Metal-organic frameworks (MOFs) have emerged as attractive electrode materials for applications in energy storage and conversion, owing to their high porosity and surface area. In this communication, we report a hierarchically structured Co-MOF supported on nickel foam (Co-MOF/NF) serving as a high-performance electrode material for supercapacitors. The as-obtained Co-MOF/NF exhibits an ultrahigh areal specific capacitance of 13.6 F cm-2 at 2 mA cm-2 in 2 M KOH, exceeding those of the previously reported MOF-based materials. It also shows an excellent rate performance of 79.4% at a current density of 20 mA cm-2. An asymmetric supercapacitor (ASC) device employing Co-MOF/NF as the positive electrode and activated carbon (AC) as the negative electrode achieves a high energy density of 1.7 mW h cm-2 at a power density of 4.0 mW cm-2 with a capacitance retention of 69.7% after 2000 cycles.

The classical Local Cubic Law (LCL) generally overestimates flow through real fractures. We thus developed and tested a modified LCL (MLCL) which takes into account local tortuosity and roughness, and works across a low range of local Reynolds Numbers. The MLCL is based on (1) modifying the aperture field by orienting it with the flow direction and (2) correcting for local roughness changes associated with local flow expansion/contraction. In order to test the MLCL, we compared it with direct numerical simulations with the Navier-Stokes equations using real and synthetic three-dimensional rough-walled fractures, previous corrected forms of the LCL, and experimental flow tests. The MLCL performed well and the effective errors (d) in volumetric flow rate range from 23.4% to 13.4% with an arithmetic mean of |d| (<|d|>) equal to 3.7%. The MLCL is more accurate than previous modifications of the LCL. We also investigated the error associated with applying the Cubic Law (CL) while utilizing modified aperture field. The d from the CL ranges from 214.2% to 11.2%, with a slightly higher <|d|> 5 6.1% than the MLCL. The CL with the modified aperture field considering local tortuosity and roughness may also be sufficient for predicting the hydraulic properties of rough fractures.

Hyporheic flow in aquatic sediment controls solute and heat transport thereby mediating the fate of nutrients and contaminants, dissolved oxygen, and temperature in the hyporheic zone (HZ). We conducted a series of numerical simulations of hyporheic processes within a dune with different uniform temperatures, coupling turbulent open channel fluid flow, porous fluid flow, and reactive solute transport to study the temperature dependence of nitrogen source/sink functionality and its efficiency. Two cases were considered: a polluted stream and a pristine stream. Sensitivity analysis was performed to investigate the influence of stream water [NO 3 À ]/[NH 4 + ]. The simulations showed that in both cases warmer temperatures resulted in shallower denitrification zones and oxic-anoxic zone boundaries, but the trend of net denitrification rate and nitrate removal or production efficiency of the HZ for these two cases differed. For both cases, at high [NO 3 À ]/[NH 4 + ], the HZ functioned as a NO 3 À sink with the nitrate removal efficiency increasing with temperature. But at low [NO 3 À ]/[NH 4 +] for the polluted stream, the HZ is a NO 3 À sink at low temperature but then switches to a NO 3 À source at warmer temperatures. For the pristine stream case, the HZ was always a NO 3 À source, with the NO 3 À production efficiency increasing monotonically with temperature. In addition, although the interfacial fluid flux expectedly increased with increasing temperature due to decreasing fluid viscosity, the total nitrate flux into the HZ did not follow this trend. This is because when HZ nitrification is high, uniformly elevated [NO 3 À ] lowers dispersive fluxes into the HZ. We found that there are numerous confounding and interacting factors that combined to lead to the final temperature dependence of N transformation reaction rates. Although the temperature effect on the rate constant can be considered as the dominant factor, simply using the Arrhenius equation to predict the reaction rate would lead to incomplete insight by ignoring the changes in interfacial fluid and solute fluxes and reaction zone areas. Our study shows that HZ temperature and stream [NO 3 À ]/[NH 4 + ] are key controls for HZ sink/source functions.

Non-Fickian transport ubiquitously occurs across all scales within fractured geological media.Detailed characterization of non-Fickian transport through single fractures is thus critical for predicting the fate of solutes and other fluid-borne entities through fractured media. Our direct numerical simulations of solute transport through two-dimensional rough-walled fractures showed early arrival and heavy tailing in breakthrough curves (BTCs), which are salient characteristics of non-Fickian transport. Analyses for dispersion coefficients (D ADE ) using the standard advection-dispersion equation (ADE) led to errors which increased linearly with fracture heterogeneity. Estimated Taylor dispersion coefficients deviated from estimated D ADE even at higher Peclet numbers. Alternatively, we used continuous time random walk (CTRW) model with truncated power law transition rate probability to characterize the non-Fickian transport. CTRW modeling markedly and consistently improved fits to the BTCs relative to those fitted with ADE solutions. The degree of deviation of transport from Fickian to non-Fickian is captured by the parameter b of the truncated power law. We found that b is proportional to fracture heterogeneity. We also found that the CTRW transport velocity can be predicted based on the flow velocity. Along with the ability to predict b, this is a major step toward prediction of transport through CTRW using measurable physical properties.

