Particle motion in multiphase reactors is a critical determinant of reaction efficiency, mixing quality, and overall process performance in industries ranging from metallurgy to chemical engineering. This paper provides a critical review of the current research status of particle motion characterization, systematically examining both experimental techniques (high-speed imaging, PIV, PDPA) and numerical simulation methodologies (DNS, TFM, CFD-DEM, DPM, DDPM-KTGF, MP-PIC). On the experimental side, the principles, applications, and inherent limitations of optical diagnostic methods are critically evaluated, with particular attention to the trade-off between measurement fidelity and reactor relevance. On the numerical side, methods are analyzed in terms of their underlying assumptions, computational costs, and applicability to industrial-scale problems. Beyond summarizing existing work, this review critically assesses the persistent disconnect between idealized experimental systems and industrial reactor conditions, identifies five grand challenges facing the field − (i) bridging scale disparity, (ii) handling non-ideal particles, (iii) knowledge extraction from big data, (iv) multi-physics coupling, and (v) generalizability of AI models − and prospects future directions including multi-scale coupling algorithms, physics-informed machine learning, and the integration of advanced characterization with predictive modeling. This critical perspective provides a roadmap for researchers seeking to bridge the gap between fundamental understanding and engineering application in particle-laden multiphase flows.

Coal exhibits heterogeneous pore networks and chemically diverse surfaces, resulting in complex competitive adsorption among CH4, CO2, and H2O. The underlying molecular mechanisms remain unclear. In this work, molecular simulation methods were applied to investigate the adsorption behavior and interaction characteristics of CH4/CO2/H2O mixtures on two typical coal components (inertinite and vitrinite) under different CO2 enrichment levels, corresponding to gas-phase CO2 mole fractions of 4.8%, 9.1%, and 16.7%. The results demonstrate that CH4 dominates surface occupation in all cases, maintaining 30-70 adsorbed molecules, whereas CO2 adsorption is significantly weaker, remaining below 5 at low loading and increasing to only 10-17 at high loading. This indicates a limited competitive capability of CO2 for adsorption sites. From an interaction perspective, water governs the electrostatic environment, with surface-water Coulombic energies consistently distributed around - 600 to - 750 kJ mol-1. In contrast, CO2-water interactions decrease from - 220 to - 360 kJ mol-1 to - 100 to - 170 kJ mol-1 as CO2 loading increases, reflecting a pronounced screening effect. Meanwhile, direct CO2-surface interactions remain weak (typically - 5 to - 15 kJ mol-1). Overall, CH4 adsorption is primarily controlled by dispersion interactions, while CO2 is constrained by weak surface affinity and reduced hydration strength, resulting in a secondary role in multicomponent competitive adsorption within coal systems.

Electro-fused magnesium furnace (EFMF) is an important equipment for producing electric melting magnesium, and its operating performance will have a significant impact on the final product quality and economic benefits. Traditional process operating performance assessment (POPA) technologies usually establish models by mining the potential relationship between process data and performance grade labels, which heavily depend on many manually labeled samples. Inspired by transfer learning, a semi-supervised transfer adversarial domain adaptation network (STADAN) is developed for the POPA of EFMF, which is based on the challenging situation where only limited source domain (SD) data is labeled and all target domain (TD) data is unlabeled. In order to fully utilize unlabeled data and expand the labeled dataset, a pseudo-label predictor consisting of a direct predictor and an auxiliary predictor is constructed. By mining the relationship between process data and labels from the aspects of input–output mapping and data distribution, the pseudo-label predictor can ensure the accuracy and reliability of the prediction. Based on the expanded labeled dataset, a performance grade classifier is further established for the TD operating performance assessment. To narrow the data distribution discrepancy between SD and TD, a domain discriminator is simultaneously established. Through an adversarial training mechanism, the feature distribution of both TD and SD tends to be consistent, improving the accuracy of pseudo-label prediction and POPA. The simulation comparison results verify the effectiveness of the proposed method.

