Liposomes are lipid vesicles used to carry medicines and other therapeutic payloads. Their size, morphology, composition and stability can affect how they interact with cells, circulate in the bloodstream, release their cargo and withstand environmental stresses. These properties are therefore treated as critical quality attributes in the manufacture of liposomal drugs. Microfluidic systems, which guide liquids through tiny channels, have become an attractive production platform because researchers can adjust total flow rate, the ratio between the two liquid streams, solvent conditions and channel geometry to influence lipid self-assembly in a controlled environment.

Not all liposomes are the same size, and that variation matters. PDI is typically derived from dynamic light-scattering measurements and describes the breadth of a particle-size distribution rather than its average. A low PDI indicates a comparatively uniform population, whereas a higher value indicates a broader range of vesicle sizes. Broad distributions can make it harder to correlate dose with biological response and can contribute to problems with encapsulation, payload release, stability and sensitivity to temperature changes, residual solvent or purification. The variables that determine liposome dispersion are interconnected: fluid dynamics, diffusion-limited solvent exchange, lipid phase behavior and downstream processing can act together, making conventional one-factor-at-a-time experiments incomplete.

The researchers addressed that challenge by building a data set linking formulation and operating variables to two measurable outcomes: particle size, expressed in nanometers, and PDI. The original inputs included total flow rate, the flow-rate ratio between the two liquid streams, the concentrations of egg sphingomyelin, hydrogenated soy phosphatidylcholine, cholesterol and PEG-lipid, the identity of the aqueous phase, either ultrapure water or phosphate-buffered saline, and the type of microfluidic chip. The data were divided into 214 training samples, 46 validation samples and 46 test samples. Twelve additional wet-laboratory samples were reserved as an external validation set, although the reported results do not state how the models performed on that set.

To give the algorithms more useful information, the team expanded the original nine predictors to 19 engineered variables. These included the fractions of cholesterol, PEG-lipid, sphingomyelin and the principal membrane-forming lipid; the absolute concentration of the main lipid; interaction terms such as cholesterol multiplied by PEG and total flow rate multiplied by flow-rate ratio; and squared terms intended to capture nonlinear effects. The transformations were calculated directly from the measured inputs, allowing the resulting relationships to remain linked to recognizable aspects of liposome self-assembly rather than turning the analysis into an opaque numerical exercise.

Eleven predictive algorithms were evaluated, including ridge, lasso and elastic-net regression; radial-basis support vector regression; random forest, gradient boosting, XGBoost, LightGBM and CatBoost; and shallow and deep multilayer perceptrons. Hyperparameters were selected through grid search with fivefold cross-validation, while neural networks used the Adam optimizer and early stopping based on validation loss. Performance was assessed with the coefficient of determination, or R², root mean squared error and mean absolute error. The models were also examined with permutation importance and SHAP, a model-agnostic method that decomposes individual predictions into the contributions of different features and can provide global feature rankings as well as local explanations.

PDI proved to be the more predictable target. Gradient boosting achieved a validation R² of 0.7650, an RMSE of 0.1058 and an MAE of 0.0589. Its predictions followed the ideal diagonal across PDI values from 0.05 to 0.80 with little systematic bias. Random forest ranked second for PDI with a validation R² of 0.6653, followed by XGBoost at 0.6192. The leading gradient-boosting result also exceeded one previously reported mixture-of-experts benchmark with an R² of 0.7307. This performance is consistent with the ability of tree ensembles to capture nonlinear relationships and interactions in modest-size tabular data without requiring the very large samples often needed by deep neural networks. XGBoost’s very high reported training fit, with a training R² of 0.99, also suggested that it could be at risk of overfitting given the limited data set.

