The reactor in question stores hydrogen in LaNi5, a lanthanum-nickel alloy that absorbs hydrogen reversibly into its crystal lattice. Solid-state storage in metal hydrides is attractive because it packs hydrogen at high volumetric density, operates safely at moderate pressures, and avoids the cryogenic or high-pressure tanks required for gaseous hydrogen. But desorption, the process of releasing hydrogen from the hydride, is endothermic: it consumes heat. If heat cannot reach the reactive bed quickly enough, the reaction slows, part of the bed sits idle, and the reactor’s discharge rate suffers. Thermal management has long been identified as a major obstacle for practical hydride devices.

Previous work had established that inserting conductive metal foams into the hydride bed shortens the thermal path from the heated wall to the reactor core. Among fixed alternatives, a CuCr1Zr foam at 89 percent porosity gave the strongest desorption response, completing discharge in about 10 minutes. The new study asks a more ambitious question: what if the foam is not uniform at all, but instead graded radially, with a dense, highly conductive CuCr1Zr-rich region near the heated wall and a lighter, more permeable AlSi10Mg-rich composition toward the core? The researchers also coupled this structural grading with a transient operating schedule, using stronger heating and lower desorption pressure in the opening minutes before conditions relax to milder values.

To explore this continuous design space, the team developed PG-SADE-GHF, a physics-guided self-adaptive differential evolution framework for graded hybrid foam design. The method parameterizes the foam with smooth radial porosity profiles, spatial alloy allocation, and time-dependent heat-transfer and pressure schedules, all encoded in eight design variables. A self-adaptive differential evolution algorithm, which adjusts its mutation and crossover parameters based on successful trials, searches the space. In an equal-budget stress test, the adaptive variant achieved a lower final diagnostic objective in 29 of 30 paired runs compared with a fixed-parameter version, supporting its use for the search procedure.

Crucially, the study does not rely on a cheap surrogate model for its final claims. The original MATLAB surrogate predicted a desorption completion time of 7.95 minutes for its selected design. But when those exact coordinates were evaluated directly in OpenFOAM, a high-fidelity finite-volume CFD solver, the same design took 12.192 minutes. This 53 percent mismatch is retained transparently in the paper as a negative result, demonstrating that the CFD model was not tuned to recover the desired value. Instead, the researchers re-optimized the same eight variables using actual OpenFOAM evaluations within the original design bounds, arriving at a high-fidelity optimum of 7.817 minutes, only 1.68 percent from the original surrogate magnitude and 21.83 percent faster than the 10-minute uniform CuCr1Zr benchmark.

The team then performed an expanded-bound sensitivity study, widening the engineering envelope for heating intensity, pressure, and schedule duration. This separate extension reached 6.442 minutes, 35.58 percent faster than the uniform reference. Full 360-degree three-dimensional verification on a 196,608-cell mesh confirmed both results, with the expanded-bound wedge, standard full-3D, and high-resolution full-3D calculations all giving identical 6.442-minute completion times. Mesh and time-step independence checks showed maximum deviation of only 0.129 percent from the finest result, confirming that the reported performance is not an artifact of numerical resolution.

Beyond the reactor design itself, the study makes a methodological contribution to how AI-assisted engineering should handle the gap between cheap and expensive models. The researchers trained a CFD-corrected multifidelity model on the difference between surrogate predictions and OpenFOAM outcomes across 32 development designs. They then generated 12 additional Sobol/maximin challenge designs whose predictions were frozen and SHA-256 locked before their CFD outcomes were computed. On this locked held-out challenge, the original surrogate yielded a root-mean-square error of 3.354 minutes, while the CFD-corrected model achieved R-squared of 0.982, RMSE of 0.159 minutes, and 100 percent coverage of the nominal 95 percent prediction intervals. This corresponds to a 95.27 percent RMSE reduction, showing that sparse high-fidelity information can systematically correct low-fidelity bias.

