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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Formate-Induced Dissolution and Reprecipitation of a Copper Electrocatalyst during Electrochemical CO 2 Reduction Reaction

Catalyst size, morphology, and crystal structure play crucial roles in determining the activity and selectivity of electrochemical CO 2 reduction reactions, which are known to change during the reaction process. A comprehensive understanding of how, when, and why these parameters evolve under operational conditions is essential for developing stable, efficient, and selective catalysts. In this study, we reveal that formate, one of the reaction products, contributes to the degradation of copper catalysts through a ligand-assisted dissolution mechanism. Utilizing in situ electrochemical atomic force microscopy and ex-situ scanning and transmission electron microscopies, we observed a significant reduction in the size of copper nanoparticles, which decreased from over 30 nm to less than 10 nm in diameter within 60 min of CO 2 RR. The temporal production of formate correlated with the particle size changes. Furthermore, analysis of the electrolyte using inductively coupled plasma optical emission spectroscopy confirmed the dissolution of copper nanoparticles. Control experiments involving various reaction products (H 2 , CO, and HCOO – ) demonstrated that formate significantly promotes copper dissolution, thereby highlighting its role in the ligand-assisted dissolution mechanism of copper electrocatalysts. In conclusion, our findings provide critical insights into copper catalyst behavior during electrochemical CO 2 reduction, facilitating the design of more resilient and effective electrocatalysts.

Catalysts↗
DOE OSTI2024

Influence of metal ion complexation on the radiolytic longevity of butyramide extractants under direct dissolution conditions

The direct dissolution of volox-treated used nuclear fuel (UNF) into an organic solution—comprised of diluent and specialized extractants—poses a promising alternative to the traditional liquid-liquid solvent extraction approach to reprocessing UNF. However, moving to direct dissolution removes the presence of a concentrated nitric acid aqueous phase, which has been shown to significantly influence the radiolytic longevity of extractants in liquid-liquid solvent extraction flowsheets. With this in mind, and given the limited knowledge of radiation effects under direct dissolution conditions, we present a time-resolved and dose accumulation study on the impact of direct dissolution conditions on the radiolytic longevity of two candidate butyramide extractants—N,N-di-(2-ethylhexyl) butyramide (DEHBA) and N,N-di-(2-ethylhexyl)isobutyramide (DEHiBA)—in pre-equilibrated n-dodecane solvent in the presence and absence of process relevant metal ions, uranium and rhenium. Rhenium, and by extension technetium, extraction had little impact (=10%) on the overall radiolytic stability of these ligands, despite observed increases in chemical kinetic reactivity (>2×) of the corresponding complexes with the n-dodecane radical cation. Uranium-loading on the other hand, significantly improved the lifetime of both ligands (>30%) under gamma irradiation, with a greater stabilization observed for DEHBA over DEHiBA. This draft manuscript has been prepared in fulfillment of NTRD-MRWFD-2024 M3FT-24IN030101115.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2025

Learning the factors controlling mineral dissolution in three-dimensional fracture networks: applications in geologic carbon sequestration

We perform a set of high-fidelity simulations of geochemical reactions within three-dimensional discrete fracture networks (DFN) and use various machine learning techniques to determine the primary factors controlling mineral dissolution. The DFN are partially filled with quartz that gradually dissolves until quasi-steady state conditions are reached. At this point, we measure the quartz remaining in each fracture within the domain as our primary quantity of interest. We observe that a primary sub-network of fractures exists, where the quartz has been fully dissolved out. This reduction in resistance to flow leads to increased flow channelization and reduced solute travel times. However, depending on the DFN topology and the rate of dissolution, we observe substantial variability in the volume of quartz remaining within fractures outside of the primary subnetwork. This variability indicates an interplay between the fracture network structure and geochemical reactions. We characterize the features controlling these processes by developing a machine learning framework to extract their relevant impact. Specifically, we use a combination of high-fidelity simulations with a graph-based approach to study geochemical reactive transport in a complex fracture network to determine the key features that control dissolution. We consider topological, geometric and hydrological features of the fracture network to predict the remaining quartz in quasi-steady state. We found that the dissolution reaction rate constant of quartz and the distance to the primary sub-network in the fracture network are the two most important features controlling the amount of quartz remaining. This study is a first step towards characterizing the parameters that control carbon mineralization using an approach with integrates computational physics and machine learning.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

