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Keywords = immiscible fluids

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16 pages, 7964 KB  
Article
Ore Textures and the Late Exsolution of Troilite from Pyrrhotite, Iken Nickel Deposit, Kun-Manie Complex, Amur Oblast, Russian Far East
by Andrei Y. Barkov, Ivan I. Nikulin, Robert F. Martin and Boris M. Lobastov
Minerals 2026, 16(7), 665; https://doi.org/10.3390/min16070665 (registering DOI) - 24 Jun 2026
Abstract
The magmatic Ni-Co-Cu mineralization in the Iken deposit in the central part of the Kun-Manie complex, Amur Oblast, Russia, hosted by an olivine-bearing websterite, is of a low-sulfide type. The fine-grained disseminations of base metal sulfides (BMS), dominantly pyrrhotite, pentlandite (a major source [...] Read more.
The magmatic Ni-Co-Cu mineralization in the Iken deposit in the central part of the Kun-Manie complex, Amur Oblast, Russia, hosted by an olivine-bearing websterite, is of a low-sulfide type. The fine-grained disseminations of base metal sulfides (BMS), dominantly pyrrhotite, pentlandite (a major source of Ni of industrial importance), and chalcopyrite, are followed by a scarce Pd-Pt-Ag mineralization. Elevated contents of Al in orthopyroxene (mean 2.78 wt.% Al2O3) along with Al–Na enrichment in clinopyroxene (diopside; mean 5.10 wt.% Al2O3) are associated with highly aluminous compositions of low-chromium members of the spinel–hercynite series. High levels of TiO2 in kaersutite and titanian phlogopite also reflect a pronounced degree of fractionation of the ore-forming melt. Minor portions of sulfide melt are distributed evenly as a result of immiscibility at advanced stages of orthopyroxene crystallization, after the formation of olivine. Differentiated grains of droplet-like BMS largely settled in situ close to grain boundaries of orthopyroxene or occupied interstitial spaces of pyroxenes and olivine in association with spinel–hercynite and fluorapatite. A combination of late saturation in S with relatively quick cooling rates of the hypabyssal body prevented the effective settlement and accumulation of sulfide droplets in the ore zone. The well-developed lamellae of troilite (Fe50S50) exsolved from the host pyrrhotite Fe48S52 during subsolidus cooling, as a consequence of a low-temperature reaction triggered by a sudden drop in fO2. An influx of mantle-derived fluid bearing CO2, CO, and CH4 with the rising magma could be the primary cause of the fO2 reduction. Also, graphite-bearing metasedimentary rocks could have been assimilated. Tiny grains of minerals of noble metals (moncheite and merenskyite with essential amounts of melonite component, sperrylite, hessite, alloy Au63.2Ag36.8, and argentopentlandite) deposited late in a fluid-enriched medium under submagmatic conditions. Full article
(This article belongs to the Section Mineral Deposits)
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37 pages, 4303 KB  
Article
Nonlinear Dynamics of Displacement Fronts in Two-Phase Flows Propagating Through Porous Media
by Diana Kerimbekova, Almatbek Kydyrbekuly, Julius Kaplunov and Altynshash Naimanova
Mathematics 2026, 14(11), 2000; https://doi.org/10.3390/math14112000 - 4 Jun 2026
Viewed by 334
Abstract
A generalized mathematical model is constructed to describe the isothermal two-phase flow of a three-component system and to investigate light non-aqueous phase liquid (LNAPL) displacement during surfactant-enhanced remediation in vertical porous media. The model integrates the dominant physical mechanisms governing immiscible fluid redistribution, [...] Read more.
A generalized mathematical model is constructed to describe the isothermal two-phase flow of a three-component system and to investigate light non-aqueous phase liquid (LNAPL) displacement during surfactant-enhanced remediation in vertical porous media. The model integrates the dominant physical mechanisms governing immiscible fluid redistribution, including gravitational and capillary forces under different wettability conditions. The hyperbolic part of the system is analyzed within the framework of a Riemann problem, allowing for the characterization of shock and rarefaction wave formation in saturation and concentration profiles. Numerical simulations performed using a first-order upwind (FOU) scheme reveal pronounced artificial dissipation, as confirmed by von Neumann stability analysis. To overcome this limitation, a high-order non-oscillatory scheme based on nonlinear flux limiters and polynomial reconstruction is developed, enabling accurate resolution of sharp displacement fronts. A comparative analysis of limiter functions reveals that their suitability depends on the degree of nonlinearity in relative phase permeabilities, highlighting the necessity for careful selection in multiphase flow modeling. Parametric investigations quantify the effects of gravity, capillary parameters, Peclet number, and wettability alteration on displacement efficiency in homogeneous porous media. The proposed framework is validated against experimental MRI data, demonstrating its reliability for describing two-phase displacement in porous media. Overall, the developed numerical model provides a predictive framework for resolving nonlinear front dynamics and optimizing surfactant-enhanced remediation strategies in contaminated subsurface reservoirs. Full article
(This article belongs to the Section E: Applied Mathematics)
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24 pages, 15341 KB  
Article
Ore Genesis of the Shizui Cu-Pb-Zn Deposit in Central Jilin Province, NE China: Constraints from Geology, Fluid Inclusions, H–O Isotopes Studies
by Zhibo Ge, Wenqiang Bai, Haoran Li, Yunsheng Ren, Chan Li, Bin Wang, Haozhe Li, Sitong Chen and Qun Yang
Minerals 2026, 16(6), 579; https://doi.org/10.3390/min16060579 - 27 May 2026
Viewed by 385
Abstract
The Shizui Cu–Pb–Zn deposit is located in central Jilin Province. It sits at the tectonic junction between the eastern Xing’an–Mongolia Orogenic Belt (XMOB) and the northeastern North China Craton (NCC). This is the first discovered Paleozoic Cu-polymetallic deposit in the region. Our study [...] Read more.