The optimized coordinates reveal why the high-fidelity solution differs from the original surrogate point. OpenFOAM places more CuCr1Zr in the core-side transition, extends the conductive wall zone, uses stronger early heat transfer, and maintains a lower early outlet pressure for longer. These trends suggest a stronger need for heat delivery and desorption driving force than the reduced model estimated. A matched-condition decomposition also prevents over-attribution of the total speed-up to grading alone: within the original bounds, most of the gain comes from operating-schedule optimization, while the expanded design exhibits a larger independent architecture benefit.

The study is careful to distinguish its contribution from prior graded-foam work. Graded porosity itself is not new; previous studies reported roughly 11.5 to 20 percent improvements during hydrogen absorption with gradient-porosity foams. The novelty here is narrower and process-specific: desorption is endothermic and requires sustained heat input while hydrogen pressure is kept below equilibrium, so the design problem couples where conductive material is placed with when heat-transfer intensity and outlet pressure are applied. This simultaneous radial material allocation and transient scheduling, followed by transparent surrogate-to-CFD re-optimization, is the central contribution.

The researchers define a concrete experimental validation pathway rather than leaving future work unspecified. A first prototype should manufacture the conductive outer and more porous inner lattice regions as separately controlled additively manufactured inserts, with X-ray micro-CT and gravimetric measurements verifying porosity, strut dimensions, and pore connectivity. The assembled reactor should be instrumented with radial and axial thermocouples, pressure sensing, and hydrogen mass-flow measurement, with the primary comparison being measured desorption time against the same-bound OpenFOAM prediction. Critical uncertainties include foam-wall and foam-hydride contact resistance, manufactured pore size, alloy-interface behavior, and kinetic drift with cycling. The OpenFOAM model is a porous-continuum representation rather than a pore-resolved strut simulation, and the authors state these limitations explicitly. Experimental validation remains required before the predicted performance can be considered established.

Subject of Research: hydrogen storage

Article Title: Artificial intelligence-assisted design and CFD re-optimization of graded hybrid metal foams for faster hydrogen desorption in LaNi5 metal-hydride reactors

Article References: Djeffal, S., Bendriss, B., Chibani, A., Ghoul, A., Morakchi, M. R., & Rashid, F. L. (2026). Artificial intelligence-assisted design and CFD re-optimization of graded hybrid metal foams for faster hydrogen desorption in LaNi5 metal-hydride reactors. Frontiers in Energy Research, 14, Article 1956543. https://doi.org/10.3389/fenrg.2026.1956543

Image Credits: AI Generated

DOI: 10.3389/fenrg.2026.1956543

Keywords: hydrogen storage, LaNi5, metal hydride, metal foam, CFD, OpenFOAM, differential evolution, surrogate model, desorption, thermal management, additive manufacturing, multifidelity

Most existing models of pollutant transport rely on what mathematicians call Dirichlet boundary conditions. In plain terms, these assume that the concentration of contaminant at the source is known and imposed, as if a valve were holding the chemical at a constant level. That assumption is convenient for solving equations, but it rarely matches reality. Landfill liners leak at rates governed by the mass of waste and the permeability of the barrier. Industrial discharge zones release pollutants according to source strength and release kinetics, not according to a fixed concentration dial. When the real world controls the flux of contaminant entering the soil, a model that prescribes concentration instead can badly distort predictions, particularly near the source where regulators and engineers care most.

The new study addresses this gap by formulating the problem with a Neumann boundary condition, which specifies the rate at which contaminant mass flows into the soil rather than the concentration itself. Li and Liang derived an exact analytical solution for two-dimensional reactive transport in a homogeneous, isotropic porous medium, incorporating advection, hydrodynamic dispersion, linear equilibrium adsorption, first-order decay, and a finite-width line source. According to the authors, no previous closed-form solution had simultaneously combined a Neumann flux boundary, a two-dimensional line source, linear adsorption, and first-order decay. The derivation proceeds by transforming the two-dimensional advection-dispersion equation into an equivalent one-dimensional form and then applying Laplace transforms in both time and space, ultimately yielding a general solution expressed in terms of complementary error functions and source integrals.

