Particle Flow Research Articles

Physics-informed dynamic mode decomposition for reconstruction and prediction of dense particulate pipe flows

Dynamic mode decomposition (DMD) effectively captures the growth and frequency characteristics of individual modes, enabling the construction of reduced-order models for flow evolution, thereby facilitating the prediction of fluid dynamic behavior. However, DMD's predictive accuracy is inherently constrained by its inability to inherently incorporate physical principles. Therefore, for dense particulate pipe flows with complex flow mechanisms, we introduce a physics-informed dynamic mode decomposition (PIDMD) approach, which augments the purely data-driven DMD framework by incorporating the conservation of mass as a constraint. This ensures that the extracted dynamic modes adhere to known physical principles. Initially, we apply the DMD to reconstruct and predict the velocity field, comparing the results against benchmark computational fluid dynamics-discrete element method (CFD-DEM) simulations. Findings indicate that while DMD can reconstruct the flow field simulated by CFD-DEM and provide predictions of future flow states, its predictive accuracy gradually deteriorates over time. Next, we utilize both PIDMD and DMD to reconstruct and predict particle volume fraction, evaluating both models based on CFD-DEM outcomes. The results indicate that both PIDMD and DMD can predict particle aggregation toward the center, but PIDMD provides more accurate predictions regarding the size of particle aggregations and their distribution near the tube wall. Furthermore, the average prediction error for particle volume fraction using PIDMD is 6.54%, which is lower than the error of 13.49% obtained by DMD. Both qualitative and quantitative comparisons highlight the superior predictive capability of PIDMD. The methodology developed in this study provides valuable insights for high-precision predictions of particulate flows.

A conditional deep learning model for super-resolution reconstruction of small-scale turbulent structures in particle-Laden flows

Super-resolution reconstruction of turbulent flows using deep learning has gained significant attention, yet challenges remain in accurately capturing physical small-scale structures. This study introduces the Conditional Enhanced Super-Resolution Generative Adversarial Network (CESRGAN) for reconstructing high-resolution turbulent velocity fields from low-resolution inputs. CESRGAN consists of a conditional discriminator and a conditional generator, the latter being called CoGEN. CoGEN incorporates subgrid-scale (SGS) turbulence kinetic energy as conditional information, improving the recovery of small-scale turbulent structures with the desired level of energy. By being aware of SGS turbulence kinetic energy, CoGEN is relatively insensitive to the degree of detail in the input. As shown in the paper, its advantages become more pronounced when the model is applied to heavily filtered input. We evaluate the model using direct numerical simulation (DNS) data of forced homogeneous isotropic turbulence. The analysis of Q-criterion isosurfaces, energy spectra, and probability density functions shows that the proposed CoGEN reconstructs fine-scale vortical structures more precisely and captures turbulent intermittency better compared to the traditional generator. Particle-pair dispersion simulations validate the physical fidelity of CoGEN-reconstructed fields, closely matching DNS results across various Stokes numbers and filtering levels. This paper demonstrates how incorporating available physical information enhances super-resolution models for turbulent flows.

Comparative analysis of machine learning models for particle flow reconstruction

Abstract. Using the simulation data of different calorimeters, we investigate the use of machine learning and python algorithms for the simulation and reconstruction of particle flow energy in high-energy physics. We train models based on simulated pixel value image instead of common numerical data. We define two models that use different Regressor algorithms. Multi-layer Perceptron (MLP) Regressor offer stable and accurate prediction under less affection situation. Convolutional Neutral Networks (CNN) Regressor provided better and stronger modeling and reconstruction ability; however, it could cause overfitting results in certain situations. Furthermore, we optimize our models with the use of PyTorch. These models can serve as fast method for particle flow reconstruction in future studies and experiments.

Analysis and mitigation of erosion wear of transfer ducts in a falling particle CSP system

Solid particles are effective heat capture and transfer media for next-generation (Gen3) concentrating solar power (CSP) plants that offer high-temperature operability, lower levelized cost, and higher efficiency. However, the relative motion of the solid particles with respect to the CSP system components causes significant wear of the wall materials in the form of erosion and abrasion. The transfer duct is one of the prevalent components in the falling particle CSP system that experiences erosion wear due to the impact of particles on its surface, which depends on several factors, such as duct design, material, and particle flow rate, among others. In this work, erosion wear in the transfer duct and its mitigation were studied computationally through different duct designs and particle flow parameters, including transfer duct length, diameter, slanted angle of the duct, and entrance velocity. Computational simulations based on particle tracking and discrete element modeling were used to understand erosion behavior systematically and, in turn, identify areas most prone to erosive wear. It was found that the use of erosion-resistant coatings in selected locations determined from the simulations was sufficient to mitigate overall erosion wear in the component. This study provides fundamental insight into the erosion wear of a key component of the falling particle CSP system for the first time and the design approaches to mitigate wear.