The Shizui Cu–Pb–Zn deposit is located in central Jilin Province. It sits at the tectonic junction between the eastern Xing’an–Mongolia Orogenic Belt (XMOB) and the northeastern North China Craton (NCC). This is the first discovered Paleozoic Cu-polymetallic deposit in the region. Our study combines detailed geological investigation with systematic fluid inclusion analysis. We analyzed samples from four distinct paragenetic stages. Analytical methods include microthermometry, laser Raman spectroscopy, and hydrogen-oxygen isotope analysis. These data constrain the source, evolution, and precipitation mechanisms of the ore-forming fluids. The results delineate a clear evolutionary path: the ore-forming fluid originated as a high-temperature (346–437 °C), high-salinity (up to 51.68 wt.% NaCl equiv.) NaCl–H2O–CO2 system during the early quartz-sulfide stage (Stage I, Quartz ± Arsenopyrite ± Pyrite Stage), as evidenced by the coeval presence of high-salinity S-type and CO2-rich C-type inclusions, indicating fluid immiscibility. The fluid then evolved into a boiling, medium temperature to high temperature (262–355 °C), high-salinity NaCl–H2O system during the later part of early quartz-sulfide stage (Stage II, Quartz-Cu Polymetallic Sulfide Stage), a transition marked by the common coexistence of liquid-rich (L-type) and vapor-rich (V-type) inclusions with similar homogenization temperatures. This phase separation (boiling) served as the primary trigger for the massive deposition of chalcopyrite, arsenopyrite, and pyrite. Subsequently, the system cooled and diluted, transforming into a medium- to low-temperature (182–275 °C), low-salinity, partially homogeneous NaCl–H2O system in the late quartz-sulfide stage (Stage III, Quartz-Pb-Zn Polymetallic Sulfide Stage). Finally, in the quartz-carbonate stage (Stage IV, Quartz-Carbonate Stage), the fluid temperature further decreased, resulting in a low-temperature (128–211 °C), low-salinity, homogeneous NaCl–H2O system. Hydrogen-oxygen isotope data show that the calculated δ18OH2O values decreased from +6.6‰ to +6.7‰ in Stage I to +3.4‰ to +3.9‰ in Stage II, and further to −0.4‰ in Stage III, while the δD values shifted from −91.6‰ to −90.6‰, to −94.4‰ to −94.2‰, and finally to −95.7‰. This trend indicates that the initial magmatic fluid progressively mixed with meteoric water. The geological characteristics, spatial association with Hercynian biotite monzogranite, developed skarn alteration, and the documented fluid evolution trajectory collectively affirm that the Shizui deposit is a typical skarn-type system. The deposit shares significant similarities in mineralization conditions, age, and tectonic setting with the skarn-type Tianbaoshan Pb–Zn–Cu–Mo deposits in the western segment of the XarMoron–Changchun Metallogenic Belt (XCMB). This correlation strongly suggests that the Paleozoic XCMB extends eastward and holds considerable potential for the discovery of late Paleozoic skarn-type Cu-polymetallic deposits in its eastern part. Full article
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26 pages, 49843 KB  
Article
Lamprophyre Zircon Geochronology and Pyrite–Arsenopyrite S-Fe Isotopes: Implications for Magmatic Mineralization at the Jinshan Gold Deposit, Western Qinling Metallogenic Belt
by Hang Li, Zhongkai Xue, Jianxiang Luo, Cheng Ma, Kang Yan, Li Chen, Haiyang Wang, Xutao Yang and Haomin Guo
Geosciences 2026, 16(6), 208; https://doi.org/10.3390/geosciences16060208 - 22 May 2026
Viewed by 370
Abstract
The lamprophyre dikes and multi-generational pyrite and arsenopyrite developed in the Jinshan gold deposit in the West Qinling metallogenic belt provide critical evidence for understanding the role of mantle-derived magmatism in gold mineralization processes. In this study, we conducted zircon U-Pb dating of [...] Read more.
