Editorial: Multiphase flow in energy studies and applications—A special issue for MTCUE-2022

This special topic has been initiated by the newly established World Conference on Multiphase Transportation, Conversion & Utilization of Energy (MTCUE-2022). To date, 55 papers have been published, covering a broad spectrum of research from fundamental studies to practical applications. The main topics encompass a wide range of areas, including interfacial phenomena and mechanisms, multiphase flow and heat transfer, reactive multiphase flow, multiphase flow in industrial processes, resource exploitation (such as rare-earth, oil and gas), hydrogen production and utilization, low carbon technology and new energy, as well as interdisciplinary applications of multiphase flow in areas such as medicine and bionics. These studies have employed various numerical methodologies, experimental techniques, theoretical methods, and machine learning approaches to investigate and address the challenges in multiphase flows.

Regarding multiphase flow and heat transfer: Kureshee et al.¹ investigated the impact of an acoustic field at different frequencies on the evaporation and internal circulation of twin drops, while varying the distance between them. The study revealed that the lowest frequency and the largest spacing resulted in the highest evaporation rate and circulation. Additionally, a critical spacing was observed when acoustic incidence was introduced. Specifically, the authors discovered that increasing the amplitude of the acoustic field facilitated the removal of accumulated vapor, thereby enhancing the evaporation process for drops positioned closer to each other. Liu et al.² proposed a novel axial swirl blade combined with a multi-jet component to enhance the efficiency of water evaporation in a spouted bed. Numerical simulations of the integrated internal structure demonstrated improved particle turbulence and mixing within the central bed region, thereby enhancing the fluidization quality. Consequently, the mass transfer during the water evaporation process was intensified by 91% and 161% compared to a traditional spouted bed without internal structures. Based on a first-order differential inequality, Li and Chen³ investigated the spatial characteristics of solutions to the generalized heat conduction equations on a semi-infinite cylinder with Dirichlet-type boundary conditions. They demonstrated the Phragmén–Lindelöf alternative for the solutions and developed an approach to obtain explicit bounds for the total energy in the case of decay. In the context of supercritical thermal multiphase flow, Jiang et al.⁴ conducted particle-resolved direct numerical simulation to explore the flow of high-temperature supercritical CO₂ passing a low-temperature fixed spherical particle. The study focused on Stefan flow near the particle surface without considering gravity and buoyancy effects. They demonstrated that the introduction of Stefan flow can reduce the flow resistance in the freestream, but it hinders heat transfer performance. Fang et al.⁵ developed a new coefficient correlation to describe the flow condensation heat transfer process. The correlation was formulated based on a large database comprising 5607 data points and 30 fluids, covering a wide range of operational parameters. The proposed correlation showed an overall better performance than the 38 existing correlations, with a mean absolute deviation of 14.1%. Collado⁶ introduced a novel void fraction thermo-kinematics model for subcooled flow boiling by employing new mass and energy balances. The model estimated the distribution of slip ratio, calculated the mixture enthalpy, and obtained the void fraction. The author developed an equation to describe the evolution of slip by ensuring the continuity of the first derivative of the specific volume of the mixture at saturation. Furthermore, a kinematic equation relating the onset of nuclear boiling and vapor velocity was discovered. The three additional parameters needed to fit the measured void fraction were determined through a trial-and-error process. Li et al.⁷ presented a proposal to eliminate water-steam flooding in condenser tubes, both in bare tubes and modulated heat transfer tubes where a mesh membrane tube is inserted, based on the principle of phase separation. The study demonstrated that a smaller pore size enhances the ability to prevent gas phase infiltration into the mesh screen, resulting in a stronger driving force to draw liquid into the interior of the mesh membrane tube. These findings suggest that the mechanism for preventing flooding involves the addition of a tunnel for upward transport of water-steam. In recent years, there has been a growing interest in multiphase flows involving nanofluids due to their exceptional heat transfer efficiency. For instance, Hosseini et al.⁸ synthesized stable nanofluids containing rod-shaped and spherical-shaped ZnO nanoparticles with mass fractions ranging from 0.2% to 1%. They conducted an investigation to assess the impact of these nanofluids on the operation of a plate heat exchanger. Experimental results demonstrated that, compared to pure water and the nanofluid containing spherical nanoparticles, the heat transfer rate increased by 29.2% and 7.5%, respectively, when utilizing the nanofluid with rod-shaped nanoparticles, at a flow rate of 1 ML/min. In addition to the aforementioned research articles, Gao et al.⁹ reviewed the development of electrical capacitance tomography (ECT) for cryogenic fluids. It discussed the evolution of ECT techniques, including two-electrode uniform electric field measurement, multi-electrode nonlinear measurement, and phase distribution imaging. The review also summarized and analyzed advanced ECT technologies in other fields, such as imaging algorithms, electrical capacitance volume tomography (ECVT), and data acquisition systems. Furthermore, the paper emphasized the existing challenges encountered in cryogenic ECT and proposed that future investigations should prioritize the optimization of sensor structures, the development of vacuum visualization devices, the design of micro-capacitive signal acquisition systems, and the creation of noise-resistant image reconstruction algorithms utilizing machine learning.