By contrast, the best model for particle size was a deep multilayer perceptron, but its validation R² reached only 0.4598, with an RMSE of 368.42 nanometers and an MAE of 272.83 nanometers. The size data were highly skewed, with a reported skewness of 5.70, and 9.2% of samples were classified as outliers. Predictions became especially variable above 500 nanometers. The authors noted that size can change sharply when formulations move between operating regimes, including when they cross a lipid-concentration threshold, undergo a phase transition or experience changes in solvent-composition kinetics. The size distribution contained a few large-size formulations and a longer tail of smaller-size formulations, a pattern that is difficult to capture reliably with a limited amount of data.

The interpretability analysis nevertheless produced useful clues. The primary lipid proportion ranked first in feature importance, followed by the PEG-lipid ratio, sphingomyelin fraction, flow-rate ratio and cholesterol fraction. SHAP analysis indicated that higher values of the main-lipid ratio were generally associated with lower PDI. PEG-lipid was also important, but at high concentrations its relationship with uniformity became detrimental. The results indicate that composition ratios and flow dynamics are not interchangeable controls: developers may need to adjust the balance among membrane constituents while simultaneously setting the rate at which the streams mix to achieve a narrow distribution. These are model-derived associations, not evidence that any single factor has been proven to cause a particular biological or manufacturing outcome.

The immediate application is model-assisted screening rather than fully autonomous formulation. The strongest PDI predictor could first identify regions of the formulation space that merit laboratory attention, after which targeted experiments could refine both size and dispersion. The authors also point to logarithmic size targets, robust loss functions, quantile or interval predictions, multi-task learning and explicit uncertainty estimates as possible ways to improve the weaker size model. More data are especially needed for large-particle and underrepresented operating regimes, while reporting performance on the 12-sample external validation would help establish whether predictions transfer across batches, operators, chips and measurement conditions. The study therefore does not remove the need for experimental testing, but it offers a way to make experiments more informed and to identify candidate conditions for narrower liposome populations without yet establishing improved clinical performance or product outcomes.

Subject of Research: Explainable machine learning for predicting liposome polydispersity in microfluidic manufacturing

Article Title: Data-driven prediction of polydispersity in microfluidic liposome production for pharmaceutical formulation optimization

Article References: Olamat, A., Abu Owida, H., Arabiat, A., & Ozel, P. (2026). Data-driven prediction of polydispersity in microfluidic liposome production for pharmaceutical formulation optimization. Pharmacia, 73, Article e200497. https://doi.org/10.3897/pharmacia.73.e200497

Image Credits: AI Generated

DOI: 10.3897/pharmacia.73.e200497

Keywords: liposomes, microfluidics, machine learning, polydispersity index, pharmaceutical formulation, gradient boosting, particle size, process optimization, SHAP analysis, drug delivery, Data-driven, prediction

The premise behind the special issue is straightforward but ambitious: many of today’s most promising drug molecules fail not because they lack pharmacological activity, but because they cannot be formulated into products that dissolve, stabilize, and reach their targets in the body. Poorly water-soluble compounds now dominate discovery pipelines, and the gap between a molecule’s intrinsic potency and its clinical performance is frequently a formulation problem. Particle engineering, the deliberate manipulation of particle size, shape, morphology, and solid-state form, offers a toolkit for closing that gap. Techniques such as micronization, nanosizing, spray drying, hot-melt extrusion, and controlled crystallization can transform an intractable compound into a powder with the dissolution profile, flow properties, and physical stability needed for a viable tablet, capsule, inhaler, or injectable suspension.

The scope of the issue, as outlined by the editors, covers six broad thematic areas. The first is particle engineering approaches for enhancing solubility, stability, and bioavailability, which sits at the heart of the bioavailability crisis in drug development. Reducing particle size increases the surface area available for dissolution, and when particles are pushed into the nanometer range, additional phenomena such as increased saturation solubility and improved adhesion to biological membranes come into play. Amorphous solid dispersions, in which a crystalline drug is molecularly dispersed in a polymer matrix, represent another cornerstone strategy, trading the thermodynamic stability of the crystal lattice for dramatically faster dissolution, at the cost of requiring careful control of recrystallization risk over a product’s shelf life.