The lamprophyre dikes and multi-generational pyrite and arsenopyrite developed in the Jinshan gold deposit in the West Qinling metallogenic belt provide critical evidence for understanding the role of mantle-derived magmatism in gold mineralization processes. In this study, we conducted zircon U-Pb dating of lamprophyre to constrain the timing of magmatic activity and the mineralization age, and performed EMPA and LA-ICP-MS analyses on sulfides from the main metallogenic stage (Py II–III, Apy II–III) and lamprophyre-hosted pyrite (Py L) to constrain the formation conditions and metal sources of the Jinshan deposit. The results show that the mantle-derived magmatism represented by lamprophyre yields an age of 206 ± 2 Ma, which provides a lower-limit constraint on the timing of gold mineralization, corresponding to the subduction-to-extension transition period in the region. Stage II mineralization occurred at 270–320 °C with logƒS2 of −9 to −5, dominantly as Au-HS complexes, indicating medium-temperature hydrothermal conditions with low sulfur fugacity, consistent with microscopic mineral assemblages and thermodynamic simulations. Systematic δ34S variations reveal: stage II values (9.24–5‰) indicate granitic/Devonian sedimentary sources; Py L values (2.19–3.6‰) reflect mantle contributions; stage III signatures (−2.3–1.93‰) record late meteoric water mixing. Complementary δ56Fe data show that Py II (0.2–0.3‰) and Py L (0.58–0.68‰) preserve magmatic fingerprints, while negative values of Py III (−2.29 to −0.71‰) document increasing sedimentary Fe incorporation. Combined with geochronology, S-Fe isotopes, and physicochemical constraints, we propose that the Jinshan gold deposit formed in a tectonic setting transitioning from compression to extension during the Late Indosinian (ca. 237–201 Ma). Mineralization was initiated by the partial melting of the metasomatized mantle, where hydrous magmas efficiently extracted Au and volatiles. These components ascended through transcrustal faults, with Au partitioning into exsolved fluids that precipitated gold through immiscibility and boiling in secondary structures. Full article
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25 pages, 3344 KB  
Article
Buckley–Leverett Solution for Two-Phase Displacement in a Composite Porous–Cavernous–Porous System
by Fang-Fang Chen, Xu-Jian Jiang, Ting Yan, Xiao-Ping Ma, Zhen-Yu Zhang, Ming-Jie Li and Zhao-Qin Huang
Energies 2026, 19(10), 2463; https://doi.org/10.3390/en19102463 - 20 May 2026
Cited by 1 | Viewed by 342
Abstract
Fluid flow in fractured-vuggy carbonate reservoirs is characterized by extreme multiscale heterogeneity, where the coexistence of tight matrix rock and macroscopic cave challenges traditional Darcy-based continuum models. This paper presents a semi-analytical solution for two-phase immiscible displacement in a one-dimensional composite porous–cavernous–porous (PCP) [...] Read more.
Fluid flow in fractured-vuggy carbonate reservoirs is characterized by extreme multiscale heterogeneity, where the coexistence of tight matrix rock and macroscopic cave challenges traditional Darcy-based continuum models. This paper presents a semi-analytical solution for two-phase immiscible displacement in a one-dimensional composite porous–cavernous–porous (PCP) system. The main feature of the model is that the cave region is treated separately from the porous domains: classical Darcy flow is used in the surrounding matrix, whereas an idealized free-flow representation is introduced for open caves based on a simplified one-dimensional treatment of the cave momentum balance. To elucidate the impact of distinct flow regimes on displacement dynamics, three physical models are compared for the cave region: (1) an open-cave model represented by a simplified free-flow formulation; (2) a filled-cave non-Darcy model governed by the Forchheimer equation using the Ergun correlation; and (3) a creeping-flow model governed by Darcy’s law. A piecewise semi-analytical solution procedure is established to enforce flux continuity, characterize interfacial state remapping, and determine the downstream front under global water-balance closure. The results show that both cave geometry and internal cave-flow mechanism critically control water-front advancement. While the open-cave model exhibits piston-like displacement behavior with high local displacement efficiency but stronger preferential flow, the Forchheimer model shows that inertial resistance can modify the saturation profile and delay breakthrough relative to the Darcy prediction. The proposed framework provides an idealized theoretical reference for benchmarking numerical simulators and for interpreting waterflooding behavior in complex vuggy reservoirs under one-dimensional, incompressible, gravity-free, and capillarity-free conditions. Full article
(This article belongs to the Special Issue New Advances in Oil, Gas and Geothermal Reservoirs—3rd Edition)
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25 pages, 24157 KB  
Article
Source and Evolution of Ore-Forming Fluids in the Dulanggou Gold Deposit, Danba, Sichuan, China: Constraints from Fluid Inclusions and C–H–O Isotopes
by Yan Zhang, Bing Chen, Xiang Lai, Yangyan Xiang, Cuihua Chen, Ying Gu, Haoyang Xiao, Hesen Zhao, Yulong Yang, Mengyi Qiao, Haijun Zhang, Wenbin Cheng, Chaofei Luo, Yaru Zhang, Qiang Wang and Kaijun Yang
Minerals 2026, 16(5), 523; https://doi.org/10.3390/min16050523 - 14 May 2026
Viewed by 248
Abstract
The Danba–Dadu River gold belt on the western Yangtze Craton margin is a major gold province in China. The Dulanggou gold deposit is a large quartz-vein-type deposit recently discovered in this belt. Ore bodies are fault-controlled veins hosted in high-grade metamorphic rocks of [...] Read more.