In the field of interfacial phenomena and mechanisms: Zhou et al.¹⁰ introduced a robust multi-relaxation-time phase-field lattice Boltzmann model for the simulation of droplet dynamics in the presence of soluble surfactants. Their findings unveiled the profound impact of Marangoni stress, arising from the interfacial nonuniformity of the surfactant, on droplet deformation and the prevention of droplet coalescence. Far et al.¹¹ presented a straightforward and practical cumulant phase-field lattice Boltzmann method. This method effectively incorporated interfacial tension and accurately accounted for the diagonal and off diagonal elements of the pressure tensor through their proposed equilibrium distribution function. By integrating this method with the Cahn–Hilliard equation, they successfully tracked interfaces in multiphase flows with multiple components. The effectiveness of the methodology was demonstrated through simulations of various fluid flow processes, including droplet coalescence and breakup. To control the dynamic interfacial wettability for spray cooling of electronic devices, Park et al.¹² conducted a study where they designed and fabricated various nanoscale architectures to investigate the effects of their nanotextured surfaces on drop impact phenomena and evaporative cooling. The results demonstrated that the nanotextured surfaces with increased dynamic wettability facilitated the Leidenfrost limit and drop spreading, leading to improved heat removal capabilities. Notably, the thorny-devil nanofiber surface exhibited the highest heat flux at the Reynolds and Weber numbers investigated in the study. Qian et al.¹³ performed high-speed imaging experiments on a liquid–liquid flow system to examine the hydrodynamic characteristics of sedimentation in metal droplets. By analyzing the mechanical oscillations observed during the coalescence process, the researchers proposed a critical impact velocity that determines whether the droplets will coalesce or rebound. Interestingly, it was found that this impact velocity is positively correlated with the inherent surface tension of the metal droplets. Denys et al.¹⁴ introduced a novel Lagrangian particle-based superdroplet approach to simulate the formation of cloud droplets while accounting for the presence of surfactants. The results of their mechanistic exploration revealed that the size and number of cloud droplets can be enhanced, thereby promoting their formation. Additionally, the study confirmed the presence of a circulation pattern among the droplets, wherein growth and activation processes occur from the bottom to the top of the cloud. Gao et al.¹⁵ conducted a study in which they enhanced the horizontal mobility of coalesced jumping droplets on superhydrophobic surfaces. The research revealed that the dynamics of coalesced droplets can be controlled by the design of surface structures, uncovering the underlying mechanism behind this phenomenon. Wang et al.¹⁶ conducted experiments using a high-speed camera to visualize the electrohydrodynamic instability and disintegration of a low viscous liquid jet. The study focused on characterizing and analyzing the spray features and evolution of droplet breakup morphology of the electrified jet. The experimental visualization provided insights into the generation of homogeneous drops in the simple-jet regime and the gradual transformation of the cone-jet into the simple-jet with an increased liquid flow rate. Li et al.¹⁷ employed a volume of fluid-discrete particle model solver to study the transformation between continuous and discrete phases of bubbles or droplets. The study also presented the algorithms for two-way transition and interface capture, ensuring the reasonable and valid representation of the complex phase structure. Liu et al.¹⁸ utilized a high-speed imaging technique to investigate the near-field spray behavior, specifically the transition of spray modes, in electrohydrodynamic atomization of viscous liquids. The study explored the effects of various factors such as temperature, electric Bond numbers, and dimensionless flow rate. The findings revealed that temperature had a significant impact on the spray angle, semi-angle of the Taylor cone, and droplet size distributions. The improvement observed was attributed to the reduction in viscosity of highly viscous fluids with increasing temperature, which led to a decrease in viscous dissipation during atomization. As a result, the increased kinetic energy effectively resisted surface energy, resulting in improved spray quality. Xiang et al.¹⁹ developed a measurement system that combined the tail jet and supercavity, allowing for the study of various flow patterns by manipulating the model shape and jet rate. The results demonstrated that a high-intensity re-entrained liquid jet had the ability to destabilize the supercavity. Additionally, this system effectively suppressed the re-entrained jet; however, it also introduced another form of instability resulting from the interaction between the cavity and the body when the cavity made contact with the wall.