Langevin dynamics for a heavy particle immersed within a flow of light particles

A micro-hydrodynamics model based on elastic collisions of light point solvent particles with a heavy solute particle is investigated in the setting where the light particles have velocity distribution corresponding to a background flow. Considering a range of stationary background flows and distributions for the solvent particle velocities, the macroscopic Langevin-type description of the behaviour of the heavy particle is derived in the form of a generalized Ornstein–Uhlenbeck process. At leading order, the drift term in this process depends upon both the geometric structure of the background flow and the size of the heavy particle, while both drift and diffusion terms scale with moments of the light particle velocity distribution. Computational methods for simulating the micro-hydrodynamics model are then designed to confirm the theoretical results. To enable long-time calculations, simulations are performed in a frame co-moving with the heavy particle. Efficient methods for sampling the position and velocity distributions of incoming solvent particles at the boundaries of the co-moving frame are derived for a range of distributions of solvent particles. The simulations show good agreement with the theoretical results.

Simulation of unsteady ice accretion on horizontal axis wind turbine blade sections in turbulent wind shear condition

This study presents a comprehensive simulation approach to quantify power losses in horizontal axis wind turbines under environmental icing conditions. It investigates how wind shear and turbulence affect a 2.5 MW wind turbine's performance, particularly under ice accretion. Turbulence intensity, ranging from 1% to 20%, impacts the relative flow fluctuations and angle of attack on the blade sections, influencing the aerodynamic penalty ratio. The incoming wind speed and the flow angle at various blade sections were determined using the unsteady blade element momentum method, considering vortex induction effects and Prandtl and Glauert corrections. For ice accretion analysis, a fully unsteady simulation of computational grid motion due to ice accretion was performed, along with the solution of the multiphase flow of water dispersed particles in cold air, derived from the psychrometric chart. The findings highlight the significant impact of the incoming turbulent wind fluctuations on the dispersion of the ice shape formed at sections corresponding to their radial position on the blade according to the momentary angle of attack fluctuations. The formation of ice profiles along the blade has led to a subsequent degradation in the aerodynamic efficiency of the blade sections, which is directly proportional to the escalation in turbulence intensity. This phenomenon leads to a continual reduction in the power output of the wind turbine. This research provides valuable insights into the performance of wind turbines under icing conditions in real wind fluctuations.

Numerical study of the effects of unmatched pressure on the supersonic particle-laden mixing layer

The dispersion of monodisperse, inertial particles in a supersonic mixing layer consisting of two sheared flows with differing pressures (P1 for the particle-laden jet flow and P2 for the airflow) is numerically investigated using large Eddy simulation and Euler–Lagrange methods. The calculations reveal the following insights: The pressure disparity between the two flows induces a transverse gas flow effect, which swiftly deflects the mixing layer from the high-pressure side to the low-pressure side. The growth rate of mixing layer increases with the ratio of P2/P1 and while the deflected displacement correlates with the pressure difference |P2-P1|. However, the particles exhibit delayed tracking characteristics to the deflected mixing layer because of their relative relaxation to the transverse gas velocity, particularly in the upstream region of the mixing layer (also known as the Kelvin–Helmholtz instability developing zone or KH zone). Notably, when the P2 exceeds that of the P1, particles can more easily penetrate into the vortices of KH zone, significantly enhancing the downstream gas–particle mixing. This mixing enhancement is particularly pronounced for larger particles due to their increased inertia, which allows them to advance into the vortices of KH zone more effectively than smaller ones.