The Danba–Dadu River gold belt on the western Yangtze Craton margin is a major gold province in China. The Dulanggou gold deposit is a large quartz-vein-type deposit recently discovered in this belt. Ore bodies are fault-controlled veins hosted in high-grade metamorphic rocks of the Devonian Weiguan Formation. Mineralization includes three stages: early (quartz–minor sulfide), main (quartz–abundant sulfide–native gold–Te–Bi minerals), and late (quartz–minor sulfide–calcite). Fluid inclusion studies show the following. Early-stage inclusions are mainly CO2–H2O-type (homogenization temperature 307–388 °C, salinity 0.4–7.1 wt.% NaCl eqv.) with minor NaCl–H2O-type. Main-stage inclusions are dominated by CO2–H2O and NaCl–H2O types, with minor pure CO2 inclusions (homogenization temperature 207–307 °C, salinity 0.2–11.2 wt.% NaCl eqv.). Late-stage inclusions are mainly NaCl–H2O-type (168–223 °C, 4.6–10.1 wt.% NaCl eqv.). Laser Raman analysis detects CH4 in the fluid. The ore-forming fluid is a reducing, medium–low temperature, low-salinity H2O–CO2–NaCl–CH4 system. Thermodynamic calculations of CO2–H2O inclusions yield total densities of 0.94–1.03 g/cm3 and total homogenization pressures of 170–276 MPa for the early stage, and slightly lower densities (0.94–1.01 g/cm3) with pressures of 170–246 MPa for the main stage, indicating a progressive pressure decrease during fluid evolution. Hydrogen and oxygen isotopes (early stage: δD −96.4‰ to −78.9‰, δ18OH2O 6.1‰ to 6.5‰; main stage: δD −104.3‰ to −75.1‰, δ18OH2O 5.3‰ to 7.1‰) indicate that the ore-forming fluid was mainly derived from primary magmatic water. Immiscible CO2–H2O and NaCl–H2O inclusion assemblages in the main stage suggest that fluid immiscibility was the key mechanism for gold precipitation. The Dulanggou deposit resembles classic orogenic gold deposits in host rocks, ore-controlling structures, mineral assemblages, and low-salinity CO2-rich fluids. However, its H–O isotopes and thermodynamic data point to a magmatic water source, distinct from the metamorphic water source of typical orogenic gold deposits. This highlights the diversity of fluid sources in orogenic gold systems along the western Yangtze Craton margin. Full article
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22 pages, 2662 KB  
Article
Enhanced Reservoir Performance Prediction Using a Pseudo-Pressure-Based Capacitance Resistance Model for Immiscible Gas Injection
by Meruyet Zhanabayeva and Peyman Pourafshary
Energies 2026, 19(9), 2215; https://doi.org/10.3390/en19092215 - 3 May 2026
Viewed by 504
Abstract
The capacitance resistance model (CRM) is an analytical tool widely used to forecast reservoir performance in enhanced oil recovery (EOR) methods. By representing flow dynamics and the connectivity between injection and production wells through the parameter of interwell connectivity, CRM offers fast computational [...] Read more.
The capacitance resistance model (CRM) is an analytical tool widely used to forecast reservoir performance in enhanced oil recovery (EOR) methods. By representing flow dynamics and the connectivity between injection and production wells through the parameter of interwell connectivity, CRM offers fast computational processing and minimal input data requirements. These advantages make CRM a practical alternative for rapid reservoir analysis, especially when full-scale numerical simulations are infeasible due to time and budget constraints. CRM, rooted in material balance and productivity equations, uses injection/production rates and bottom-hole pressure data to construct reservoir models through optimization techniques, which can then be combined with oil fractional flow models for predictive purposes. Initially designed for waterflooding operations, CRM has seen limited but promising applications in gas injection projects, where research remains incomplete. This study presents a new formulation of CRM tailored for immiscible gas injection, incorporating the pseudo-pressure concept coupled with a saturation profile. The pseudo-pressure concept is a mathematical transformation that linearizes gas flow equations by accounting for variations in gas compressibility and viscosity with pressure. The proposed CRM was evaluated using a PUNQ-S3 benchmark reservoir model in the CMG IMEX black oil simulator, involving two injectors and four producers. History- matching results for fluid production rates showed that the newly developed CRM achieved the lowest NRMSE, outperforming other CRM models across a wide range of reservoir properties. Sensitivity analyses were conducted to examine the effects of gas and oil PVT properties on the model’s performance. The newly developed CRM, incorporating the pseudo-pressure concept and saturation profiles, demonstrates superior performance in predicting fluid production rates, achieving an average NRMSE of 15.3% in a base case scenario, compared to other tested CRM models. Additionally, the sensitivity analysis on the effect of fluid properties shows that higher gas viscosity, lower gas formation volume factor, and increasing oil API gravity improve the CRM model’s performance, and under all tested conditions the newly developed CRM provides the most accurate production history match. This study not only establishes the new CRM as a robust and accurate predictive tool for immiscible gas injection but also provides a comprehensive discussion on reservoir parameter ranges and model limitations, advancing the applicability of CRM in EOR processes. Full article
(This article belongs to the Section H1: Petroleum Engineering)
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16 pages, 6806 KB  
Article
Simulation of Non-Isothermal Two-Phase Flow in a Heterogeneous Shale Porous Medium
by Pinghua Shu, Kairui Ye, Chao Qian, Wei Jiang, Chao Xu and Lin Du
Processes 2026, 14(9), 1391; https://doi.org/10.3390/pr14091391 - 27 Apr 2026
Viewed by 372
Abstract
The characteristics of two-phase flow in heterogeneous shale porous structures are of critical importance for oil and gas extraction and for evaluating the efficiency of underground resource recovery and carbon sequestration. However, although non-isothermal two-phase flow has been investigated in previous studies, systematic [...] Read more.