The water quality and ecosystem health of river corridors depend on the biogeochemical processes occurring in the hyporheic zones (HZs) of the beds and banks of rivers. HZs in riverbeds often form because of bed forms. Despite widespread and persistent variation in river flow, how the discharge‐ and grain size‐dependent geometry of bed forms and how bed form migration collectively and systematically affects hyporheic exchange flux, solute transport, and biogeochemical reaction rates are unknown. We investigated these linked processes through morphodynamically consistent multiphysics numerical simulation experiments. Several realistic ripple geometries based on bed form stability criteria using mean river flow velocity and median sediment grain size were designed. Ripple migration rates were estimated based primarily on the river velocity. The ripple geometries and migration rates were used to drive hyporheic flow and reactive transport models which quantified HZ nitrogen transformation. Results from fixed bed form simulations were compared with matching migrating bed form scenarios. We found that the turnover exchange due to ripple migration has a large impact on reactant supply and reaction rates. The nitrate removal efficiency increased asymptotically with Damköhler number for both mobile and immobile ripples, but the immobile ripple always had a higher nitrate removal efficiency. Since moving ripples remove less nitrogen, and may even be net nitrifying at times, consideration for bed form morphodynamics may therefore lead to reduction of model‐based estimates of denitrification. The connection between nitrate removal efficiency and Damköhler number can be integrated into frameworks for quantifying transient, network‐scale, HZ nitrate dynamics.

Recirculation zones (RZs) are common in many geophysical flows. These zones form near irregular solid boundaries and are separate from the main flow. Since mass can be trapped and later released locally from RZs, bulk transport can exhibit long tails—an anomalous behavior that is challenging to predict. The underlying RZ mass transfer and retention in this situation is poorly understood despite common parameterization by effective exchange coefficients in mobile‐immobile (MIM) domain models. We analyzed the mass transfer process using computationally resolved flow and transport fields inside two‐dimensional rough fractures. RZs were delineated by a novel technique followed by quantification of mass transfer across the interface with the main flow zone. The results showed that the first‐order mass transfer coefficient is a function of Reynolds number and velocity difference between the RZ and bulk flow. A distributed mobile‐immobile model with the directly estimated parameters accurately reproduced bulk anomalous transport. While the distributed mobile‐immobile model is not yet predictive, its development showed that mass transfer coefficients for flows involving RZs are physically meaningful, potentially predictable, and useful for elucidating local mass transfer processes within the general framework of mobile‐immobile transport modeling.

[1] We present a theory for dynamic longitudinal dispersion coefficient (D) for transport by Poiseuille flow, the foundation for models of many natural systems, such as in fractures or rivers. Our theory describes the mixing and spreading process from molecular diffusion, through anomalous transport, and until Taylor

Although nonlinear fracture flow and non-Fickian transport are common in natural settings, the mechanisms driving and controlling these intertwined phenomena are seldom scrutinized together. Here we investigated the critical role of recirculation zones (RZs) in controlling both nonlinear flow and non-Fickian transport through numerical simulation experiments within three-dimensional real fractures. RZs were quantitatively mapped from fully resolved flow fields directly simulated across increasing Reynolds number (Re). The development and growth of RZs, which are related to aperture expansion and contraction, determine the degree of flow nonlinearity. Moreover, expanding RZs have more capacity to capture and later release solutes back to the main flow. This always results in non-Fickian transport with bimodal and sometimes multimodal breakthrough curves (BTCs). The time interval between the BTC modes is related via a power law. The Re and RZ volume are sufficient for characterizing the bimodal BTC. Plain Language Summary Subsurface fluid flow and solute transport are typically described by first-order or linear rate laws. However, deviations from the first-order rate laws (or anomalous behavior) are typical and lead to nonlinear flow and non-Fickian transport phenomena. The shared underlying mechanisms for these "anomalous" flow and transport phenomena, which are actually typical of fractures, are seldom analyzed. We investigated the co-occurrence of nonlinear flow and non-Fickian transport through numerical simulation experiments of pore-scale flow and solute transport processes through three-dimensional natural fractures. In these fractures, 3-D recirculation zones (RZs) developed and grew with increasing flow rates. Flow nonlinearity resulted from the RZ development and growth, which shrank the main flow channel. Moreover, the same RZs also captured solutes from the main flow channel and released them back later. This retardation resulted in non-Fickian transport. Thus, nonlinear flow and non-Fickian transport are intertwined via their shared dependence on RZs.