A second thematic pillar concerns advanced formulation strategies across the full spectrum of dosage routes, including oral, injectable, inhalable, and transdermal delivery, along with broader advanced drug delivery systems. Each route imposes its own particle-level demands. Inhaled medicines, for example, require particles in a narrow aerodynamic size range, typically around one to five micrometers, to deposit in the deep lung rather than being exhaled or trapped in the throat. Dry powder inhalers depend on engineered particle surfaces and carrier interactions to achieve reproducible dispersion upon inhalation. Injectable suspensions demand particles that are small and uniform enough to pass through fine needles without clogging while remaining physically stable in suspension over months of storage. Transdermal systems, meanwhile, must balance drug loading with the permeability constraints of the stratum corneum, often relying on particle-based carriers or crystallinity control to maintain a stable thermodynamic driving force for skin penetration.

Solid-state characterization and control form the third focus area, and they represent the analytical backbone of everything else in the issue. The same molecule can exist in multiple crystalline forms, known as polymorphs, each with distinct solubility, melting point, mechanical behavior, and stability characteristics. The infamous case of ritonavir, an HIV drug whose market product failed in the late 1990s when a previously unknown, far less soluble polymorph spontaneously appeared during manufacturing, remains a defining cautionary tale for the industry. Modern pharmaceutical science responds with a battery of techniques, including powder X-ray diffraction, differential scanning calorimetry, dynamic vapor sorption, and solid-state nuclear magnetic resonance, to identify, quantify, and monitor the solid forms present in a drug product. The special issue invites contributions on how such characterization can be used not merely descriptively but predictively, guiding formulators toward solid states and processing conditions that will remain stable from first clinical batch to final commercial lot.

The fourth theme, translational formulation science and scale-up, addresses what many researchers consider the most difficult step in the entire pipeline. A formulation that performs beautifully in a one-liter beaker may behave entirely differently in a thousand-liter high-shear granulator. Scale-up introduces changes in mixing dynamics, heat transfer, drying rates, and mechanical stress that can alter particle size distributions, polymorphic outcomes, and blend uniformity. Translational formulation science seeks to understand and anticipate these shifts, building in vitro and in silico models that predict how a process will behave at production scale before expensive equipment is committed. The editors’ emphasis on translation signals a deliberate editorial preference for work that demonstrates this kind of industrial relevance, rather than purely mechanistic studies that stop at the laboratory bench.

Emerging manufacturing technologies constitute the fifth pillar, and this is where the field is arguably changing fastest. Continuous manufacturing, in which drug product is produced in a flowing integrated line rather than in discrete batch steps, is gaining regulatory and industrial acceptance because it enables real-time quality control and more flexible production volumes. Additive manufacturing, most prominently three-dimensional printing, has already produced the first FDA-approved printed medicine, a rapidly disintegrating levetiracetam tablet whose highly porous structure was made possible only by the printing process. Other emerging approaches include electrospinning for nanofiber drug matrices, supercritical fluid technologies for producing solvent-free engineered particles, and hot-melt extrusion lines capable of continuous amorphous dispersion production. Each of these technologies reshapes what particle and dosage form designers can achieve, and each brings its own scale-up and regulatory questions.

The sixth theme, Quality by Design and Process Analytical Technology, provides the regulatory and methodological framework that ties the others together. Quality by Design, or QbD, is a paradigm in which product and process understanding is built systematically into development: instead of testing quality into a finished product, manufacturers design the formulation and process so that critical quality attributes are controlled by understood relationships between input materials and process parameters. Process Analytical Technology, or PAT, supplies the real-time sensing tools, such as near-infrared spectroscopy, Raman spectroscopy, and focused beam reflectance measurement, that make this control possible on the factory floor. Together, QbD and PAT allow particle properties to be monitored and adjusted during production rather than discovered afterward in quality control testing, a shift with profound implications for both efficiency and patient safety.