The characteristics of two-phase flow in heterogeneous shale porous structures are of critical importance for oil and gas extraction and for evaluating the efficiency of underground resource recovery and carbon sequestration. However, although non-isothermal two-phase flow has been investigated in previous studies, systematic research on non-isothermal CO2–crude oil displacement in heterogeneous shale porous structures remains relatively scarce. In this study, a multi-phase simulator was employed to simulate non-isothermal CO2–crude oil displacement in heterogeneous porous structures, and the effects of injection rate, injection temperature, and wettability on two-phase flow characteristics in heterogeneous porous media were systematically analyzed. The results indicate that changes in the viscosity ratio between the displacing and displaced phases—induced by heat transfer—may be a key factor governing immiscible two-phase interfacial dynamics and flow behavior in heterogeneous porous structures. Injection temperature exerts a significant influence on both the main flow channels and local flow pathways within the porous structure; increasing the injection temperature of the displacing phase can effectively enhance displacement efficiency, with the steady-state CO2 saturation increasing from 43.15% to 50.62% as the injection temperature increased from 293.15 K to 363.15 K. In addition, increasing the injection rate improves CO2 sweep efficiency, with the steady-state CO2 saturation increasing from 45.35% to 55.98% as the injection rate increased from 50 to 250 μm/s; however, excessively high injection rates lead to non-piston-like displacement and premature fluid breakthrough, and the CO2 saturation decreased to 49.81% at 350 μm/s. Under strongly water-wet conditions, the CO2 saturation after displacement stabilization is higher. Full article
(This article belongs to the Section Petroleum and Low-Carbon Energy Process Engineering)
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30 pages, 13456 KB  
Article
Numerical Simulation of Co-Continuous Morphologies in PEO/PS Polymer Blends
by Seungjae Lee, Yongho Choi and Junseok Kim
Appl. Sci. 2026, 16(8), 3909; https://doi.org/10.3390/app16083909 - 17 Apr 2026
Viewed by 339
Abstract
This paper investigates co-continuous structures in immiscible polymer blends through three-dimensional (3D) computational calculations based on a multiphase phase-field equation for fluid flow. The mathematical model describes phase separation with the Cahn–Hilliard (CH) equation and fluid motion with the incompressible Navier–Stokes (NS) equations. [...] Read more.
This paper investigates co-continuous structures in immiscible polymer blends through three-dimensional (3D) computational calculations based on a multiphase phase-field equation for fluid flow. The mathematical model describes phase separation with the Cahn–Hilliard (CH) equation and fluid motion with the incompressible Navier–Stokes (NS) equations. Both polymers are treated as Newtonian viscous fluids, and the model includes surface tension, viscosity, and volume fraction effects. A semi-implicit finite difference method (FDM) solves the CH equation, and a projection method maintains the incompressibility of the flow field. Multigrid techniques solve the nonlinear systems efficiently. In addition, a connectivity-based detection algorithm determines whether a phase forms a connected structure that reaches all boundaries of the numerical domain. The numerical results show that the morphology changes from a droplet–matrix structure to a co-continuous structure as the volume fraction increases. The interfacial area per unit volume reaches a local maximum near the transition between these two regimes. Full article
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30 pages, 15335 KB  
Article
Effect of Density Ratio and Surface Tension on Vortex–Interface Interactions: A Numerical Study
by Xiaobin Yang, Yiding Hu, Zhihan Li, Chenghan Wu, Ping Wei, Weige Liang and Shiyan Sun
J. Mar. Sci. Eng. 2026, 14(4), 326; https://doi.org/10.3390/jmse14040326 - 7 Feb 2026
Viewed by 553
Abstract
In two-phase flow, the interaction between multi-scale vortex structures and interfaces (bubbles or free surfaces) triggers a range of complex physical phenomena. This study employs numerical simulations to investigate the interaction between a horizontal vortex and the interface separating two layers of immiscible [...] Read more.