How exudates production along a phosphorus gradient influences mineral dissolution across contrasting soil development stages

Harnessing rhizosphere processes offers a valuable opportunity to optimize nutrient use efficiency in agroecosystems. In nutrient-limited soils, plants discharge part of photosynthate surplus via root exudation, including carboxylates, which may enhance mineral dissolution and nutrient mobilization. We aimed to assess how plant responses to nutrient limitation translated into changes in exudate profiles, and how these exudates, in turn, drive bioweathering processes across soils of contrasting mineralogy and weathering degree. We conducted a hydroponic experiment with Lupinus albus grown under five phosphorus (P) concentrations (5, 10, 20, 30, and 50 µM) over seven weeks. We measured plant biomass and root traits, performed a metabolomics analysis and quantified seven carboxylates in root exudates using gas chromatography-mass spectrometry. To assess bioweathering processes across contrasted soil domains, we conducted batch dissolution tests with exudates using three soil horizons—35 each with distinct physicochemical properties: enriched in organic matter, iron oxides, or primary silicates. At the intermediate level of P supply, shoot biomass was comparable to that under high P, but plants produced more root biomass and a higher total carboxylate exudation rate. Despite low carboxylate concentrations (<100 ppb), exudates promoted the dissolution of Ca, Mg, Si, Fe, P and K in all horizons. Yet, the degree of element released varied among horizons. These findings highlight the importance of root exudates in enhancing mineral dissolution, with effects dependent on soil physicochemical properties. The results suggest that managing agroecosystems under moderate nutrient limitation could be a sustainable strategy to increase root-to-shoot ratios, enhance bioweathering processes and nutrient release in soil solution.

Pollet, Sasha L.↗
DOE OSTI2026

Cobalt Dissolution from Metal Oxides and Battery Cathode Materials with Acetic Acid-Based Deep Eutectic Solvents

Recovery of critical metals with alternative solvents beyond those in traditional pyrometallurgy and hydrometallurgy is needed in consideration of environmental challenges and the growing demand for metals in energy technologies. Deep eutectic solvents (DESs) have emerged as sustainable alternatives for solvometallurgy in metal separation and recovery. In this study, DESs based on hydrogen bond acceptors (HBAs) including choline chloride (ChCl), acetylcholine chloride (AChCl), and betaine (Bet) were investigated for their effectiveness when paired with acetic acid (AA) as the hydrogen bond donor (HBD) for the dissolution of cobalt from cobalt oxide (CoO), lithium cobalt oxide (LiCoO 2 ), and lithium nickel manganese cobalt oxide (LNMC). Based on the spectroscopic analysis of the metal dissolution and coordination, Bet:AA was found to provide the highest solubility for CoO (0.33 M) in the form of an octahedral complex. On the other hand, ChCl:AA solvent was more effective at dissolving LiCoO 2 with 0.04 M Co 2+ corresponding to 17% dissolution efficiency and LNMC with 0.06 M Co 2+ corresponding to 72% dissolution efficiency at 50 °C, compared to Bet:AA (9% for LiCoO 2 and 31% for LNMC). Although the solubilities of LiCoO 2 and LNMC have not significantly improved in ChCl:AA, this difference in effectiveness between the solvents clearly reveals the role of the HBA in solubilization. The coordination synergy between the chloride and the –OH moiety facilitates the breakdown of the LiCoO 2 driven by the alteration of the solvent polarity. Cobalt in these solutions was found dominantly as a tetrahedral [CoCl 4 ] 2– complex. A chemical separation of cobalt oxalate from a mixed-metal oxide system based on Co, Fe, and Ni was also demonstrated, confirming the potential of these solvents for practical metal recovery.