Regarding reactive multiphase flow: Li et al.²⁰ developed a method to derive shock equations using an iterative algorithm. These equations were used to solve for the flow parameters behind a normal shock, based on a database of six supercritical fluids. The results revealed significant variations in the normal shock parameters within the Widom region, even with a constant inflow Mach number. These variations were attributed to the significant changes in the physical parameters of the fluids. Additionally, a correlation analysis demonstrated that the normal shock density ratio and pressure ratio were primarily influenced by the compressibility and sound speed of the inflow. Empirical equations were derived to estimate the trends of the normal shock pressure ratio and density ratio. By employing high-fidelity interface-resolved Direct Numerical Simulation (DNS), Ou et al.²¹ conducted a study on the hydrodynamics, heat transfer, and mass transport phenomena in the supercritical water gasification of coal. The results demonstrated the occurrence of expanded boundary layers for velocity, heat, and mass components, which were attributed to the outgoing Stefan flow from the solid surface. Additionally, temperature variations surrounding a reacting sphere were found to increase the drag force while weakening the transport phenomena. Further investigations revealed that the presence of reaction heat release and changes in gas species inside the thermal boundary layer contributed to a gentle intensification of heat transport. Overall, the study provided a presentation and quantification of the primary factors influencing interphase transfer and reactive aspects in supercritical-water fluid flows passing through a reactive coal sphere. In order to characterize the hydrodynamics and reaction performance in fluidized-bed reactors for dry reforming of methane, Al-Otaibi et al.²² conducted multiphase particle-in-cell simulations for reactors operating under various reactive flow regimes. The results revealed that the turbulent fluidization regime exhibited the most favorable reactor performance in terms of CH₄ and CO₂ yields, CO+H₂ productivity, and CO/H₂ ratio. On the other hand, the bubbling regime demonstrated the poorest reaction performance. This study emphasized the significant role of flow hydrodynamics in determining the performance of fluidized-bed reactors in the dry reforming of methane process.