In two-phase flow, the interaction between multi-scale vortex structures and interfaces (bubbles or free surfaces) triggers a range of complex physical phenomena. This study employs numerical simulations to investigate the interaction between a horizontal vortex and the interface separating two layers of immiscible fluids with different densities (e.g., water and air). The vortex is initialized as an internal motion within the heavier phase. We focus specifically on the impact of the phase density ratio and surface tension. Numerical simulations reveal that when the density ratio is near unity, interface rupture occurs only at high Weber numbers (We), where low surface tension enables the rupture of sharp interface points. Conversely, at high surface tension (low We), these sharp points stretch into thin liquid films, significantly increasing the surface area without causing breakage. As the density ratio increases, interface rupture at sharp points accelerates, even under high surface tension, leading to faster dissipation of the initial vortex. In high-We scenarios, an increased density ratio promotes the faster formation and greater intensity of new vortex layers at the interface. However, increasing surface tension enhances the vorticity of these layers but simultaneously slows their generation rate. The findings highlight the critical interplay between surface tension and density differences in vortex–interface interactions, with surface tension stabilizing the interface and density differences driving more intense vortex shedding and deformation. These insights offer valuable guidance for understanding two-phase flow behavior and improving the design of systems involving multiphase fluids. Full article
(This article belongs to the Section Physical Oceanography)
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32 pages, 3323 KB  
Article
Specificity of Ore Generation (Tin, Pegmatites, and Gems) in Trans-Porphyry Deposits
by Jean-Louis Vigneresse
Minerals 2026, 16(2), 157; https://doi.org/10.3390/min16020157 - 30 Jan 2026
Viewed by 919
Abstract
During the magmatic stage, base and rarer metals segregate from silicate melts to form ore deposits. The usual case is the porphyry (PD) type (Cu, Mo, and W) above subduction zones. The metal grade increases from some ppb or ppm up to percent [...] Read more.
During the magmatic stage, base and rarer metals segregate from silicate melts to form ore deposits. The usual case is the porphyry (PD) type (Cu, Mo, and W) above subduction zones. The metal grade increases from some ppb or ppm up to percent levels. A new type of trans-porphyry (TPD) deposits (Sn, Ta, Nb, and gems) results from large-scale shear between cratons within continental plates, internal decoupling, and vertical motion. The bulk ore generation process develops along three stages: from magma generation, emplacement, and the formation of an immiscible magmatic phase (MIP), fluids, and melt. However, in TPD, metals segregate from the crust during melting below 800 °C, biotites break down, and the melt remains below the critical point (731 °C). Fluid advection competes with chemical diffusion, yielding the required enrichment. The subcritical MIP splits into a silicate-rich and an aqueous-rich phase, which are both incompatible with each other. Granite, pegmatites, and greisen coexist in the magma chamber. Their respective extraction from a composite mush involves electron exchanges between charges, or orbitals, yielding metal oxides through chemical diffusion. In contrast, in metals (Nb and Ta) observed in pegmatites, and also in gems, electrons rearrange their electronic cloud through their polarizability. Lastly, gems independently grow under the influence of the extremely hard fluids (Li, Be, and B). Magma generation, involving the lower crust (garnet and pyroxene), results in melts that form the two observed pegmatite groups (NYF and LCT), with each being associated with alkaline (A-type) or continental (S-type) granitic melts. Full article
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24 pages, 5941 KB  
Article
A Fully Implicit Model of Compressible Capillary Flows
by Jean-Paul Caltagirone
Fluids 2026, 11(2), 34; https://doi.org/10.3390/fluids11020034 - 27 Jan 2026
Viewed by 588
Abstract
Small-scale two-phase flows are subject to intense capillary accelerations that must be treated with care in order to avoid artifacts often associated with the numerical methodologies used, such as excessive fragmentation of structures. This analysis proposes a formulation of capillary actions for compressible [...] Read more.
Small-scale two-phase flows are subject to intense capillary accelerations that must be treated with care in order to avoid artifacts often associated with the numerical methodologies used, such as excessive fragmentation of structures. This analysis proposes a formulation of capillary actions for compressible viscous two-phase flows within the framework of discrete mechanics, where the concept of mass is abandoned in favor of a law of motion that describes the conservation of accelerations, one related to inertia and the other to external actions. With the introduction of the capillary term, the sum of a capillary potential gradient and the dual curl of a vector potential is consistent with the other terms of the law of motion, a formal Helmholtz–Hodge decomposition. This fully compressible formulation reproduces the capillary waves generated by the source terms and the contact and shock discontinuities in the two immiscible fluids. This methodology completely eliminates parasitic currents due mainly to the presence of residual curl in the capillary source terms. Several classic examples demonstrate the validity of this approach. Full article
(This article belongs to the Special Issue Multiphase Simulations with the Volume-of-Fluid (VOF) Approach)
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27 pages, 1905 KB  
Article
Analytical Solutions for One-Dimensional Water Flow Driven by Immiscible Fluid in Porous Medium
by Jianyi Wu, Yang Zhou, Xuhai Feng, Wenbo Fan and Deying Ma
Appl. Sci. 2026, 16(3), 1208; https://doi.org/10.3390/app16031208 - 24 Jan 2026
Viewed by 500
Abstract
In fields such as rock and soil grouting and petroleum extraction, the flow of water driven by an immiscible fluid (or vice versa) within a porous medium is frequently encountered. Due to the presence of an interface between the two fluids, whose position [...] Read more.