Cobalt separation↗
DOE OSTI2026

Kinetic Pathways to Diblock Copolymer Micelles via Thin Film Dissolution and Cosolvent Variation

We investigate how processing pathways control micelle formation during dissolution of lamellar diblock copolymers using dissipative particle dynamics (DPD) simulations and DPD-selfconsistent field theory (DPD-SCFT). Comparing thin film (TF) and cosolvent-assisted (CS) dissolution reveals fundamentally different micellization mechanisms and final states. In the TF pathway, dissolution proceeds through a metastable cylindrical intermediate that dictates final micelle dimensions. The lamellar melt first transforms into cylindrical micelles, which then fragment into spherical micelles. The final spherical radius is intrinsically linked to the cylinder radius by a constant ratio, Rsphere ≈ 1.4Rcylinder. DPD-SCFT confirms that both cylinders and spheres are near their equilibrium dimensions. In contrast, CS dissolution produces kinetically trapped micelles with sizes significantly below equilibrium. Micellization is hindered by high free energy barriers to single-chain exchange and fusion. Growth occurs primarily via fusion, but increasing corona repulsion suppresses further coarsening, preventing equilibration. These results demonstrate that, when starting from a bulk copolymer phase, the metastable cylindrical intermediate plays a central role in determining final micelle size.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Ion-Specific Effects on PuO 2 Nanoparticle Aggregation and Dissolution in Concentrated Electrolytes

Hydrolytic PuO 2 nanoparticles (NPs) are a dominant aqueous Pu-bearing phase in high ionic strength nuclear wastes, yet their reactivity in nonideal brines remains poorly constrained. We quantify how electrolyte identity and concentration control PuO 2 NP aggregation and ligand-assisted dissolution in acidic, high salinity solutions (NaCl, NaNO 3 , NaClO 4 , Na 2 SO 4 , Na 2 C 2 O 4 up to 5 M). A multitechnique workflow combining liquid scintillation counting (operationally defined aqueous [Pu]), scattering/electrokinetic measurements (aggregate size and zeta potential), and spectroscopy (UV–vis, XPS, Raman) resolves electrolyte-dependent partitioning between colloidal and molecular Pu species. Weakly coordinating anions (ClO 4 – , Cl – , NO 3 – ) largely preserve the (aggregated) nanoparticulate fraction but generate distinct dissolved species at high concentration, i.e., Pu(IV)–nitrato complexes in NaNO 3 and Pu(VI)–chloro complexes in NaCl. In contrast, stronger ligands substantially perturb PuO 2 NP stability: sulfate promotes partial dissolution to Pu(IV)–sulfate complexes at low concentration but reduces aqueous [Pu] at higher sulfate levels via secondary Pu(IV) sulfate formation, whereas oxalate drives strong dissolution to aqueous Pu–oxalate complexes. Aged NPs show similar trends with reduced aqueous fractions and more dominant aggregation mechanisms. In conclusion, these spectroscopically constrained speciation data provide a foundation for incorporating PuO 2 NP reactivity into thermodynamic and reactive transport models for high salinity waste and brine environments.

Aggregation↗
DOE OSTI2024

Incorporation of trace metals in Hanford waste boehmite mineral phases and dissolution rate impacts

Abstract Data from radioactive Hanford tank waste samples was analyzed to assess whether trace metals present were incorporated into the bulk boehmite matrix or were simply intermingled with the bulk material and subsequent impacts to the boehmite dissolution rate. Results suggest that chromium is primarily blended into the bulk boehmite, with a small fraction present on the surface of the solids. However, increasing the level of chromium incorporation 30‐fold decreased the dissolution rate of boehmite by only 8%, suggesting incorporation of chromium into these samples had a minimal impact on the dissolution rate. Iron was also found to be incorporated in the boehmite solids. Silicon appears to be simply intermingled and not blended into the boehmite crystals.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2025

Dissolution of Nb(C,N) and (Ti,V)N in the Coarse-Grained Heat-Affected Zone of Electric Resistance Welded X65 Line Pipe

Nb-rich and Ti/V-rich precipitates were introduced into the X65 linepipe via thermomechanical controlled processing. Their dissolution kinetics were investigated in the coarse-grained heat-affected zone after electric resistance welding. Nb-rich precipitates were found to dissolve completely, whereas Ti/V-rich precipitates were found to dissolve partially, because of slower dissolution kinetics. In conclusion, a complete dissolution of Nb-rich precipitates was associated with significant austenite grain coarsening, which promoted bainite as a quench product, which might have reduced the impact toughness.