For researchers considering submission, the June 30, 2026 deadline places the issue roughly a year and a half out, a timeline that accommodates both completed studies and work currently in progress. The guest editors’ institutional affiliations reflect the strength of South Korea’s pharmaceutical formulation research community, which has produced significant contributions in areas such as amorphous formulations, nanocrystal technology, and orally disintegrating dosage forms. The Journal of Pharmaceutical Investigation, published by Springer, serves as a venue where Asian and international pharmaceutical science converge, and a special issue of this scope is likely to draw contributions from academic groups, generic and innovative drug manufacturers, and contract development organizations alike.

The broader significance of the initiative lies in its insistence that particle engineering and formulation science are not peripheral support disciplines but central drivers of translational medicine. As biologics, poorly soluble small molecules, and combination products increasingly dominate therapeutic pipelines, the ability to engineer particles and design robust formulations determines whether scientific discoveries ever reach patients. By soliciting work that spans the full arc from particle design through solid-state control, scale-up, emerging manufacturing, and regulatory quality frameworks, the special issue is positioning formulation science where it increasingly belongs in practice: at the center of drug product development, with a direct line of sight from the crystallization vessel to the clinic.

Subject of Research: Translational pharmaceutical dosage form development based on particle engineering and formulation science

Article Title: Special Issue: Translational Advances in Pharmaceutical Dosage Form Development Based on Particle Engineering and Formulation Science

Article References: Special Issue: Translational Advances in Pharmaceutical Dosage Form Development Based on Particle Engineering and Formulation Science. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: particle engineering, formulation science, drug delivery, bioavailability, solid-state characterization, Quality by Design, Process Analytical Technology, continuous manufacturing, amorphous solid dispersions, scale-up, pharmaceutical manufacturing, Journal of Pharmaceutical Investigation

The problem the researchers tackled is known as base heating. As a rocket ascends, the hot exhaust plume radiates energy toward the aft structures of the vehicle, including the base region between clustered nozzles and the surfaces surrounding them. At sea level, the surrounding air constrains the plume and much of the heat is convected away, but at high altitudes the plume expands freely into the rarefied environment. Under these vacuum-like conditions the gas cools rapidly as it diffuses, yet the condensed particles suspended in the flow remain hot and continue to radiate. Understanding how much of that particle-driven radiation strikes the rocket base is critical for thermal protection design, particularly for solid rocket motors, whose propellants typically contain substantial amounts of aluminum powder to boost performance.

Simulating such a flow is notoriously difficult because the physics spans two very different regimes. The gas in a high-altitude plume is so rarefied that the continuum assumptions underlying ordinary computational fluid dynamics break down; molecular collisions become infrequent and the flow must be treated statistically. The research team therefore employed the direct simulation Monte Carlo method, using the SPARTA code, to model the rarefied plume field particle by particle, or more precisely molecule by simulated molecule. This approach, rooted in the molecular gas dynamics framework pioneered by Graham Bird, tracks representative molecules and their collisions to build up a statistical picture of the flow without solving the continuum equations at all.

The alumina particles, however, demanded a different treatment. Because they are far more massive than gas molecules and travel on largely ballistic trajectories punctuated by drag interactions with the thin gas, the team modeled them with Lagrangian particle tracking implemented in the open-source OpenFOAM toolkit. The two solvers were then coupled to an in-house radiative base-heating solver based on the discrete ordinates method, which computes how thermal radiation propagates through the particle-laden plume and how much of it is intercepted by the base region. This integrated computational framework, combining DSMC gas dynamics, Lagrangian particle dynamics, and radiative transfer, is one of the study’s central technical contributions, allowing each physical ingredient to be resolved with the method best suited to it.

The first major finding concerns what happens to the gas itself. The exhaust plume analysis revealed substantial diffusion and backflow under vacuum conditions: instead of forming a narrow, directed jet, the exhaust spreads laterally and a portion of it reverses direction, flowing back toward the vehicle. This expansion causes a pronounced drop in gas temperature. That cooling has a welcome simplifying consequence for the modelers, because the reduced gas temperature justified neglecting radiative heat transfer from the gas phase altogether. In other words, at high altitude the radiative threat to the rocket base comes almost entirely from the hot alumina particles, not from the glowing exhaust gases, a conclusion that sharply focuses where design attention should be directed.