What sets the formulation apart is its treatment of desorption. Many classical models treat adsorption as a simple equilibrium process with first-order decay, or handle desorption only as a function of time. The new model introduces directional desorption terms along both the longitudinal and transverse axes, capturing the fact that in real soils, the release of adsorbed metals back into pore water is coupled to concentration gradients and exhibits spatial directionality. Physically, this means that as a plume moves and its concentration field evolves, metals previously locked onto soil particles can be remobilized preferentially along the main transport directions, accelerating migration in ways that simpler models miss entirely.

The researchers tested two release scenarios relevant to landfill leakage. The first is an instantaneous release, modeled with a Dirac delta impulse in time, representing a sudden one-time injection of pollutant along a line within the soil. The second is an exponentially decaying release, in which source strength diminishes over time according to a decay coefficient, a more realistic picture of long-term leakage from a degrading liner. For both cases, the closed-form solution was verified against a finite-element numerical solver, with relative errors below 0.5 percent, confirming that the analytical expression correctly satisfies the governing equations and boundary conditions. Because the solution requires no numerical Laplace inversion or discretization of the boundary condition, it runs quickly and serves as a rigorous benchmark for testing more complex numerical codes.

The simulations, run with parameters typical of sandy aquifers, reveal how strongly chemistry controls the fate of a plume. The single most influential parameter is the retardation factor, which measures how much the soil matrix slows contaminant movement relative to groundwater. A sensitivity analysis showed that a 20 percent increase in retardation reduces the peak concentration by roughly 19.6 percent, a sensitivity index of negative 0.979, by far the dominant effect among the parameters tested. The adsorption coefficient also reduces peak concentrations, though more modestly, while the width of the contaminating line source has only a weak positive influence on peak magnitude and essentially no effect on where the peak occurs. Effective groundwater velocity, meanwhile, mainly shifts the location of the peak rather than changing its height.

Perhaps the most striking results come from the direct comparison between Neumann and Dirichlet boundary conditions. At early times, when the plume has not yet reached the boundary, the two formulations agree closely. But as time passes, they diverge dramatically. By ten days of simulated transport, the Neumann solution retains nearly twice as much mass in the domain as the Dirichlet solution, and the peak concentration ratio climbs to nearly three. The reason is physical: a Dirichlet boundary continuously drains mass from the system, steepening gradients and artificially removing contaminant, whereas the Neumann formulation preserves mass and allows the plume to spread more evenly. Compared with the equivalent Dirichlet model, the Neumann formulation predicts a 22 percent lower peak concentration, a peak located 18 percent farther away, and up to 28 percent lower near-field concentrations at early times. For long-term, dispersion-dominated simulations, the choice of boundary condition is not a technicality; it can flip the answer.

The adsorption-desorption comparison carries practical weight as well. When both processes are included, concentrations decline gradually over time, reflecting a dynamic, reversible exchange between dissolved and adsorbed phases. With adsorption alone, concentrations drop faster because metals are irreversibly retained on solid surfaces. Without either process, the decline is steepest of all, governed only by advection, dispersion, and decay. Desorption, in other words, acts as a slow-release reservoir that keeps contaminant levels elevated long after the source has faded, a mechanism that any credible risk assessment or remediation plan must account for.

To demonstrate real-world relevance, the authors applied the model to a demonstrative case of lead leakage from a landfill. The simulation showed that the plume advances only a few meters over a decade, with concentrations falling below drinking-water limits beyond 20 meters from the source. That kind of quantitative result directly supports the design of buffer zones and monitoring networks around waste facilities, giving engineers a defensible basis for deciding how far a safety perimeter must extend.

The authors are candid about the model’s limits. It assumes homogeneous, isotropic soil, steady uniform flow, linear equilibrium adsorption, and no chemical reactions beyond first-order decay. Natural aquifers violate all of these assumptions to some degree: they are heterogeneous, prone to preferential flow, and often exhibit nonlinear, kinetically limited sorption. Transient recharge and pumping further complicate real flow fields. The researchers therefore position the solution as an effective-medium approximation and a screening tool, valuable for benchmarking numerical codes, conducting preliminary site assessments, and building more elaborate models through superposition of multiple sources. Future extensions could incorporate scale-dependent dispersion, nonlinear desorption isotherms, and time-varying velocities. For now, the work delivers something the field has lacked: an exact, fast, mass-conserving answer to how reactive contaminants spread from a leaking source, and a clear demonstration that the boundary conditions we write into our equations shape, sometimes decisively, the environmental futures we predict.

