MnO₂ are 0.18–0.21 and 0.28μmoL/m² for AuCl₄ ⁻ and Au(S₂O₃)₂ ^3-, respectively, and the Au surface coverage is approximate to or lower than 1%. This adsorption of the two Au complexes decreases as the solution pH increases, which conforms to the sorption regularity of the anion on δ-MnO₂. The Au sorption decreases in the sequence of Au(S₂O₃)₂ ^3- >AuCl₄ ⁻ >AuC1₂ ⁻. The intrinsic equilibrium constants (logK ^int) of the three Au complexes are 1.17–2.7, much higher than those of Cu and Cd. The hydrolysis products of AuCl₄ ^- are preferentially adsorbed by δ-MnO₂ and the inner-sphere Au-surface complexes are formed on the surface. Project supported by the National Studying-abroad Foundation, the National Natural Science Foundation of China (Grant No. 49573200) and the Australian Mining Industry.     

Effects of initial soil water content and saturated hydraulic conductivity variability on small watershed runoff simulation using LISEM

Abstract

Soil water content (θ) and saturated hydraulic conductivity (K_s) vary in space. The objective of this study was to examine the effects of initial soil water content (θ_i) and K_s variability on runoff simulations using the LImburg Soil Erosion Model (LISEM) in a small watershed in the Chinese Loess Plateau, based on model parameters derived from intensive measurements. The results showed that the total discharge (TD) and peak discharge (PD) were underestimated when the variability of θ_i and K_s was partially considered or completely ignored compared with those when the variability was fully considered. Time to peak (TP) was less affected by the spatial variability compared to TD and PD. Except for TP in some cases, significant differences were found in all hydrological variables (TD, PD and TP) between the cases in which spatial variability of θ_i or K_s was fully considered and those in which spatial variability was partially considered or completely ignored. Furthermore, runoff simulations were affected more strongly by K_s variability than by θ_i variability. The degree of spatial variability influences on runoff simulations was related to the rainfall pattern and θ_i. Greater rainfall depth and instantaneous rainfall intensity corresponded to a smaller influence of the spatial variability. Stronger effects of the θ_i variability on runoff simulation were found in wetter soils, while stronger effects of the K_s variability were found in drier soils. For accurate runoff simulation, the θ_i variability can be completely ignored in cases of a 1-h duration storm with a return period greater than 10 years, while K_s variability should be fully considered even in the case of a 1-h duration storm with a return period of 20 years.

Editor D. Koutsoyiannis; Associate editor A. Fiori     

Incorporating spatially heterogeneous infiltration capacity into hydrologic models with applications for simulating post‐wildfire debris flow initiation

Soils in post‐wildfire environments are often characterized by a low infiltration capacity with a high degree of spatial heterogeneity relative to unburned areas. Debris flows are frequently initiated by run‐off in recently burned steeplands, making it critical to develop and test methods for incorporating spatial variability in infiltration capacity into hydrologic models. We use Monte Carlo simulations of run‐off generation over a soil with a spatially heterogenous saturated hydraulic conductivity (K_s) to derive an expression for an aerially averaged saturated hydraulic conductivity ( ) that depends on the rainfall rate, the statistical properties of K_s, and the spatial correlation length scale associated with K_s. The proposed method for determining is tested by simulating run‐off on synthetic topography over a wide range of spatial scales. Results provide a simplified expression for an effective saturated hydraulic conductivity that can be used to relate a distribution of small‐scale K_s measurements to infiltration and run‐off generation over larger spatial scales. Finally, we use a hydrologic model based on to simulate run‐off and debris flow initiation at a recently burned catchment in the Santa Ana Mountains, CA, USA, and compare results to those obtained using an infiltration model based on the Soil Conservation Service Curve Number.     

Start‐Up Study on Biohydrogen from Palm Oil Mill Effluent in a Pilot‐Scale Reactor

A start‐up study for biohydrogen production from palm oil mill effluent (POME) is carried out in a pilot‐scale up‐flow anaerobic sludge blanket fixed‐film reactor (UASFF). A substrate with a chemical oxygen demand (COD) of 30 g L^?1 is used, starting with molasses solution for 30 days and followed by a 10% v/v increment of POME/molasses ratio. At 100% POME, a hydrogen content of 80%, hydrogen production rate of 36 L H₂ per day, and maximum COD removal of 48.7% are achieved. Bio‐kinetic coefficients of Monod, first‐order, Grau second‐order, and Stover‐Kincannon kinetic models are calculated to describe the performance of the system. The steady‐state data with 100% POME shows that Monod and Stover‐Kincannon models with bio‐kinetic coefficients of half‐velocity constant (K_s) of 6000 mg COD L^?1, microbial decay rate (K_d) of 0.0015 per day, growth yield constant (Y) of 0.786 mg volatile suspended solids (VSS)/mg COD, specific biomass growth rate (μ_max) of 0.568 per day, and substrate consumption rate of (U_max) 3.98 g/L day could be considered as superior models with correlation coefficients (R²) of 0.918 and 0.989, respectively, compared to first‐order and Grau's second‐order models with coefficients of K₁ 1.08 per day, R² 0.739, and K_2s 1.69 per day, a = 7.0 per day, b = 0.847.     