With the gas-phase radiation set aside, the researchers systematically explored how particle characteristics shape base heating. Holding the propellant composition fixed, they varied the size of the alumina particles and computed the resulting radiative flux. The results reveal a strikingly nonlinear relationship. Radiative base heating increases rapidly as particle diameters move from the submicron range into the micron range, but beyond that transition the rate of increase diminishes markedly for larger particles. The physical explanation lies in the interplay between how much thermal radiation a particle emits, which scales strongly with its surface area and temperature, and how those particles are distributed and transported through the expanding plume. Small particles cool quickly and radiate inefficiently in aggregate, while the largest particles contribute less per unit mass than the intermediate sizes where the effect peaks.

The second axis of the study examined propellant composition. For a fixed particle size, the team varied the aluminum mass fraction in the propellant and found that base heating rises steadily as more aluminum is added. This makes intuitive sense once the chemistry is considered: aluminum powder burns in the motor to form aluminum oxide, so a propellant richer in aluminum produces a greater loading of radiating oxide particles in the exhaust. The finding carries a practical tension for rocket designers, because aluminum is added to solid propellants precisely to raise performance, yet every additional percentage point of aluminum buys a hotter radiative environment at the vehicle base. The new results quantify that trade-off in a form that thermal engineers can use during early design studies.

The authors are careful to frame the reliability of their numbers. Because formal benchmark validation of the modified radiation coupling procedure has not yet been completed, they caution that the predicted radiative-heating levels should be interpreted as engineering-level comparative sensitivity indicators for particle-driven base heating, rather than as fully validated absolute local heat-flux predictions. In practical terms, the study tells designers with confidence how base heating changes when particle size or aluminum content is changed, but the absolute magnitudes await experimental or high-fidelity benchmark confirmation. That honesty about validation status is a valuable feature of the work, distinguishing robust trends from numbers that should still be treated as provisional.

The study builds on a long lineage of plume radiation research stretching back decades, from early analyses of large solid propellant rocket plumes using DSMC in the 1980s, through finite-volume radiation analyses of rocket plume base heating in the 1990s, to more recent investigations of how the optical properties of alumina particles influence radiative base heating. What distinguishes the new effort is the tight coupling of three state-of-the-art tools, SPARTA for rarefied gas dynamics, OpenFOAM for particle tracking, and a dedicated radiation solver, into a single pipeline capable of answering parametric questions about particle size and propellant formulation. The work was supported by the National University Development Project of Jeonbuk National University, and the corresponding author, Man Young Kim, has previously published related predictions of radiative base heating from solid rocket exhaust plumes.

For the aerospace community, the implications extend across launch vehicles, upper stages, and missile systems that operate solid rocket motors in the upper atmosphere and beyond. As missions increasingly demand precise thermal margins rather than conservative overdesign, knowing that the submicron-to-micron transition in alumina particle size is the critical regime, and that aluminum loading drives heating upward, allows engineers to target both their propellant specifications and their thermal protection layouts more intelligently. The study also highlights the growing power of multiscale simulation, in which molecular-level gas kinetics, particle mechanics, and radiative transfer are stitched together to illuminate phenomena that neither wind tunnels nor flight tests can easily isolate. As validation matures, frameworks of this kind could become standard instruments for predicting the invisible thermal weather that surrounds every rocket climbing toward orbit.