Subject of Research: Analytical modeling of two-dimensional reactive heavy metal contaminant transport in soil under flux-controlled boundary conditions with landfill leakage application

Article Title: Analytical solution for two-dimensional reactive contaminant transport under a Neumann flux boundary: Adsorption, release mode, and landfill leakage application

Article References: Li, Y., & Liang, R. (2026). Analytical solution for two-dimensional reactive contaminant transport under a Neumann flux boundary: Adsorption, release mode, and landfill leakage application. Results in Engineering, 32, Article 113278. https://doi.org/10.1016/j.rineng.2026.113278

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113278

Keywords: groundwater contamination, heavy metals, advection-diffusion equation, Neumann boundary condition, adsorption, desorption, landfill leakage, analytical solution, retardation factor, soil pollution, contaminant transport, sensitivity analysis

The research, published in the journal Discover Soil by Francesca Pedron and Gianniantonio Petruzzelli of Italy’s National Research Council’s Institute of Research on Terrestrial Ecosystems in Pisa, tackles a question that has been largely ignored: what happens to a soil’s ability to trap cobalt long after compost spreading has stopped? Most studies of organic amendments focus on soils that are actively being treated. The Italian team instead examined soils from a single Tuscan farm where compost applications had ceased either five or ten years earlier, comparing them with a neighboring field that had never received compost at all.

Cobalt occupies an unusual position among trace metals. In tiny amounts it is essential, serving as the metallic core of vitamin B12 and supporting crop growth, but above certain thresholds it becomes harmful to plants, disrupting nutrient transport within cells and producing symptoms such as leaf yellowing, premature leaf drop, reduced photosynthesis, and stunted biomass. It enters soil from natural events such as volcanic eruptions and forest fires, and from human activities including mining, smelting, road traffic, and the manufacture of cobalt-containing alloys and chemicals. Material flow analyses indicate that its dispersion in the environment is increasing as demand for batteries and green technologies accelerates, and recent machine-learning maps of European soils have revealed rising cobalt concentrations in some agricultural areas.

Whether that rising cobalt actually threatens crops and groundwater depends on a set of chemical reactions collectively called sorption, the transfer of dissolved metal ions from soil water onto solid soil surfaces. A soil with strong sorptive capacity holds cobalt immobilized, keeping it away from plant roots and aquifers. A soil with weak sorption lets the metal remain in solution, where it can be taken up by crops or leached away. The researchers hypothesized that compost-induced changes in soil organic matter and acidity would persist long enough to maintain enhanced cobalt sorption for a decade or more, and their experiments were designed to test exactly that.

The three soils came from the plough layer of a farm in the Province of Pisa, in a flat alluvial plain with a Mediterranean climate. Two of them had received green compost, produced from garden trimmings, crop residues, and other plant waste, for eight consecutive years at a rate of five megagrams of dry matter per hectare per year. On one plot, applications stopped ten years before sampling; on another, five years before. The third plot had never been treated. Texture, iron content, and total cobalt concentration were nearly identical across all three soils, but the chemical fingerprints of compost were unmistakable. Organic matter had risen from 1.15 percent in the untreated soil to 2.08 percent in the ten-year-old plot and 3.13 percent in the five-year-old one, while pH had shifted from a slightly acidic 6.25 to near-neutral values around 7.0. Cation exchange capacity, a measure of the soil’s ability to hold positively charged ions, climbed in parallel.

Those differences translated directly into cobalt retention. In laboratory batch experiments, the team shook one-gram soil samples with cobalt nitrate solutions of increasing concentration for twelve hours at controlled temperatures, then measured how much metal disappeared from solution. Fitting the resulting curves to the Langmuir isotherm model revealed maximum sorption capacities of 222 millimoles per kilogram in the five-year soil and 196 in the ten-year soil, against just 141 in the untreated control. The shape of the isotherms, an L-type pattern, showed that at low cobalt concentrations sorption rose almost linearly, indicating that high-affinity binding sites dominate initially; only as those sites fill do weaker domains take over, flattening the curve toward a plateau.