The non-isothermal hydrogen reduction kinetics of the MoS2–CaO system (molar ratio 1:2) were investigated using TG-DSC under a 50% H2Ar atmosphere at heating rates of 5–20 °C/min. The apparent activation energy was determined by the FWO and KAS isoconversional methods, and the reaction mechanism functions were screened using the Šatava–Šesták method. The reduction process exhibits a clear three-stage characteristic with a critical boundary at 450 °C, dividing the process into physical desorption (<200 °C), surface structure adjustment (200–450 °C), and bulk reduction with crystal phase evolution (>450 °C). Stage II (200–450 °C) is identified as a surface-controlled pre-reaction stage with an average activation energy of 258.76 kJ/mol, following the Anti-Jander eq. (D5) for three-dimensional reverse diffusion (A = 1.985 × 1017 s−1). Stage III (>450 °C) is the bulk reduction stage characterized by multi-step coupling, with an average activation energy of 224.95 kJ/mol, following the Avrami-Erofeev equation (n = 3) for nucleation and growth (A = 5.360 × 107 s−1). XRD analysis reveals a complex reaction pathway: initial reduction to Mo and CaS (≥700 °C), followed by intermediate CaMoO4 (≥800 °C) and stable CaMo6S8 (Chevrel phase, ≥950 °C). The transition in mechanism functions from D5 to A3 quantitatively reveals the promoting mechanism of CaO, shifting the rate control from surface diffusion to bulk nucleation and growth. This work provides the first quantitative kinetic framework describing CaO's dual role—surface activation in Stage II and deep reduction promotion via in-situ sulfur fixation in Stage III—while identifying competing reaction pathways leading to stable Chevrel phase formation. These findings offer theoretical insights for optimizing clean molybdenum extraction processes.

The rapid growth of the electric vehicle market has made the disposal of used lithium-ion batteries (LIBs) a pressing global concern. Conventional recycling methods, such as hydrometallurgy and pyrometallurgy, are often hindered by high energy costs, chemical consumption, and secondary pollution. This study therefore proposes an ultrafast, selective chlorination strategy based on flash Joule heating (FJH) for the recycling of spent LiNi0.8Co0.1Mn0.1O2 (NCM811) cathode materials. Applying a 36 V pulse for just 3 s rapidly heated a mixture of spent NCM811, sodium chloride (NaCl) and carbon black to over 1500 degrees C. Under these conditions, a carbothermal reduction and chlorination process was triggered, which selectively converted lithium into the watersoluble compound lithium chloride (LiCl). This allowed a high Li leaching efficiency of 92.4 % to be achieved using only water as the lixiviant. Meanwhile, the transition metals (nickel, cobalt and manganese) were reduced to lower valence states or metallic forms and remained in the solid residue. Mechanistic analysis confirmed that the process involves the outward migration of Li+ and O2- , followed by a reaction between lithium oxide (Li2O) and NaCl facilitated by carbon. The method demonstrated excellent versatility, achieving lithium recovery rates of 90.3 %, 87.0 % and 89.6 % for spent LiNi0.6Co0.2Mn0.2O2 (NCM622), LiCoO2 (LCO) and LiMn2O4 (LMO) cathodes, respectively. This work provides a promising, energy-efficient, and rapid approach to the selective recovery of lithium from various spent LIBs cathodes, showing great potential for industrial application.

In recent years, the burgeoning growth of the aluminum industry, coupled with the depletion of high-quality bauxite resources, has intensified the quest for alternative raw materials. This is particularly imperative in light of the "dual carbon" policy and stringent environmental regulations governing the national aluminum oxide industry. While low-quality bauxite resources are abundantly available, their high silicon impurity content poses several challenges. These include equipment scaling, compromised product quality, and the generation of substantial red mud, all of which are incongruent with the current Bayer process. This paper provides a comprehensive review of the occurrence and behavior of impurity Si in bauxite, as well as technologies for its removal, outlining the strengths and limitations of each method. Nevertheless, these techniques are seldom employed in industrial applications due to their intricate processes, elevated energy costs, and demanding equipment operational requirements. In line with the principles of sustainable development and emphasizing resource recycling and high-value utilization, this paper introduces a novel "Chlorination-Bayer method" for extracting metallurgical-grade aluminum oxide from low-quality bauxite. This approach exhibits robust adaptability to diverse raw materials, concurrently recovering strategic rare metals like lithium, gallium, and scandium, and eliminating wastes generation, thereby affirming its environmental sustainability.