In the context of multiphase flow in industrial processes: Fan et al.²³ conducted a study on the spatiotemporal evolution of droplets on a target particle surface. This investigation involved advanced high-speed photography and theoretical analysis, considering the Weber and Reynolds numbers. The observations revealed that more prominent oscillation features were observed at high Reynolds numbers and low Weber numbers. Additionally, the size of the droplet relative to the particle influenced the period of oscillations during collisions. Taking into consideration mesoscale factors such as the equivalent diameter of turbulent eddies, obtained through the energy-minimization multi-scale methodology, Jiao et al.²⁴ proposed a novel closure model for bubble-induced turbulence. The aim was to enhance the accuracy of gas–liquid two-phase flow simulations. The effectiveness of incorporating this model into the Eulerian–Lagrangian simulation was verified, and the study demonstrated how the mechanisms of bubble-induced and shear-induced turbulence dominate the energy dissipation at different velocities. Tang et al.²⁵ devised a method for designing a squealer tip on the impeller blade with the aim of mitigating the negative effects of tip leakage flow in a multiphase pump. The study demonstrated that implementing the proposed blade squealer tip can lead to a 4.15% enhancement in the pump's hydraulic efficiency. Mechanistic findings indicated that the reverse flow of leakage can be restrained, preventing it from propagating from the pressure region to the suction region of the impeller blade. As a result, the energy dissipation caused by unsteady fluid motions in the mainstream can be reduced. Jiang et al.²⁶ utilized a computational fluid dynamics (CFD) model coupled with coarse-graining discrete element method (DEM) to investigate the reverse segregation mechanisms in vibrated fluidized beds containing both light and heavy particles. The simulation results revealed that vertical vibration induces relative movements between the bed and solids, which affects the negative gauge pressure. Moreover, the combined effects of the downward fluid pressure gradient force, solids transport, and the formation of local dilute regimes contribute to the occurrence of reverse segregation. Yang et al.²⁷ developed a nonlinear mathematical model to examine the behavior of a spring-damped vibrator under the influence of a harmonic exciting force, considering the effects of squeeze film. They derived an expression for the cylindrical squeeze film force using simplified Navier–Stokes equations. The study demonstrated that the fundamental frequency of the response corresponds to the exciting frequency, and an evident superharmonic phenomenon was observed. Zhang et al.²⁸ conducted experimental investigations to examine the impact of upscaling atomizers on different aerodynamic variables, such as the gas-to-liquid ratio and Weber number. The measured parameters from the experiments were used as reference data for CFD simulations. Both numerical and experimental results demonstrated that the degree of upscaling has minimal influence on the breakup morphology, and a reasonable estimation of liquid breakup behavior can be achieved using a first-order approximation. Through statistical analysis of data generated from discrete particle modeling, He et al.²⁹ provided evidence for the validity and accuracy of the standard kinetic theory in uniform granular flows. However, they found that the applicability of this theory is challenged when it comes to predicting solid pressure and collision frequency in inhomogeneous and nonequilibrium particle-gas flows, as many of its assumptions do not hold in such conditions. Therefore, using solid phase stress closures obtained from the standard kinetic theory alone is insufficient for simulating inhomogeneous and nonequilibrium particle-gas flows. Li et al.³⁰ combined the compressive force closure with a compressible multiphase particle-in-cell approach to investigate the underlying mechanism of dust lifting physics associated with shock waves. Analysis of the simulation results revealed that shock-induced flows generate downward drag and pressure gradient forces on the particles, which impede their upward movement. Interestingly, significant collision forces were observed on the dust particles, and the initial dust lifting process was significantly enhanced when the reflected wave reached the surface. Cai et al.³¹ proposed an efficient numerical model to investigate the electrohydrodynamic flow characteristics, such as the gas flow field, electric field, and space charge profiles, in a pump equipped with needle-ring-net electrodes. The numerical results revealed that the strongest electric field was observed near the needle tip and the edge of the ring electrode. However, there was no clear evidence of a higher concentration of space charges around the ring electrode. Moreover, this study improved the energy conversion efficiency, reaching an optimal value of 4.26%. This achievement surpassed the efficiency of most existing electrohydrodynamic pumps, which typically range from 0.11% to 2.56%. Taking into account the multiphysics and multiphase effects, Li et al.