microstructure↗
DOE OSTI2024

Concurrent measurement of strain and chemical reaction rates in a calcite grain pack undergoing pressure solution: Evidence for surface-reaction controlled dissolution

Pressure solution is inferred to be a significant contributor to sediment compaction and lithification, especially in carbonate sediments. For a sediment deforming primarily by pressure solution, the compaction rate should be directly related to the rate of calcite dissolution, transport along grain contacts, and calcite reprecipitation. Previous experimental work has shown that there is evidence that deformation in wet calcite grain packs is consistent with control by pressure solution, but considerable ambiguity remains regarding the rate limiting mechanism. We present the results of laboratory compaction experiments designed to directly measure calcite dissolution and precipitation rates (recrystallization rates) concurrently with strain rate to test whether measured rates are consistent with predicted rates both in absolute magnitude and time evolution. Recrystallization rates are measured using trace element chemistry (Sr/Ca, Mg/Ca) and isotopes (87Sr/86Sr) of fluids flowing slowly through a compacting grain pack as it is being triaxially compressed. Imaging techniques are used to characterize the grain contacts and strain effects in the post-experiment grain pack. Our data show that calcite recrystallization rates calculated from all three geochemical parameters are in approximate agreement and that the rates closely track strain rate. The geochemically inferred rates are close to predicted rates in absolute magnitude. Uncertainty in grain contact dimensions makes distinguishing between surface reaction control and diffusion control difficult. Measured reaction rates decrease faster than predicted from standard pressure solution creep flow laws. This inconsistency may indicate that calcite dissolution rates at grain contacts are more complex, and more time-dependent, than suggested by geometric models designed to predict grain contact stresses.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Solvation-guided inhibition of manganese dissolution of lithium- and manganese- rich cathode via cyclic carbonate molecular engineering

Lithium and manganese-rich (LMR) layered oxides represent a leading class of high-energy cathode materials, but their practical realization is fundamentally limited by severe manganese (Mn) dissolution, a process that triggers structural degradation and rapid capacity fade. While mitigation efforts have predominantly focused on interfacial engineering, the intrinsic contribution of bulk electrolyte solvation to this degradation pathway remains largely unexplored, primarily due to the difficulty of deconvolving its effects from concurrent cathode-electrolyte interphase (CEI) formation. Here, we report an experimental design to isolate the role of solvation. We systematically varied the electrolyte solvent solvation power by substituting the strongly coordinating ethylene carbonate (EC) with its weaker coordinating fluorinated derivatives, fluoroethylene carbonate (FEC) and trans-4,5-Difluoro-1,3-dioxolan-2-one (DFEC), while maintaining a consistent interfacial chemistry. Remarkably, the electrolyte formulated with the weakest solvent, DFEC, exhibits superior cycling stability, suppressing Mn dissolution by up to 63% relative to the conventional EC-based system. Post-mortem analysis unequivocally attributes this performance enhancement to the preservation of the LMR cathode's structural integrity, a direct consequence of mitigated Mn dissolution. This work provides conclusive evidence that modulating bulk electrolyte solvation is a potent and direct strategy for stabilizing LMR cathodes, establishing a vital design principle for next-generation battery systems.

25 ENERGY STORAGE↗
DOE OSTI2024

Speciation and Aqueous Dissolution of Macronutrients in Fire Ash: Variation across Ecosystems and the Effects on Nutrient Cycling