The vortex feeder utilizes fluid rotation to generate a negative pressure, which entrains and rapidly disperses lightweight particles into molten slag. This process is crucial for converting acidic slag to basic slag. While labscale mechanisms are clear, scaling up faces challenges: attenuated momentum transfer and reduced heat transfer-diffusion efficiency.This investigation employs computational fluid dynamics modeling to conduct an amplification study on vortex feeders at different scales. The numerical simulation and mechanism analysis in this study only focus on simplified physical mixing, fluid flow and particle transport processes. It centers on the particle momentum transfer (e.g., particle concentration, centrifugal acceleration, axial velocity) and particle heat transfer and diffusion (e.g., particle temperature, basicity, diffusion coefficient), aiming to pinpoint the primary limiting factors in large-scale operation. Range analysis was used to evaluate factor-level impacts on the diffusion coefficient and determine the optimal combinations. The findings clarify that the key mechanism of fluid-solid coupling: the velocity difference between the fluid and the particles is the primary driving force for the drag force; equipment size and flow field controlled momentum transport, the fluid velocity affected the swirl intensity and basicity; larger equipment suffered from an inhomogeneous flow field and synergy between particle dispersion. Range analysis shows optimal combinations are A1B4 (uin= 1 m/s, Qp = 23.63 kg/s), A1B4 (uin= 1 m/s, Qp = 33.63 kg/s), A2B4 (uin= 2 m/s, Qp = 43.63 kg/s) and A2B4 (uin= 2 m/s, Qp = 53.63 kg/s). The dominant factor for diffusion coefficient shifts from particle concentration to inlet velocity. This study discusses scale-up challenges and potential solutions.

Internal explosions within large asymmetric multi-cabin structures involve complex coupling between shockwave propagation and dynamic structural response, making accurate and efficient assessment inherently challenging. This study develops a rapid prediction framework that integrates internal blast load reconstruction with structural damage assessment using a small data sample. The validated high-fidelity internal-blast numerical simulations is conducted to extract characterized blast and damage parameters in the multi-cabin structure. Under random internal blast locations, a two-stage Kriging surrogate model is proposed to reconstruct the full-field blast load in the asymmetric multi-cabins. Then, a grid-based energy model is employed to evaluate the relationship between internal blast load and structural damage of the cabins. With the integrated model, the internal blast load field, failure modes of each bulkhead, and the damage state of the overall multi-cabin structures can be rapidly estimated. The framework is validated on a realistic large asymmetric multi-cabin structure under both interpolation and extrapolation conditions, requiring about 10 s per scenario with high accuracy. The integrated framework provides a practical and efficient load–damage prediction method for large asymmetric multi-cabin structures under internal and external explosions.

The process operating performance assessment (POPA) plays a pivotal role in enhancing industrial production efficiency and product quality. Open-set domain adaptation (OSDA) presents a significant challenge when label space discrepancies and unknown classes exist in the target domain. However, existing OSDA methods often homogenize unknown classes, hindering fine-grained assessment and under-exploiting in-domain knowledge. To address the above open-set POPA problem, this paper proposes a novel cross-domain fine-grained unknown class separation network (CFUCS) for industrial processes. In the assessment phase for known samples, the CFUCS method leverages inter-class relationships within the source domain to obtain performance grade soft-label prototypes. By integrating Kullback-Leibler (KL) divergence, target known-unknown samples are effectively distinguished. Furthermore, maximum mean discrepancy (MMD) is employed to reduce distributional discrepancies of known samples across domains, thereby improving the classification accuracy of known performance grades. In the assessment phase for unknown samples, existing studies typically group all unknown classes into a single category to mitigate negative transfer. To achieve fine-grained partitioning, spaces are first reserved for different unknown classes. Subsequently, a performance grade similarity matrix (PGSM), which is a quantitative expression of the intrinsic relationship between performance grades, is designed to assign labels to unknown samples. Then, expert experience is combined to determine specific performance grade labels. Experiments on two industrial datasets have confirmed the feasibility of the CFCUS method in addressing the open-set POPA problem, thereby providing clear guidance for the performance optimization of subsequent production processes.