Subject of Research: Radiative base heating from alumina particles in high-altitude solid rocket motor exhaust plumes

Article Title: Effect of Particle Size and Propellant Composition on Base Heating in High-Altitude SRM Plumes

Article References: Joo, H. C., Kim, J. S., & Kim, M. Y. (2026). Effect of Particle Size and Propellant Composition on Base Heating in High-Altitude SRM Plumes. International Journal of Aeronautical and Space Sciences. https://doi.org/10.1007/s42405-026-01252-1

Image Credits: AI Generated

DOI: 10.1007/s42405-026-01252-1

Keywords: solid rocket motor, exhaust plume, base heating, alumina particles, particle size, propellant composition, direct simulation Monte Carlo, rarefied flow, radiative heat transfer, discrete ordinates method, Lagrangian particle tracking, high altitude

The experiment centered on two well-characterized graphite powder samples with different particle size ranges. That difference in size turned out to matter enormously. The angular dependence of the reflected light, known as the scattering phase curve, showed a non-trivial dependence on particle size, meaning that the brightness of the powder as a function of viewing and illumination geometry changed in ways that cannot be captured by a simple scaling. Most strikingly, the reflectance curves of the two samples crossed over one another at intermediate phase angles, a behavior consistent with earlier laboratory measurements of graphite powders by Kamei and Nakamura in 2002. Such crossover behavior is a reminder that the photometric fingerprints of particulate surfaces are subtle and that particle size must be treated as a first-order variable in any attempt to interpret asteroid photometry.

To produce these measurements, Deb used a goniometric setup, an instrument that rotates a light source and detector around a sample so that reflectance can be recorded at many combinations of incidence, emergence, and phase angles. The illumination was monochromatic at 535 nanometers, a wavelength in the green part of the visible spectrum. Goniometric measurements of this kind are the gold standard for building bidirectional reflectance distribution functions, the mathematical descriptions of how a surface redirects incoming light. For planetary scientists, such functions are the bridge between a telescope or spacecraft photometry and the physical properties of the surface, including grain size, porosity, and roughness.

A key strength of the study lies in the independent characterization of the samples. The graphite powders were examined with scanning electron microscopy to reveal their microscopic morphology, with X-ray diffraction to confirm their crystallographic structure, and with particle size analysis to quantify the distribution of grain dimensions. This multi-technique approach matters because light scattering depends on far more than the average particle diameter. Shape, surface texture, and internal structure all influence how photons interact with individual grains and with the packed medium as a whole. By documenting these properties alongside the optical measurements, the study produces datasets that modelers can use with confidence rather than guesswork.

The theoretical framework most widely used to interpret such measurements is the Hapke bidirectional reflectance model, which describes the reflectance of a semi-infinite particulate surface in terms of the single-particle scattering albedo, the single-particle phase function, and terms accounting for multiple scattering and the opposition effect. The opposition effect, a sharp surge in brightness when the Sun, the surface, and the observer are nearly aligned at phase angles below about ten degrees, arises largely from shadow hiding, the mutual masking of grains that disappears as the viewing geometry approaches zero phase. The new graphite measurements, spanning a wide range of phase angles, offer a demanding test for such models on a strongly absorbing material where multiple scattering is weak and the physics of single-particle scattering dominates.

Graphite is a particularly instructive analog because of its optical properties. It is one of the most strongly absorbing common materials in the visible, which means that photons penetrating a graphite powder surface are absorbed quickly and rarely survive to be scattered multiple times. This makes the reflectance of graphite powders sensitive to the outermost layer of grains and to their individual scattering phase functions. The material also has direct planetary relevance: graphite grains and graphitic carbon have been identified in samples returned from carbonaceous asteroids, including a graphite spherule reported in material from asteroid Ryugu, and carbonaceous chondrite meteorites carry abundant dark, absorbing phases. Understanding how such material scatters light in powdered form therefore speaks directly to the interpretation of dark asteroid surfaces.

The study also addresses a practical problem that often plagues laboratory work with powders: converting between different descriptions of the size distribution. Commercial sieves sort powders by mesh size, which yields a distribution expressed in weight percentage per size class. But scattering theory typically requires a number-based distribution, counting how many particles of each size are present. The paper includes a detailed appendix showing how to convert a weight-based sieve distribution into a normalized number frequency distribution, using the fact that particle mass scales with the cube of the diameter. This seemingly technical step is essential, because a small number of large grains can dominate a weight distribution while contributing little to the scattering behavior of the surface.