The mechanism behind this enhanced retention lies in the chemistry of compost-derived organic matter. Humified materials introduce abundant carboxyl, phenolic, and hydroxyl functional groups that form stable complexes with divalent cations such as cobalt. The near-neutral pH produced by composting amplifies the effect in two ways: it reduces competition between cobalt ions and hydrogen ions for reactive surfaces, and it encourages the deprotonation of those functional groups, making them more negatively charged and chemically reactive. Experiments that varied the ionic strength of the background solution added a further clue. Sorption in the untreated soil dropped by 40 to 48 percent as ionic strength increased, a signature of weak, electrostatically held outer-sphere complexes. In the compost-amended soils the decline was far smaller, 18 to 22 percent in the five-year soil and 28 to 36 percent in the ten-year one, pointing to a predominance of inner-sphere complexes, in which cobalt coordinates directly and strongly with organic and mineral surfaces.

Thermodynamic analysis reinforced the picture. Across temperatures from 298 to 318 kelvin, the Gibbs free energy of sorption was negative in all soils, confirming a spontaneous process, but the values were most favorable in the compost-amended plots. Enthalpy changes were positive, indicating an endothermic process that likely reflects the energy cost of partially dehydrating cobalt ions and forming specific surface complexes, and entropy changes were negative, consistent with metal ions becoming immobilized on ordered surface sites. The distribution coefficient, a ratio that summarizes how strongly a soil partitions cobalt between solid and solution phases, told the same story: differences among the soils were largest at low cobalt concentrations, precisely the range most relevant to real agricultural contamination, and converged only as high-affinity sites approached saturation.

Perhaps the most striking evidence came from desorption experiments, in which previously loaded soils were challenged with a harsh 0.5 molar calcium chloride solution designed to displace loosely held metal. In the untreated soil, between 1.6 and 24 percent of the sorbed cobalt was released, depending on loading. In the ten-year compost soil the released fraction ranged from 1.2 to 18 percent, and in the five-year soil from just 0.6 to 11 percent. At low cobalt loadings, desorption was minimal in all soils, confirming that the first metal ions to arrive occupy high-affinity sites and are effectively locked in place. The cobalt that resisted even this aggressive extraction can reasonably be considered non-bioavailable, meaning it is unlikely to reach plants or soil microorganisms.

The authors are careful to note the limits of their work. The compost’s own cobalt content was never measured because Italian law does not require it, so a complete mass balance was impossible, although total soil cobalt did not differ among the three plots, suggesting the compost added no detectable metal. Laboratory conditions, with fixed temperatures and equilibration times, cannot fully reproduce the complexity of field soils, including microbial activity, and the results apply specifically to the soils studied rather than to all soil types. Long-term effects will also depend on compost composition, climate, and farming practices. Even so, the central finding stands: in Mediterranean soils, where organic matter decomposes slowly enough to persist for decades, a single decade of composting left a chemical legacy that still suppressed cobalt mobility ten years later. As cobalt demand surges with the ecological transition, the study suggests that the humble practice of returning organic waste to farmland is not merely a fertility tool but a long-term instrument for keeping a critical, and potentially toxic, metal out of the food chain.

Subject of Research: Long-term cobalt sorption and desorption behavior in aged compost-amended Mediterranean agricultural soils

Article Title: Cobalt sorption in aged compost-amended soils

Article References: Pedron, F., & Petruzzelli, G. (2026). Cobalt sorption in aged compost-amended soils. Discover Soil, 3(1), Article 109. https://doi.org/10.1007/s44378-026-00273-2

Image Credits: AI Generated

DOI: 10.1007/s44378-026-00273-2

Keywords: cobalt, compost, soil organic matter, sorption, desorption, Langmuir isotherm, heavy metals, soil chemistry, Mediterranean soils, bioavailability, trace metal contamination, sustainable soil management