Ferrochrome slag and related chromium-bearing metallurgical solid wastes occupy a precarious position between the opportunity for secondary resource utilization and the long-term environmental liabilities they pose. Their intrinsic value is derived from the presence of chromium, iron, manganese, vanadium, zinc, and other metals; however, their associated risks are governed by factors such as spinel-hosted chromium, glassy encapsulation, soluble salts, dust formation, and alkaline leaching behavior. This review systematically reorganizes the available literature into a comprehensive chlorination-resource-utilization framework, encompassing feedstock diagnosis, selective chlorination, volatilization and condensation, valuable metal recovery, residue stabilization, and chlorine-loop management. Particular emphasis is placed on parameter-performance evidence, including basicity, temperature, roasting time, chlorinating-agent dosage, gas atmosphere, molten-salt ratio, recovery rate, and leaching concentration. The findings indicate that chlorination can be effective only when thermodynamic feasibility is aligned with mineral accessibility and product capture. Notable examples include high zinc dissolution from ferrochrome converter dust, high chromium recovery from stainless-steel slag, molten-salt multi-metal chlorination, and basicity-controlled chromium immobilization, which collectively illustrate both the potential and limitations of these processes. The primary bottleneck is not a singular reaction step but rather the lack of integrated datasets that concurrently report feedstock mineralogy, chloride conversion, condenser product distribution, residue leaching, and chlorine balance.

High-purity separation technologies are pivotal to the food and pharmaceutical industries, yet the purification of vitamin E intermediates remains challenging due to the similar physicochemical properties of target compounds and impurities, leading to low separation efficiency and high energy consumption. Here, we report an integrated process intensification strategy for crystallization that addresses these challenges. We establish comprehensive mathematical models and experimentally validated coefficients to quantitatively elucidate the fundamental relationships between operating conditions and process outcomes, including impurity migration mechanisms and solute distribution characteristics. Systematic evaluation of three intensification techniques reveals distinct trade-offs: reflux minimizes product loss but increases impurity entrapment and reduces particle size; coupled distillation-crystallization offers superior separation flexibility, with thermodynamic distribution dominating impurity migration over kinetic effects; and gassing-induced crystallization enhances heat transfer and suppresses uncontrolled nucleation, though with modest purity gains. By synergistically combining distillation with gassing crystallization, we achieve an unprecedented product purity of >99.5%, which meets the most demanding downstream synthesis specifications and enables near-equilibrium solute distribution. This study provides a generalizable framework for integrating numerical modeling with process intensification to advance high-efficiency crystallization separation in food and related chemical systems.

The process operating performance assessment (POPA) is essential for improving industrial efficiency and product quality. However, open-set domain adaptation (OSDA) remains challenging due to the presence of unknown classes in the target domain. Existing methods often lack fine-grained discrimination of unknown classes and underestimate the utilization of in-domain knowledge. To address open-set POP A problem, this paper proposes an open-set weighted transfer adversarial learning network (OSWTAL) for industrial processes. The network first achieves precise screening of target known samples by dynamically integrating predictive uncertainty weights and domain similarity weights. These selected samples then undergo transfer adversarial training with source samples, thereby effectively minimizing interference from unknown classes and preventing negative transfer. Subsequently, for the screened unknown samples, an entropy minimization-based clustering optimization mechanism is introduced. This mechanism significantly enhances both intra-cluster compactness and discriminability among unknown samples. Finally, semantic annotation of clustering results is performed by incorporating domain expert knowledge, achieving a seamless integration of data-driven approaches and knowledge-guided refinement. Experiments conducted on an electro-fused magnesia furnace (EFMF) smelting process demonstrate that OSWTAL outperforms existing methods in open-set recognition and fine-grained performance assessment.

Numerical simulation of the particle motion and swirl flow characteristics in a vortex feeder was carried out using a Dense Discrete Phase Model (DDPM). The effects of the geometrical parameters of the feeder were analyzed in terms of particle trajectory, mass flow rate, particle concentration, particle velocity, etc. The results indicate that the particle trajectory, mass flow rate, and escape time increase with the increase of inlet contraction angle (alpha) and cylinder-to-cone ratio (Hcyl : Hcon), while pitch (P) is the opposite. The radial concentration of alpha = 16 degrees, Hcyl = 4Hcon, P = 300 mm increased by 3.12, 1.18, and 1.4 times, respectively, and the particle dispersion was enhanced. The variance values of particle mass flow rate were reduced by 33.3 %, 34 %, and 32.7 %, respectively, and the particle output stability was improved. With the increase of alpha and Hcyl : Hcon, the tangential velocity increases, and vortex negative pressure entrainment was enhanced. As P decreases, the axial velocity near the wall decreases significantly, and the time required for particles to completely escape was prolonged. The correlation equation about particle concentration was established using dimensional analysis. The results improve the sustainable utilization of hot copper slag and the efficiency of melt reduction and reduce the environmental pollution of copper slag stockpiling.