Numerical simulation and experimental study of microplastic transport under open channel shear flow: Roles of particle physical properties and flow velocities

Microplastic (MP) transport patterns under open channel shear flow remain unclear. This study investigates the transport laws of MPs at various flow velocities, MP densities, sizes and concentrations in the U-shaped experimental flume and the numerical flume based on Lattice Boltzmann Method (LBM). The results indicate that the average horizontal particle velocity and the transport distances of Polyvinyl chloride (PVC) and Polystyrene (PS) particles increase with the average cross-sectional flow velocity, while the average vertical particle velocity decreases with it. The total average particle velocity closely matches the average vertical particle velocity, regardless of the variation in MP size, density and concentration. Formula-based analysis reveals that the acceleration of spherical MP transport mainly depends on the particle size and its consequent relative drag force term (RDFT) under the conditions with a single type of MP particles, but on the particle density and its consequent RDFT and relative gravity term (RGT) in the case concerning different types of MP particles with identical particle sizes. The average horizontal particle velocity maximum of PVC and PS are both strongly correlated with the average flow velocity maximum in the cross-section. This correlation lowers with the MP particle size and concentration, and is independent of MP density. Our findings can provide reference for the prevention and control of MP pollution in rivers.

The Mother's Day Geomagnetic Storm on 10 May 2024: Aurora Observations and Low Latitude Space Weather Effects in Mexico

AbstractOn 10 May 2024, a severe geomagnetic storm coinciding with Mother's Day in Mexico lasted over 40 hr and produced polar auroras observable at low latitudes. This storm, the most intense since 2003, resulted from a series of solar flares and coronal mass ejections from active region 3664. The event was significant for space weather studies in Mexico, marking a milestone by enabling comprehensive measurements of its effects. The Mexico Space Weather Service (SCIESMEX) and the National Space Weather Laboratory (LANCE) had prepared for such an event since their inception. LANCE's instrument networks recorded solar chromospheric images, solar radio bursts, geomagnetic variations, Schumann resonances, ionospheric disturbances, and energetic particle flows. They also monitored Geomagnetically Induced Currents (GICs) in three strategic substations of the national electrical system. This provided unprecedented insights into the dynamics of severe space weather events at the North‐American low‐latitude environment. Citizen science efforts documented auroras and regional responses, capturing variations in geomagnetic indices, ionospheric disturbances, cosmic ray fluxes, GICs, and technological impacts. SCIESMEX worked with the National Civil Protection System (SINAPROC) to issue warnings, ensuring public awareness and preparedness. This coordination underscores the importance of effective communication and collaboration in mitigating impacts. The May 2024 geomagnetic storm demonstrated the critical role of preparedness, research, and public education in reducing the effects of future space weather events in Mexico.

CFD analysis of microscopic particle separation in low-volumetric classifiers: DPM tracking and experimental validation for enhanced efficiency using geometric modification strategy

The increasing demand for advanced air quality management technologies highlights the need for efficient separators capable of classifying microparticles by size. This study introduces a novel approach of geometric modifications to optimize low-volumetric environmental separators through Computational Fluid Dynamics (CFD) simulations. This study investigated micron particle flow behaviour, vortex strength, and separation chamber design using Lagrangian particle tracking to capture the complex particle–fluid interactions. Key geometry modifications included optimizing internal configurations, such as tube arrangements and discharge tube lengths, which resulted in significantly improved separation efficiency. The CFD simulations were validated against experimental data with flow rates ranging from 10 to 20 LPM (Re = 1008, 1512, 2016), demonstrating flow patterns, vorticity, and particle retention. A major contribution of this study is the particle retention efficiency analysis across a wide range of particle sizes. Particles larger than 10 µm were captured with near-perfect efficiency, while capturing finer particles (1–8 µm) proved more challenging, highlighting areas for future improvement. Notably, increasing the number of separation tubes from 3 to 4 and adjusting their heights led to a 10 % increase in particle retention for particle diameters of 10 and 20 µm. Additionally, higher flow rates, especially at 17 LPM (Re = 1714), increased capture rates for medium-sized particles by prolonging residence times through increased turbulence. This research advances micron particle separation technologies through design optimizations, supported by experimental and numerical analysis. The findings have broad implications for improving the performance of environmental separators in industrial applications, and for future developments in air quality management systems.

Toward a Plasmon-Based Biosensor throughout a Thermoresponsive Hydrogel.