In fields such as rock and soil grouting and petroleum extraction, the flow of water driven by an immiscible fluid (or vice versa) within a porous medium is frequently encountered. Due to the presence of an interface between the two fluids, whose position changes over time and needs to be solved concurrently with the fluid pressure field, this issue represents a special two-phase moving boundary problem. In this paper, fundamental governing equations for this moving boundary problem in one-dimensional Cartesian, cylindrical, and spherical coordinate systems are developed. Analytical solutions for the pore pressure distribution and interface movement are obtained through the method of similarity transformation. By disregarding the pressure variation in the original underground water, this two-phase moving boundary problem can be reduced into a one-phase moving boundary problem. Consequently, analytical solutions for this one-phase problem are also obtained. The analytical solutions mainly address specific boundary conditions. For cases with general boundary conditions, numerical solutions are provided through a combination of finite volume method and moving node approach. By assuming the instantaneous establishment of a steady-state pore pressure distribution within the medium, the transient two-phase flow model is transformed into a quasi-steady model. Subsequently, an approximate solution for the quasi-steady model is also established. After verifying the model solutions, computational examples are presented to evaluate the effectiveness of the one-phase approximation and the quasi-steady approximation. The one-phase model tends to underestimate fluid pressure within the porous medium under pressure boundary conditions, thereby overestimating the movement speed of the two-phase interface. Additionally, under flow rate boundary conditions, the one-phase model tends to underestimate the pressure required to achieve the design flow rate. As the stiffness of the porous medium increases, the influence of the pressure variation rate term in the transient model equations gradually diminishes. Consequently, the interface movement and pore pressure distribution obtained from the quasi-steady solutions are essentially consistent with those obtained from the transient model, and the quasi-steady solutions are convenient to apply under these circumstances. Full article
(This article belongs to the Section Civil Engineering)
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30 pages, 4217 KB  
Review
Overview of Platinum Group Minerals (PGM): A Statistical Perspective and Their Genetic Significance
by Federica Zaccarini, Giorgio Garuti, Maria Economou-Eliopoulos, John F. W. Bowles, Hannah S. R. Hughes, Jens C. Andersen and Saioa Suárez
Minerals 2026, 16(1), 108; https://doi.org/10.3390/min16010108 - 21 Jan 2026
Viewed by 2158
Abstract
The six platinum group elements (PGE) are among the rarest elements in the upper continental crust of the earth. Higher values of PGE have been detected in the upper mantle and in chondrite meteorites. The PGE are siderophile and chalcophile elements and are [...] Read more.
The six platinum group elements (PGE) are among the rarest elements in the upper continental crust of the earth. Higher values of PGE have been detected in the upper mantle and in chondrite meteorites. The PGE are siderophile and chalcophile elements and are divided into the following: (1) the Ir subgroup (IPGE) = Os, Ir, and Ru and (2) the Pd subgroup (PPGE) = Rh, Pt, and Pd. The IPGE are more refractory and less chalcophile than the PPGE. High concentrations of PGE led, in rare cases, to the formation of mineral deposits. The PGE are carried in discrete phases, the platinum group minerals (PGM), and are included as trace elements into the structure of base metal sulphides (BM), such as pentlandite, chalcopyrite, pyrite, and pyrrhotite. Similarly to PGE, the PGM are also divided into two main groups, i.e., IPGM composed of Os, Ir, and Ru and PPGM containing Rh, Pt, and Pd. The PGM occur both in mafic and ultramafic rocks and are mainly hosted in stratiform reefs, sulphide-rich lenses, and placer deposits. Presently, there are only 169 valid PGM that represent about 2.7% of all 6176 minerals discovered so far. However, 496 PGM are listed among the valid species that have not yet been officially accepted, while a further 641 are considered as invalid or discredited species. The main reason for the incomplete characterization of PGM resides in their mode of occurrence, i.e., as grains in composite aggregates of a few microns in size, which makes it difficult to determine their crystallography. Among the PGM officially accepted by the IMA, only 13 (8%) were discovered before 1958, the year when the IMA was established. The highest number of PGM was discovered between 1970 and 1979, and 99 PGM have been accepted from 1980 until now. Of the 169 PGM accepted by the IMA, 44% are named in honour of a person, typically a scientist or geologist, and 31% are named after their discovery localities. The nomenclature of 25% of the PGM is based on their chemical composition and/or their physical properties. PGM have been discovered in 