This study innovatively developed a desulfurization reactor based on the principle of cyclone separation to address the desulfurization problem of high sulfur bauxite (sulfur content >0.7 %) in the production process of alumina. Conventional methods like static roasting and fluidized beds often suffer from poor gas-solid contact, uneven heating, and short or poorly controlled particle residence times. Combining experimental methods with computational particle fluid dynamics (CPFD) simulations, the study systematically investigates the influence of inlet gas velocity (5.0-7.0 m/s) on desulfurization efficiency and the gas-solid two-phase flow characteristics within the reactor. Experimental results show that at an optimal gas velocity of 6.5 m/s, the desulfurization rates for total sulfur and sulfide-type sulfur reach 55.52 % and 81.26 %, respectively. Numerical simulations reveal the mechanism by which gas velocity regulates desulfurization efficiency through its effects on particle swirling motion, temperature field distribution (wall region >900 K), and reaction kinetics. The findings provide important theoretical foundations and process optimization directions for the efficient utilization of high-sulfur bauxite resources.

Within the framework of green chemistry, additive-free and morphology-controllable synthesis of inorganic nanomaterials has become an emerging research frontier. In this study, we developed an efficient liquid-phase synthesis route using calcium hydroxy glycolate (CHG) as the calcium source, sulfuric acid as the sulfur source, and ethylene glycol as the solvent. Under ultrasound-assisted conditions, without the use of soluble salts or surfactants, high-purity nano-anhydrite calcium sulfate (CaSO4) was successfully synthesized. By systematically varying the precursor concentration and ultrasonic parameters, the resulting products were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), and Fourier transform infrared spectroscopy (FT-IR), which confirmed the formation of spherical, plate-like, and rod-shaped nano-anhydrite. Specifically, by adjusting the Ca2+ concentration, rod-like crystals (length: 300-450 nm, width: 50 nm, aspect ratio: 7), spherical particles (mean diameter: 23.19 nm), and flake-like structures (diameter: 115.40 nm, thickness: 10-30 nm) were obtained at 0.3, 0.5, and 0.7 mol·L-1, respectively. The smallest particle sizes across these morphologies were achieved under optimized ultrasonic conditions of 750 W for 30 min. Molecular dynamics simulations revealed that ethylene glycol concentration modulates its selective adsorption on specific crystal planes of anhydrite, thereby differentially inhibiting growth rates along certain directions and enabling morphology-controlled synthesis. The simulated adsorption energies for the (200), (020), (011), and (002) faces were -15.04, -7.96, -2.08, and -0.45 kJ·mol-1, respectively. These results indicate that preferential adsorption occurs particularly on the (200) and (020) planes. This integrated experimental and simulation study elucidates the coupled mechanism of "precursor concentration - crystal plane adsorption - ultrasonic dynamics," offering theoretical insights and technical support for the environmentally sustainable and controllable synthesis of nano-anhydrite and other sulfate-based nanomaterials.

Hydrogen metallurgy is a promising low-carbon ironmaking technology, yet challenges like particle sticking and sulfur dioxide emissions hinder its application when pyrite is used as the raw material in a fluidized bed. This study proposes a novel approach for pyrite hydrogen reduction in a fluidized bed equipped with an inclined agitator and alkaline oxide (CaO) additives. Single-factor experiments were conducted to optimize key parameters: reduction time, temperature, and agitation speed. Results showed that the inclined agitator significantly reduced the sticking ratio from 54.5