This study investigates the potential of thermoresponsive hydrogels as innovative substrates for future in vitro diagnostic (IVD) applications using AVAC technology, developed and patented by the Mecwins biomedical company. In order to convert the hydrogel in a substrate compatible with AVAC technology, the following prerequisites were established: (1) the hydrogel layer needs to be permeable to gold nanoparticles (AuNPs), and (2) the optical properties of the hydrogel should not interfere with the detection of AuNPs with AVAC technology. These two key aspects are evaluated in this work. A silicon substrate (Sil) was coated with a layer of a thermosensitive hydrogel (TSH) based on poly(N-isopropylacrylamide-co-N,N'-methylene bis(acrylamide) (PNIPAAm-co-MBA). The TSH offers the advantage of easy modulation of its porosity through cross-linker adjustments, crucial for the plasmonic nanoparticle (NP) permeation. The platforms, denominated as (Sil)-g-(PNIPAAm-co-MBA), were fabricated by changing the cross-linker concentrations and exploring three deposition methods: drop casting (DC), spin coating (SC), and 3D printing (3D); the DC approach resulted in a very homogeneous and thin hydrogel layer, very suitable for the final application. Furthermore, after physical-chemical characterization, the TSH demonstrated its functionality in regulating nanoparticle absorption, and AVAC technology's capability to precisely identify such NPs through the hydrogel matrix was validated. The proposed hydrogel platform fulfills the initial requirements, opening the possibility for employing these hydrogels as dynamic substrates in sandwich immunoassay devices. The next step in the development of the hydrogel substrate would be its functionalization with biorecognition groups to allow for biomarker detection. By leveraging their enhanced capture efficiency and the ability to manipulate particle flow thermally, we anticipate a significant advancement in diagnostic methodologies, combining the spatial benefits of three-dimensional hydrogel structures with the precision of AVAC's digital detection.

Experiment and modeling investigation of irregular block descent into water

The underwater motion of freely falling irregular blocks is a critical factor in various applications, including damming large rivers, sealing levee breaches, and embankment construction. This study first investigates the motion patterns of blocks with various shapes sinking in water through a series of experimental tests. To quantitatively describe the underwater motion characteristics of irregular blocks, a new motion model based on the concept of equivalent spheres is proposed. The coupled particle flow code – computational fluid dynamics (PFC-CFD) method is employed to simulate the movement of cubic, pyramidal, and cylindrical blocks at various flow speeds and dropping heights. The parameters of the proposed model are calibrated and validated through numerical simulations. The predicted trajectories of the model show good agreement with the coupled PFC-CFD simulation data and the indoor drop test results, demonstrating the reliability and accuracy of the model. This proposed model, being computationally simple and utilizing readily available parameters, provides valuable insights for designing underwater dumping construction plans and related projects.

Adaptive mesh refinement for a particle level simulation of supercritical water fluidized bed reactors

High-precision computational fluid dynamics-discrete element method (CFD-DEM) simulation serves as a foundation for the detailed design of supercritical water fluidized bed reactors (SCWFBRs). However, as the scale of these reactors increases, the computational domain and reacting particles expand exponentially. Traditional adaptive mesh refinement is constrained in dealing with dense phase zones in SCWFBRs, as the nonlinear characteristics of the dense reacting particle flow render local-field error estimation ineffective. To address this limitation, an efficient and accurate CFD-DEM framework is established, integrating adaptive mesh refinement and heterogeneous computing. The mesh adaptation strategy is based on whole-field error estimation and is defined by a set of cell-marking criteria. The effect of the criteria on the accuracy and efficiency of the computational process is evaluated. This method reduces the demand for computational resources, thereby enabling the simulation of large-scale reactors at the particle level. The optimized adaptation strategy maintains an error of 1.67% while saving 51.59% of mesh cells required and 28.4% computation time. The primary factors influencing computational accuracy are identified as fluid velocity gradient and the particle reaction rate. The scalability of the adaptation strategy is also validated. For a fivefold radial scaled-up reactor, the cell count is reduced by 46.86% and the computation time by 22.2%, while the maximum error is limited to 2.79%. This work provides a solution that can consider both the computational scale and accuracy, thereby enabling the detailed design of large-scale SCWFBRs.

High-fidelity modelling of unburnt coal flow in an industry-scale blast furnace using a hybrid CFD-DEM method