25 countries throughout the world, with 64 from Russia, 17 from Canada and South Africa (each), 15 from China, 12 from the USA, 8 from Brazil, 6 from Japan, 5 from Congo, 3 from Finland and Germany (each), 2 from the Dominican Republic, Greenland, Malaysia, and Papua New Guinea each, and only 1 from Argentine, Australia, Bulgaria, Colombia, Czech Republic, England, Ethiopia, Guyana, Mexico, Serbia, and Tanzania each. Most PGM phases contain Pd (82 phases, 48% of all accepted PGM), followed, in decreasing order of abundances, by those of Pt 35 phases (21%), Rh 23 phases (14%), Ir 18 phases (11%), Ru 7 phases (4%), and Os 4 phases (2%). The six PGE forming the PGM are bonded to other elements such as Fe, Ni, Cu, S, As, Te, Bi, Sb, Se, Sn, Hg, Ag, Zn, Si, Pb, Ge, In, Mo, and O. Thirty-two percent of the 169 valid PGM crystallize in the cubic system, 17% are orthorhombic, 16% hexagonal, 14% tetragonal, 11% trigonal, 3% monoclinic, and only 1% triclinic. Some PGM are members of a solid-solution series, which may be complete or contain a miscibility gap, providing information concerning the chemical and physical environment in which the mineral was formed. The refractory IPGM precipitate principally in primitive, high-temperature, mantle-hosted rocks such as podiform and layered chromitites. Being more chalcophile, PPGE are preferentially collected and concentrated in an immiscible sulphide liquid, and, under appropriate conditions, the PPGM can precipitate in a thermal range of about 900–300 °C in the presence of fluids and a progressive increase of oxygen fugacity (fO2). Thus, a great number of Pt and Pd minerals have been described in Ni-Cu sulphide deposits. Two main genetic models have been proposed for the formation of PGM nuggets: (1) Detrital PGM represent magmatic grains that were mechanically liberated from their primary source by weathering and erosion with or without minor alteration processes, and (2) PGM reprecipitated in the supergene environment through a complex process that comprises solubility, the leaching of PGE from the primary PGM, and variation in Eh-pH and microbial activity. These two models do not exclude each other, and alluvial deposits may contain contributions from both processes. Full article
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39 pages, 13928 KB  
Article
Genesis of the Hadamengou Gold Deposit, Northern North China Craton: Constraints from Ore Geology, Fluid Inclusion, and Isotope Geochemistry
by Liang Wang, Liqiong Jia, Genhou Wang, Liangsheng Ge, Jiankun Kang and Bin Wang
Minerals 2026, 16(1), 99; https://doi.org/10.3390/min16010099 - 20 Jan 2026
Viewed by 1679
Abstract
The Hadamengou gold deposit, hosted in the Precambrian metamorphic basement, is a super-large gold deposit occurring along the northern margin of the North China Craton. Despite extensive investigation, the genesis of the gold mineralization is poorly understood and remains highly debated. This study [...] Read more.
The Hadamengou gold deposit, hosted in the Precambrian metamorphic basement, is a super-large gold deposit occurring along the northern margin of the North China Craton. Despite extensive investigation, the genesis of the gold mineralization is poorly understood and remains highly debated. This study integrates a comprehensive dataset, including fluid inclusion microthermometry and C-H-O-S-Pb isotopes, to better constrain the genesis and ore-forming mechanism of the deposit. Hydrothermal mineralization can be divided into pyrite–potassium feldspar–quartz (Stage I), quartz–gold–pyrite–molybdenite (Stage II), quartz–gold–polymetallic sulfide (Stage III), and quartz–carbonate stages (Stage IV). Four types of primary fluid inclusions are identified, including pure CO2-type, composite CO2-H2O-type, aqueous-type, and solid-daughter mineral-bearing-type inclusions. Microthermometric and compositional data reveal that the fluids were mesothermal to hypothermal, H2O-dominated, and CO2-rich fluids containing significant N2 and low-to-moderate salinity, indicative of a magmatic–hydrothermal origin. Fluid inclusion assemblages further imply that the ore-forming fluids underwent fluid immiscibility, causing CO2 effusion and significant changes in physicochemical conditions that destabilized gold bisulfide complexes. The hydrogen–oxygen isotopic compositions, moreover, support a dominant magmatic water source, with increasing meteoric water input during later stages. The carbon–oxygen isotopes are also consistent with a magmatic carbon source. Sulfur and lead isotopes collectively imply that ore-forming materials were derived from a hybrid crust–mantle magmatic reservoir, with minor contribution from the country rocks. By synthesizing temporal–spatial relationships between magmatic activity and ore formation, and the regional tectonic evolution, we suggest that the Hadamengou is an intrusion-related magmatic–hydrothermal lode gold deposit. It is genetically associated with multi-stage magmatism induced by crust–mantle interaction, which developed within the extensional tectonic regimes. Full article
(This article belongs to the Section Mineral Deposits)
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