Carbochlorination is a promising route for valorizing high-alumina fly ash (HAFA). However, process optimization is hindered by an insufficient understanding of the reaction mechanisms governing its predominant and most refractory phase mullite. To bridge this knowledge gap, this study decouples the intrinsic behavior of mullite from the complex HAFA matrix, systematically investigating its carbochlorination through non-isothermal kinetic analysis combined with multimodal characterization techniques. Non-isothermal thermogravimetric analysis demonstrates that the carbochlorination process follows the Avrami-Erofeev nucleation-growth model (n = 2/3) with an activation energy of 70.76 kJ/mol and pre-exponential factor of 11.54 s−1. Multimodal characterization including XRD, SEM-EDS, and 27Al/29Si MAS-NMR reveals a carbon-mediated chlorination mechanism. The process initiates with the cleavage of Cl–Cl bonds, triggering the dissociation of Al-O-Si frameworks. Owing to differential chlorination affinities, Al is preferentially and completely converted into volatile AlCl3, whereas only a portion of Si forms SiCl4. The remaining Si reorganizes into SiO2, and the aluminosilicate structure subsequently transforms into defective mullite (Al4.8Si1.2O9.6) and an intermediate sillimanite phase (Al2SiO5). The deoxygenation of sillimanite facilitates its re-conversion to mullite, while the accumulated SiO2 undergoes high-temperature phase transitions, ultimately crystallizing as quartz and cristobalite. The significant mass loss observed is primarily attributed to the volatilization of AlCl3 and SiCl4, which drives the efficient separation of Al and Si. These findings provide a fundamental mechanistic framework that is essential for optimizing Al/Si separation and advancing carbochlorination processes for aluminosilicate-rich secondary resources.

The recycling of spent lithium iron phosphate (SLFP) black powder usually faces environmental and financial challenges due to the use of conventional oxidizing agents. To address this issue, the present study proposes a novel closed-loop process based on oxygen pressure selective leaching to achieve the comprehensive, ecofriendly recycling of SLFP black powder. Under mild conditions (60 degrees C and 0.6 MPa oxygen partial pressure), clean and low-cost oxygen served as the sole oxidizing agent, achieving a leaching efficiency of 98.6% for Li. Conversely, Fe and P were effectively immobilized in situ within the leach residue, limiting their dissolution to less than 3.45% and 2.08%, respectively. This resulted in ultra-high selective separation, with Li/Fe and Li/P separation factors of 28.4 and 47.3, respectively. Mechanistic studies revealed that the process is catalyzed by the Fe2+/Fe3+ redox couple, with trace copper in the raw material acting as a key electron shuttle to accelerate the oxidation cycle. The process efficiently recovers high-purity Li2CO3 from the leachate and converts the leach residue into the valuable crystalline materials, such as gamma-FePO4 and carbon (C), via an innovative 'acid dissolution-recrystallisation-calcination' pathway. By resolving the challenge of selective Li extraction and converting solid waste into valuable resources, this closed-loop system offers strong support for the sustainable, high-value industrial recycling of SLFP batteries.

The sulfate process remains the dominant route for titanium dioxide production in China due to its wide adaptability to raw materials, low equipment investment, and good particle size control. However, this process generates a large volume of highly concentrated, compositionally complex titanium white waste acid (TDWA), which poses significant corrosivity and environmental risks. This paper systematically reviews the sources, characteristics, and main treatment technologies for TDWA, with an emphasis on recent advances in acid recovery and methods for separating valuable metals. By comparing the technical features and applicability of various approaches, the advantages and limitations of current resource recovery routes are evaluated. Furthermore, considering the national “dual-carbon” goals and “Zero-Waste City” initiatives, the future development trends and key scientific challenges of green recycling are discussed, providing theoretical and technical guidance for establishing an efficient, low-carbon, and sustainable resource recovery system for TDWA.

Given the importance of predicting droplet size and its evolution for calculating the interfacial area between two phases, this study, set in the context of pulsed extraction columns, proposes a dynamic one-dimensional population balance model (1-D-PBM) coupled with direct measurement kernel functions. The calculated values obtained via this framework exhibit deviations within +/- 10% from the experimental data across various conditions, demonstrating its good predictive accuracy. The computational results indicate that plate wettability, pulse intensity, and interfacial tension all significantly influence the droplet number density. In the axial direction, drop size exhibits four changing patterns: monotonic decrease, increase followed by decrease, increase followed by stabilization, and sustained increase, reflecting the complexity of droplet swarm behavior. Under wettable conditions, the sensitivity of droplet diameter changes induced by operating condition variations is lower than that in non-wetting conditions. A 10% increase in pulse intensity leads to a 16.2% reduction in the Sauter mean diameter (d32) under non-wetting conditions, while the reduction is only 7.3% under wetting conditions. This computational framework also enables accurate prediction of droplet number density in a pilot-scale pulsed extraction column with low computational load.