Synthesis of Calix[4]arene‐grafted Magnetite Nanoparticles and Evaluation of Their Arsenate as Well as Dichromate Removal Efficiency

In this study, 5,17‐bis‐[(4‐benzylpiperidine)methyl]‐25,26,27,28‐tetrahydroxy‐calix[4]arene ( 3 ) has been prepared by the treatment of calix[4]arene with a secondary amine (4‐benzylpiperidine) and formaldehyde by means of Mannich reaction. The prepared Mannich base ( 3 ) has been grafted onto [3‐(2,3‐epoxypropoxy)‐propyl]‐trimethoxysilane‐modified Fe₃O₄ magnetite nanoparticles (EPPTMS‐MN) in order to obtain 5,17‐bis‐[(4‐benzylpiperidine)methyl]‐25,26,27,28‐tetrahydroxy calix[4]arene‐grafted EPPTMS‐MN (BP‐calix[4]arene‐grafted Fe₃O₄). All new compounds were characterized by a combination of FTIR and ¹H‐NMR analyses. The morphology of the magnetic nanoparticles was examined by transmission electron microscopy. Moreover, the studies regarding the removal of arsenate and dichromate ions from the aqueous solutions were also carried out by using 5,17‐bis‐[(4‐benzylpiperidine)methyl]‐25,26,27,28‐tetrahydroxy‐calix[4]arene in liquid–liquid extraction and BP‐calix[4]arene‐grafted Fe₃O₄ ( 4 ) in solid–liquid extraction experiments. The extraction results indicated that 3 is protonated at proton‐switchable binding sites in acidic conditions. Hence, facilitating binding of arsenate and dichromate is resulted from both electrostatic interactions and hydrogen bonding. To understand the selectivity of 3 , the retention of dichromate anions in the presence of Cl⁻, NO, and SO anions at pH 1.5 was also examined.     

Effect of SO on 1,1,1‐Trichloroethane Degradation by Fe0 in Aqueous Solution

Sulfate in groundwater has been previously shown to change the reactivity of Fe⁰ in permeable reactive barriers for reducing chlorinated organics. To better understand the effect and mechanism of SO, the degradation of 1,1,1‐trichloroethane (TCA) by Fe⁰ in unbuffered aqueous solutions with and without SO was investigated. In a Fe⁰‐TCA‐H₂O system with initial pH of 2.0 to 10.0, the maximum removal rate of TCA was achieved at the initial pH 6.0 with pseudo‐first‐order constant K_obs 9.0 × 10^?3/min. But in a Fe⁰‐TCA‐Na₂SO₄‐H₂O system, the removal rate of TCA decreased remarkably with a reduction in K_obs to 1.0 × 10^?3/min, and the pH varied from 6.0 to 9.6, indicating an inhibition of TCA dehydrochlorination by SO. Sulfate remarkably inhibited TCA degradation via changing the route of Fe⁰ dissolution. It accelerated the dissolution of Fe⁰ and transformed the intermediate form Fe(OH)_ads to Fe₂(SO₄)_ads, which weakened the affinity between Fe and TCA, and thus depressed the degradation of TCA by Fe⁰.     

A bed‐load transport model for rough turbulent open‐channel flows on plane beds

Data from flume studies are used to develop a model for predicting bed‐load transport rates in rough turbulent two‐dimensional open‐channel flows moving well sorted non‐cohesive sediments over plane mobile beds. The object is not to predict transport rates in natural channel flows but rather to provide a standard against which measured bed‐load transport rates influenced by factors such as bed forms, bed armouring, or limited sediment availability may be compared in order to assess the impact of these factors on bed‐load transport rates. The model is based on a revised version of Bagnold's basic energy equation i_bs_b = e_bω, where i_b is the immersed bed‐load transport rate, ω is flow power per unit area, e_b is the efficiency coefficient, and s_b is the stress coefficient defined as the ratio of the tangential bed shear stress caused by grain collisions and fluid drag to the immersed weight of the bed load. Expressions are developed for s_b and e_b in terms of G, a normalized measure of sediment transport stage, and these expressions are substituted into the revised energy equation to obtain the bed‐load transport equation i_b = ω G ^3·4. This equation applies regardless of the mode of bed‐load transport (i.e. saltation or sheet flow) and reduces to i_b = ω where G approaches 1 in the sheet‐flow regime. That i_b = ω does not mean that all the available power is dissipated in transporting the bed load. Rather, it reflects the fact that i_b is a transport rate that must be multiplied by s_b to become a work rate before it can be compared with ω. It follows that the proportion of ω that is dissipated in the transport of bed load is i_bs_b/ω, which is approximately 0·6 when i_b = ω. It is suggested that this remarkably high transport efficiency is achieved in sheet flow (1) because the ratio of grain‐to‐grain to grain‐to‐bed collisions increases with bed shear stress, and (2) because on average much more momentum is lost in a grain‐to‐bed collision than in a grain‐to‐grain one. Copyright © 2006 John Wiley & Sons, Ltd.