Solid fuels, such as coal or biochar, can be injected into a blast furnace for low-carbon ironmaking. However, unburnt coal or biochar powders may accumulate in the coke bed, potentially reducing bed permeability and compromising furnace stability. Current CFD-DEM methods struggle to simulate systems with significant size differences between coke particles and coal or biochar powders, where the diameter ratio dck/dcl is 100–200 times. In this work, a novel multi-resolution hybrid CFD-DEM model is developed to simulate gas-unburnt powders-coke particles flow dynamics within and around the raceway with high fidelity. The model’s accuracy is validated by comparing the simulated evolution of the raceway cavity shape with experimental results. Subsequently, the hybrid model is used to simulate unburnt powder flow through the raceway and the adjacent coke bed (dck/dcl = 100), comparing its performance with conventional smoothed CFD-DEM models. The effects of gas inlet velocity and powder wettability are also analysed. Results show that the hybrid CFD-DEM model effectively simulates detailed pore fluid flow in the coke bed, which the smoothed model fails to capture, demonstrating the hybrid model’s superiority. Increasing gas inlet velocity enlarges the raceway cavity, intensifies high-speed pore flows, and accelerates powder transport into the coke bed. Additionally, higher cohesion energy density (kCED) reduces powder penetration, aligns the peak holdup position and penetration angle, and decreases permeability at key probe positions. This work provides an effective and efficient numerical tool to help understand and optimise the injection operation in blast furnaces.

Dynamic behavior of metal droplets impacting on porous surfaces

During the operation of solid rocket motors, the behavior of condensed particles impacting the wall will have a remarkable influence on the structure and performance of the engine. Especially when the aircraft is under overload flight conditions, the condensed particles will form a local high concentration particle flow under the action of inertia force, continuously scouring the surface of the insulation layer, seriously affecting the thermal protection structure and the work safety of the engine. Therefore, it is an essential issue to master the behavior mode of the condensate particle impinging the wall and clarify its dynamic characteristics and evolutionary mechanism. In this paper, the dynamic behavior of aluminum droplets impacting on the porous surface is experimentally investigated by preparing the porous wall, the influence mechanism of the porous structure on the spreading process of aluminum droplets is clarified, and the effects of the droplet's initial parameters as well as surface environment are analyzed. Combined with the fluid of volume method, the flow process of droplets on the porous surface is simulated. With the variation of the dimensionless parameters M and N, the main behavior patterns of the droplets obtained so far are rebound, adhesion, partial rebound, partial adhesion, and porous seepage. The presence of pore structure enhances the hydrophobicity of the wall and makes the droplets more easily broken during spreading. When the droplet initial energy is certain and the wall structure conditions change, there is a strong competitive relationship between its spreading and penetration. When the droplet initial energy is increased, its spreading and penetration strengths are significantly increased. The research results can provide a reference for the erosion process of condensed-phase droplets impinging on the char layer and provide theoretical basis and data support for the design and optimization of SRMs.

Experimental and numerical simulation study of rough jointed rock samples under triaxial compression conditions

The presence of joint planes significantly affects the mechanical properties of rock and poses a threat to the safety of engineering construction. To examine the influence of Joint Roughness Coefficient (JRC) and joint plane inclination on the mechanical behavior of jointed rock masses, this research employed 3D printing technology to fabricate jointed rock samples with varying JRC and joint inclination angles. Triaxial compression tests were then conducted on these samples in the laboratory. The results indicate that an increase in JRC strengthens the serrated interlocking effect of joint planes, leading to a corresponding increase in both the peak failure strength and elastic modulus of samples with different inclination angles. For samples with the same JRC, the peak strength initially decreases with increasing inclination angle, followed by a subsequent rise. The variation trend of Poisson’s ratio, however, shows the opposite pattern. The joint inclination significantly impacts the failure mode of the samples. However, as JRC changes, the failure mode does not show significant variation. Furthermore, drawing from the laboratory test results, numerical simulations were performed using the Particle Flow Code in 2 Dimensions (PFC2D) to analyze mesoscopic crack propagation mechanisms in jointed rock models subjected to triaxial compression. Finally, this research discusses the effects of JRC and joint plane inclination on the anisotropic characteristics of jointed samples and offers a detailed analysis of the failure mechanisms.

The effect of ultrasonic treatment of a cured monolayer formed by three-dimensional printing from a prepreg reinforced with continuous carbon fiber on the resistance to the flow of solid particles

—The effect of ultrasonic processing at resonant frequencies of 22 and 44 kHz of a monolayer formed by three-dimensional printing from prepregs reinforced with continuous carbon fiber on the resistance to the flow of solid particles by imitating it by jet-abrasive treatment is investigated. The increment of the weight of both control and experimental samples in comparison with the initial state was established. It is shown that the force effect of ultrasound in rational modes contributes to a decrease in weight gain by 31.4% when processed at a frequency of 22 kHz and by 9% when processed at a frequency of 44 kHz. The decrease in weight increment is determined by an increase in the density of the monolayer structure after ultrasonic exposure, which leads to an increase in surface hardness in units of Schor-D by 13.5% at a frequency of 22 kHz and by 10% at a frequency of 44 kHz.