This study investigated the speciation and aqueous dissolution of macronutrients in fire ash from diverse ecosystems and speciation of ash and smoke from laboratory burning, exploring the variations and their causes. The speciation of phosphorus (P), calcium (Ca), and potassium (K) in fire ash from five globally distributed ecosystems was characterized by using X-ray absorption spectroscopy and sequential fractionation. Aqueous dissolution of the macronutrients was measured by batch experiments at acidic and alkaline pHs. The results showed that P existed mainly as Ca phosphates, Ca as double carbonates, calcite, and sulfates, and most K was associated with Ca carbonates. Mineralogy and the relative abundance of the species were primarily controlled by elemental stoichiometry and fire temperature. Differences in Ca and P speciation existed between ash and smoke from laboratory burning, possibly caused by the temperature difference and/or mass fractionation during burning. The rates, extents, and pH dependencies of macronutrient dissolution differed among macronutrients and depended on their speciation, with K being highly soluble and the P and Ca regulated by solution pH. The variability in ash macronutrient chemistry and ecosystemspecific fire ash loads resulted in varying loads and availability of individual macronutrient from fire among ecosystems. This study provides a mechanistic understanding of how fires transform the chemistry of macronutrients and affect macronutrient returns to soils across different ecosystems, which is essential for evaluating the disturbance to ecosystem nutrient cycling by fires.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Reconstruction and Dissolution of Copper Catalysts during Electrocatalytic Nitrate Reduction

Copper-based electrocatalysts are widely explored for electrochemical nitrate remediation, yet their stability under operating conditions remains poorly understood. While nanoscale and subnanoscale Cu motifs are known to restructure during the nitrate reduction reaction (NO 3 RR), how these transformations translate into irreversible material loss remains unclear. Here, we quantify Cu dissolution during NO 3 RR as a function of catalyst architecture and electrolyte chemistry using two model systems: single-atom Cu (Cu 1 ) and Cu nanoparticles (Cu NP ). Time-resolved leaching measurements, integrated with in situ X-ray absorption spectroscopy (XAS), reveal measurable Cu loss for both catalysts during NO 3 RR. Dissolution is concentrated at the initiation of electrolysis, coinciding with rapid restructuring, and depends strongly on morphology, with Cu NP consistently exhibiting greater Cu loss than Cu 1 . In situ XAS reveals that Cu 1 forms transient metallic clusters under reduction that largely redisperse upon returning to open-circuit voltage, whereas Cu NP undergoes reduction of an oxidized surface layer accompanied by sustained Cu loss during electrolysis. Notably, the presence of nitrate significantly intensifies restructuring and Cu loss, highlighting the critical role of electrolyte composition. Furthermore, these findings establish a direct link between electrochemical restructuring and Cu dissolution, unveiling electrolyte-dependent interactions as key determinants of catalyst durability in electrochemical nitrate conversion.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Effects of Dissolution Regimes on Flow Channelization and Solute Transport in 3D Fracture Networks: Insights From Graph‐Based Reactive Transport Modeling

We investigate how mineral dissolution reshapes flow pathways and solute transport in three‐dimensional discrete fracture networks using a computationally efficient graph‐based reactive transport model. The DFNs are inspired by field‐site observations of fractured carbonate and represent realistic connectivity and structural heterogeneity. Flow is simulated with the Reynolds equation, and dissolution follows first‐order kinetics with diffusive limitations captured through an effective mass‐transfer coefficient. By systematically varying two key dimensionless parameters, the effective Damköhler number (Da), governing reaction versus advection rates, and a transport parameter (Da), analogous to the Thiele modulus, distinct flow channelization regimes emerge: mildly channelized at low G, highly channelized at intermediate Da, and extreme wormhole formation at high Da and low G. Eulerian and Lagrangian analyses, including breakthrough curves, particle tortuosity, dispersivity, and flow channeling indicators quantitatively characterize the progression of dissolution‐driven network restructuring. Across all regimes, initial fracture heterogeneity persists. The results underscore how the interplay between this initial structure, advection, reaction, and diffusion critically shapes subsurface flow pathways, with implications for applications ranging from groundwater remediation to enhanced geothermal systems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Atomic-scale understanding of oxide growth and dissolution kinetics of Ni-Cr alloys

Aqueous corrosion of metals is governed by formation and dissolution of a passivating, multi-component surface oxide. Unfortunately, a detailed atomistic description is challenging due to the compositional complexity and the need to consider multiple kinetic factors simultaneously. To this end, we combine experiments with a first-principles-derived, multiscale computational framework that transcends thermodynamic descriptions to explicitly simulate the kinetic evolution of surface oxides of Ni-Cr alloys as a function of composition, temperature, pH, and applied voltage. In the absence of pitting, we identify three distinct voltage regimes, which are kinetically dominated by oxide growth, dissolution, and competitive dissolution and reprecipitation. Evolving compositional gradients and oxide thickness are revealed, including a transition between a metastable Ni-Cr mixed oxide and a thick, porous Ni-dominated oxide. Beyond elucidating the underlying physics, we highlight the need for competing kinetics in models to properly predict the transition from passivation to corrosion. Our results provide a key step towards co-design of alloy composition alongside environmental conditions for sustainable use across a variety of critical energy and infrastructure applications.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Toward the performance assessment of advanced nuclear waste forms: temperature dependence of lanthanide borosilicate glass dissolution