³² developed a three-tier sandwiched model using a volume of fluid technique. The aim was to investigate the interactions between gas, liquid, and solid phases and enhance the efficiency of open keyhole mode welding. The mechanistic analysis revealed that the arc reflection phenomenon occurred as a result of the arc being obstructed by the weld pool boundary. Furthermore, the movement of the welding process caused variations in the electric current path. Savari and Barigou³³ introduced a novel Lagrangian wavelet transform framework to analyze the turbulence and its modulation in liquid-particle mixing flows within a mechanically stirred tank. Using their experimental-theoretical framework, they demonstrated the significant impact of particle size and distribution, as well as the impeller pumping mode, on liquid turbulence. Specifically, the presence of larger particles intensified the liquid turbulence, leading to a broader region with high local values of turbulent kinetic energy in storage tanks. Fu et al.³⁴ conducted a study on the impact of inhomogeneous particle distributions on particle-gas heat transport calculations using particle-resolved direct numerical simulation. The numerical results revealed that the conventional Gunn correlation significantly overpredicted the heat transport coefficient near the interface between dense and dilute regions. This discrepancy was attributed to the substantial temperature differences between the clustered and dilute areas. Furthermore, the CFD-DEM simulation failed to accurately predict the heat transfer coefficient even when using a grid size twice the particle diameter. To address this issue, the researchers developed a modified Gunn correlation that incorporated the effect of inhomogeneous particle profiles. Recently, the application of supercritical multiphase flow technology has shown promise in enhancing process and device performance in the field of chemical and process engineering. Xi et al.³⁵ conducted a study to examine the flow hydrodynamics of supercritical water circulating fluidized beds using two-fluid model simulations. The researchers investigated the typical core-annulus distributions of flow characteristics, such as void fraction and particle velocities, in detail. Interestingly, they discovered similarities between these distributions and those observed in conventional gas-particle flow risers. This finding provides valuable insights into the behavior of supercritical water circulating fluidized beds and enhances our understanding of their flow dynamics. Li et al.³⁶ proposed a novel approach to calculate the drag force experienced by single particles in multiphase flows using supercritical water as the continuous phase. This new model takes into account the complex interactions between particles, which have a significant impact on the drag force. In particular, the researchers identified a control mechanism that involves the interplay between viscosity and velocity gradient. The dependence of the single particle drag on various factors, including phase holdup, Reynolds number, pressure, and temperature, was analyzed and quantified. By considering these influences, the proposed model provides a more accurate representation of the drag forces experienced by particles in supercritical water-based multiphase flows. Zhang et al.³⁷ developed a novel spatial-temporal multiscale coupling approach that enhances computational efficiency by utilizing spatially overlapped continuum and discrete systems operating at alternating time steps. This innovative method improves the prediction accuracy and computational speed in simulations. The continuum system provides the initial estimation of each particle's potential position, while the discrete system provides particle-level information to correct the continuum system's predictions. Through comparisons with traditional approaches for silo discharge, the researchers demonstrated the effectiveness and efficiency of their proposed method. Wang et al.³⁸ investigated the mechanism of the slug/churn transition and presented a novel theoretical model based on the Kelvin–Helmholtz instability of the falling film around the Taylor bubble, along with kinematic analysis of the interfacial wave traveling on the falling film. The formation of a liquid bridge or quasi-liquid bridge served as the basis for determining the transition, and the researchers introduced the term “most dangerous wave,” which considers the ratio of wave amplitude to pipe diameter. The study revealed that the position of the slug/churn boundary moves downward with increasing system pressure but upward with increasing pipe diameter. Kanda et al.³⁹ explored the visualization and measurement of heat transfer in supercritical carbon dioxide (sCO₂) and emphasized the necessity for innovative measurement techniques. Specifically, they employed a high-speed phase-shifting interferometer to evaluate heat transfer in sCO₂. By visualizing the density distribution of sCO₂ at varying temperature and pressure conditions, distinct patterns near the critical point as well as in liquid-like and gas-like states are revealed. To assess transient heat transfer in gas-like conditions, the researchers used the interferometer and validate their experimental findings through numerical simulations. A quantitative comparison is made between the experimental and numerical results. The study confirmed the feasibility of the proposed measurement technique for transient heat transfer in sCO₂.