Particulate transport in porous media at pore-scale. Part 1: Unresolved-resolved four-way coupling CFD-DEM

Computational Fluid Dynamics - Discrete Element Method (CFD-DEM) is a powerful approach to simulate particulate flow in porous media at the pore-scale, and hence decipher the complex interplay between particle transport and retention. Two separate CFD-DEM approaches are commonly used in the literature: the unresolved (particle smaller than the grid cell size) and the resolved (particle bigger than the grid cell size) approach. In this paper, we propose a novel CFD-DEM coupling approach that combines both unresolved and resolved coupling. Our new modeling technique allows for the simulation of particulate flows in complex pore morphology characteristic of porous materials. It relies on an efficient searching strategy to find grid cells covered by the particles and on an appropriate calculation of the fluid-solid momentum exchange term. The robustness and efficiency of the computational model are demonstrated using cases for which reference solutions – analytical or experimental – exist. The new unresolved-resolved four-way coupling CFD-DEM is used to investigate pore-clogging and permeability reduction due to the sieving and bridging of particles.

Migration of a slip-spin solid spherical particle in a micropolar fluid-filled circular cylindrical tube

A combined study analytically and numerically for the axially symmetric creeping flow due to a slip-spin solid sphere surface moving in a microstructure fluid of micropolar type along the centreline of a circular cylindrical tube is introduced. This investigation was presented under low Reynolds number conditions. A general solution is obtained by superposing the essential solutions in both spherical and cylindrical coordinates to solve the Eringen micropolar field equations. The condition of the microrotation, along with couple stress, is used at the surface of the solid particle; while the microrotation is used at the inner cylindrical surface. Boundary conditions are imposed initially on the inner cylindrical surface using Fourier transforms and subsequently on the outer surface of the solid particle using a collocation technique. This paper aims to study the wall interaction problem of a translating slip-spin solid spherical particle in a micropolar fluid along the centreline of a circular cylindrical tube. The study also investigates the effect of the addition of slip conditions for velocity and microrotation on the surface of a solid particle. There is good convergence in the numerical findings obtained for the normalised hydrodynamic drag force (the tube-corrected factor) applying on the surface of the solid particle for several values of the micropolarity coefficient, slip-spin coefficients, and the ratio between the radius of the solid particle and tube. Regarding the flow of a solid spherical particle along the centreline of a cylindrical tube, our drag findings compare favourably to the solutions found in the literature. We found that the normalised drag force acting on the solid particle monotonically increases with the increase of the particle-to-tube radius ratio and reaches infinity in the limitless, with the increase of the micropolarity coefficient, and with the increase of the slip-spin coefficients for a steady ratio of particle-to-tube radius.

Solid-to-gas phase transition kinetics of diverse potassium occurrence forms during biomass pellet combustion: Time-resolved detection and multi-step modeling

The solid-to-gas phase transition of potassium during biomass combustion significantly impacts ash-related issues in bioenergy systems, affecting operational efficiency and equipment longevity. However, the specific mechanisms and kinetics of this transition process remain inadequately understood. This work investigates the time-resolved transition of solid-phase potassium to the gas phase during the combustion of rice husk and wheat straw pellets, combining experimental measurements with theoretical modeling. Tunable diode laser absorption spectroscopy (TDLAS) was employed to measure atomic potassium concentrations 15 mm above burning pellets tray, where gas-phase equilibrium is approached. Key combustion characteristics including thermogravimetric profiles, spectral radiation, and temperature were simultaneously monitored. A novel multi-step model was developed to describe the transition of different forms of solid-phase potassium (organic, exchangeable, and inorganic) to the gas phase. This model integrates TDLAS measurements, observed combustion characteristics, and biomass physicochemical properties. Thermodynamic equilibrium calculations were used to estimate the atomic potassium fraction from total gaseous potassium. The results showed that the solid-to-gas phase transition of organic potassium synchronizes with volatiles release. In contrast, the maximum emission rates of inorganic and exchangeable potassium occurred at the onset of char combustion. The developed model agrees well with the online detection experiments and were further validated by offline ICP analysis of residual ash. While not directly simulating gas-solid interface reactions near the particle surface, this work lays groundwork for future multi-scale modeling of particle-laden flows and reactor-scale phenomena in biomass combustion systems.