Lanthanide borosilicate (LaBS) glasses are among the most promising waste forms for the immobilization of high-level radioactive waste generated from advanced nuclear fuel cycles. However, the temperature dependence of their dissolution kinetics remains poorly understood and constrained, limiting the integration of these materials into established performance assessment models. Here, we investigate the dissolution behavior of the legacy AmCm2-19 LaBS glass and the benchmark alkali aluminoborosilicate ISG-1 in deionized water between 50 °C and 250 °C using ASTM C1285 (Product Consistency Test-B) protocols. For AmCm2-19 LaBS glass, normalized elemental release rates for boron and silicon increase with temperature before plateauing near 150 °C, consistent with solubility-limited behavior. From data obtained at 50 °C and 100 °C, Arrhenius analysis yields activation energies of E a (B) = 24.8 ± 0.3 kJ mol⁻¹ and E a (Si) = 14.4 ± 0.2 kJ mol⁻¹, similar or slightly lower than those previously reported for two other compositions of LaBS glasses. No secondary phases or alteration layers were detected by SEM-EDX or pXRD. These results establish one of the first temperature-dependent kinetic datasets for LaBS glass dissolution, providing quantitative parameters to inform mechanistic corrosion models and predictive simulations of glass degradation in geological disposal environments.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2025

Elucidating the reversible exsolution–dissolution behaviour of high-entropy oxides in crystalline and amorphous phases

High-entropy oxides (HEOs), as a subclass of high-entropy materials (HEMs), offer a versatile platform for catalysis by leveraging entropy-stabilized solid solutions with tunable compositions, lattice structures, and electronic properties. While exsolution–dissolution of metal species in crystalline HEOs has emerged as a promising strategy for reversible active sites regeneration, the dynamic behaviour of HEOs possessing amorphous nature remains under-explored, particularly the difference with crystalline counterparts. In this work, we systematically investigate the architecture-dependent exsolution–dissolution behavior of HEOs by comparing a crystalline-phase HEO (c-HEO) and an amorphous-phase HEO (a-HEO), both comprising Ni, Mg, Cu, Zn, and Co as principal metal elements. Using a combination of in situ variable-temperature X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), electron microscopy, and in situ CO diffuse reflectance infrared Fourier transform spectroscopy (CO-DRIFTS), the structural evolution of the two HEO phases under redox conditions was elucidated. Both materials exhibit reversible exsolution of metallic species or alloys in reducing environments, followed by re-incorporation into the host lattice upon oxidation. Remarkably, the a-HEO demonstrates more facile and dynamic self-healing behavior, with alloy exsolution and dissolution occurring under milder conditions because of its enhanced reducibility and structural disorder. This study provides critical insights into the design of next-generation regenerable catalysts based on amorphous HEOs, highlighting the role of phase structure in governing reversible metal-site formation dynamics and catalytic performance.

Wang, Qingju [Univ. of Tennessee, Knoxville, TN (U↗
DOE OSTI2025

Invariant Forms of Dissolution Fingers

Dissolution of fractured and porous media introduces a positive feedback between fluid flow and reactant transport, leading to the emergence of pronounced, fingerlike channels. We investigate the formation of these structures using a microfluidic Hele-Shaw cell with a soluble bottom. Our experiments show that the shape of dissolution fingers is invariant and reveals itself over time as the fingers extend into the system. Here, by combining reactive-transport theory and conformal mapping techniques we derive these invariant forms. We relate these results to natural dissolution fingers in karst landscapes, and illustrate how to determine the groundwater flow rate responsible for their formation based on the finger shape.

Flows in porous media↗