Concerning interdisciplinary multiphase flows: Li et al.⁴⁰ presented a time-resolved three-dimensional coupled method that utilized particle tracking velocimetry and particle image velocimetry techniques to measure the spatial profiles of two-phase velocity and its fluctuations in a dilute particle-laden gas jet. The study revealed that the presence of particles in the gas flow caused downstream stretching. Furthermore, the observations indicated strong non-equilibrium and anisotropic states, as evidenced by the non-Gaussian profile of axial solid velocity and the deviation from the spanwise velocity profiles. The researchers derived an improved drag correlation by reconstructing particle trajectories and analyzing the gas fluid field around the ejector exit, focusing on particle Reynolds numbers ranging from 30 to 300. Additionally, microfluidic/nanofluidic flows have emerged as a prominent research area due to their exceptional performance in enhancing transport processes. Bernades et al.⁴¹ conducted direct numerical simulations to study and analyze supercritical microconfined turbulence under transcritical conditions at high pressure. The results were compared with equivalent low-pressure systems, revealing that microconfined turbulence at high-pressure conditions exhibited significant enhancements in mixing and heat transfer. Specifically, the mixing was found to increase by a factor of 100, while the heat transfer increased by a factor of 20, in comparison to the low-pressure systems. Zhou et al.⁴² utilized molecular dynamics simulations, finite element simulations, and theoretical analysis to investigate the entrance loss of capillary flow in narrow slit nanofluidic channels. The simulation results demonstrated that the entrance loss plays a significant role in the early stage of capillary flow, characterized by a linear increase in capillary length and a constant capillary velocity. In the subsequent period, a nonlinear variation in capillary length and a decrease in capillary velocity were observed. Based on these findings, the researchers developed a capillary flow model that incorporates the effect of entrance loss, enabling a better understanding of nanofluidic flow properties in nanochannels. Chen et al.⁴³ employed a coupled volume of fluid and level set model to comprehensively examine the influence of inclination angle on the dynamics of bubbly flow and heat transfer characteristics in a rectangular mini-channel with relatively low fluid flow velocities. The findings revealed that increasing the inclination angle from 0° to 90° promotes heat transfer and gradually facilitates the rewetting of dry patches below, leading to the detachment of bubbles from the wall due to gravity. However, as the inclination angle approaches 180°, these positive effects diminish, and there is a slight decrease in the overall heat exchange efficiency.

Regarding hydrogen production and utilization: Peng et al.⁴⁴ designed a planar electrochemical reactor for the purpose of generating hydrogen bubbles through alkaline water electrolysis. As the bubbles act as electrical insulators, their dynamics have a significant impact on the efficiency of hydrogen production. By numerically simulating the electric and flow fields using a bionic leaf-like design, the researchers observed more uniform current distribution profiles and more effective removal of microbubbles compared to the traditional mesh strategy. Consequently, the bionic leaf-like design demonstrated approximately a 50% higher hydrogen yield compared to the conventional approach. Zhan et al.⁴⁵ conducted numerical investigations on the growth and detachment behavior of hydrogen bubbles on a microelectrode flat under a normal magnetic field using the volume of fluid (VOF) multiphase model. The numerical simulations revealed several key findings. First, the supersaturated dissolved hydrogen concentration and mass transfer source were found to be significantly lower in the wider body bubble interface region compared to the wedge-shaped region near the bottom of the bubble. Additionally, the study highlighted that the higher rotational electrolyte flow rate predominantly occurred at the tilted position of the bubble equator, while the higher current density and corresponding Lorentz force were concentrated in the wedge-shaped region. Feng et al.⁴⁶ employed a time-dependent density functional theory method to examine the atomic-scale and femtosecond-scale plasmon-mediated water splitting phenomenon in a realistic H2O@Au6 model under femtosecond laser excitation. The study yielded significant insights, challenging the traditional theory that describes excitation and thermalization processes within gold. Notably, it was demonstrated that the charge transfer process deviates from the conventional understanding, with the dominant mechanism being the direct transfer of d-orbital electrons from the gold cluster to the adsorbed water molecule.

On the topic of low carbon technology and new energy: Shahzer et al.⁴⁷ conducted transient CFD simulations to investigate the impact of fins on the internal flow dynamics and hydraulic characteristics of water turbines under part load conditions, considering variations in Thoma numbers. The results revealed that the installation of fins in the draft tube led to significant reductions in swirl intensity (68%), cavitation rate (60%), and pressure pulsations (43%). This result highlights the potential of using fins to optimize stable energy production across different Thoma numbers. Furthermore, the study offers valuable insights into determining the machine reference level for ensuring the stable operation of water turbines through the installation of fins. Ye et al.⁴⁸ conducted experiments using a high-speed camera to investigate the mechanism of air entrainment in high-speed chute flows by chute bottom aerators. The measurement results revealed that the impact entrainment of inertial jets becomes dominant as the Froude number increases. However, the proportion of air flow for surface aeration under the jet increases with the height of the aerator. Building upon the experimental observations, the researchers developed a general model that incorporates these two key impact factors to predict aerator cavity entrainment. Xu et al.⁴⁹ proposed a novel variational multiscale model to characterize the dynamics of turbulent and laminar flow, as well as thermal mechanics, within solar chimneys. The model was validated and subsequently employed to investigate the thermofluid characteristics in a building with various solar chimney designs. The results showed that, compared to a standalone chimney commonly used, their proposed complex and realistic building space design increased the air flow rate by 48.9%. This improvement was attributed to the reduction of turbulence around the solar chimney inlet.

Concerning resource exploitation (rare-earth, oil and gas): Zhao et al.⁵⁰ conducted simulations to investigate the electrohydrodynamics and manipulation of viscous fingering in leaky dielectric fluids confined within a channel. They employed a combination of the finite difference approach and lattice Boltzmann method. By conducting extensive simulations with varying permittivity and conductivity ratios, they were able to establish a phase diagram that characterizes the interfacial morphologies under both horizontal and vertical electric fields. Kou et al.⁵¹ developed a thermodynamically consistent model for describing immiscible gas–liquid flows in porous media, based on the second law of thermodynamics. This model incorporated free energies to accurately represent the compressibility of the gas phase and the influence of capillarity. The thermodynamic consistency of the model was demonstrated through simulations of gas and liquid displacement processes, and its validity was confirmed by comparing the results with laboratory data. Mirazimi et al.⁵² developed a model to predict the time required for water barrier rupture caused by oil swelling. This model considers the mass transfer between tertiary-injected gas and residual oil, which is blocked by water, using Fick's law and the Maxwell–Stefan theory. The validation results showed that the Maxwell–Stefan theory accurately predicts the molecular diffusion process and the time for water barrier rupture in both pure and multicomponent systems. In contrast, Fick's law was found to be inadequate for predicting water rupture time in multicomponent mixtures.

Regarding machine learning in multiphase flows: researchers have used flexible machine learning techniques to aid in the conceptual development of robust predictive models for multiphase flows by uncovering hidden patterns and mechanisms within datasets.⁵³ This integration of machine learning with traditional methods has the potential to revolutionize our understanding and analysis of complex fluid dynamics and transport phenomena. Li et al.⁵⁴ proposed a coupling framework that combines the k-nearest neighbors regressor method with the Gaussian process algorithm to learn experimental data and capture statistical features. This framework was applied to approximate the averaged flow and its fluctuations in turbulent liquid–solid mixing flow trajectories within a mechanically agitated device. The developed coupling framework proved to be efficient and robust in predicting the desired flow characteristics. Zheng et al.⁵⁵ developed a physics-informed machine learning model based on a neural network (NN) with encoded observations. This model effectively predicts sequential multiphase flow patterns and dynamic movements by considering intense phase interactions. To ensure the strict satisfaction of mass conservation, the approximated order parameters are corrected using a mapping scheme that enforces multiphase consistency, conservative boundedness, and the preservation of mass. Furthermore, the model predicts the velocity in the next time step using another NN with the same network architecture. To reduce the parameter space, the momentum balance equation is included in the loss function during this step. The proposed physics-informed framework requires less data for approximations and achieves the absence of nonphysical characteristics of the order parameters, leading to accelerated convergence. Li et al.⁵⁶ developed an efficient machine learning-based dynamical model for studying single-phase and complex multicomponent liquid–solid turbulent flows in a stirred vessel. Their approach utilized a k-nearest neighbors regressor to estimate the primary flow dynamics by training it with short-term Lagrangian trajectories data obtained experimentally using positron emission particle tracking. Additionally, they implemented a Gaussian noise generator to introduce fluctuations in the flow conditions, generating a statistical pattern similar to the driver flow conditions. Overall, machine learning has the potential to significantly enhance the study and application of multiphase flows and transport phenomena in the field of energy.

In conclusion, this special topic of Physics of Fluids compiles exceptional papers from esteemed researchers worldwide, highlighting the significance of multiphase flow in energy studies and applications. The guest editors would like to express their sincere gratitude to all the authors and reviewers who dedicated their valuable efforts and expertise to make this special topic possible. We also extend our heartfelt appreciation to Prof. Alan Jeffrey Giacomin, the Editor-in-Chief of Physics of Fluids, and Mr. Jaimee-Ian Rodriguez, the Editorial Assistant, for their invaluable assistance and contributions.