The broader context of this work is a renaissance in small-body exploration. Missions to asteroids Bennu and Ryugu returned samples that revealed unexpectedly complex surfaces, and remote sensing of these bodies depends on photometric models calibrated against laboratory analogs. Recent years have seen a wave of goniometric measurements on regolith simulants, Apollo samples, meteorites, and artificial agglomerates, all aimed at constraining how porosity, roughness, grain shape, and absorption shape the observed brightness. The graphite datasets add a strongly absorbing end-member to this library, complementing measurements on brighter silicate materials and helping to span the range of albedos encountered on real asteroids.

Beyond planetary science, the results have relevance for remote sensing in general, for aerosol physics, and for optical characterization of materials. Strongly absorbing particulate coatings appear in contexts from soot and black carbon in the atmosphere to graphite components in high-temperature blackbody radiators used for metrology. The crossover behavior observed at intermediate phase angles suggests that photometric inversions that ignore particle size could misestimate surface properties, and the openly available datasets, released for further theoretical study, invite computational groups working with discrete dipole approximations, T-matrix methods, and geometric optics codes to test their models against real measurements on irregular, absorbing grains.

What makes this study notable is its economy: a single carefully constructed instrument, two well-documented samples, and a systematic sweep of scattering geometry have produced results that speak to one of the oldest problems in planetary photometry. Every interpretation of asteroid phase curves, every estimate of regolith grain size from spacecraft data, ultimately rests on laboratory measurements of exactly this kind. As sample-return missions continue to deliver material from the early solar system, the demand for precise, well-characterized scattering measurements of relevant analog materials will only grow. This work demonstrates that even a familiar substance like pencil lead, ground into powder and measured with patience, can sharpen our view of worlds hundreds of millions of kilometers away.

Subject of Research: Experimental measurement of angular light scattering from graphite powder analogs of asteroid regolith

Article Title: Light scattering from graphite powders – an experimental investigation

Article References: Deb, D. (2026). Light scattering from graphite powders – an experimental investigation. Astrophysics and Space Science, 371(10), Article 114. https://doi.org/10.1007/s10509-026-04646-5

Image Credits: AI Generated

DOI: 10.1007/s10509-026-04646-5

Keywords: graphite powder, light scattering, regolith, asteroids, bidirectional reflectance, Hapke model, goniometry, planetary science, remote sensing, particle size, opposition effect, carbonaceous asteroids

The motivation for the work stems from two of the most consequential applications of coal gas science. Gas diffusion behavior in coal particles underpins the development of coalbed methane, an increasingly important energy resource, and it also governs how quickly methane can desorb from freshly exposed coal during mining operations, which is central to predicting and preventing gas outbursts and explosions in underground mines. Because laboratory measurements of gas desorption are usually performed on crushed particles, the mathematical interpretation of those measurements depends directly on the assumed particle geometry. If that geometry is wrong, every diffusion coefficient extracted from the data inherits the error.

To confront the problem, the team began not with equations but with images. They obtained two-dimensional contours of real coal particles and extracted quantitative shape parameters, allowing them to characterize particle morphology across different scales in a statistically meaningful way. The results were unambiguous about the gap between idealization and reality. Coal particles exhibited median roundness values of 0.73 to 0.80, well below the value of 1.0 that a perfect circle would show, and median axial ratios ranging from 1.34 to 1.49, meaning the particles are substantially longer in one direction than another. Taken together, these measurements indicate that the actual particle shape is much closer to an ellipsoid than to a sphere.

That distinction might sound like a matter of academic pedantry, but the mathematics of diffusion is acutely sensitive to boundary geometry. In the standard spherical model, derived from the classical analytical framework established by Crank in 1975, gas molecules are assumed to diffuse radially inward from a spherical surface toward the center, with the surface-to-volume ratio determined entirely by the particle radius. An ellipsoid has a different distribution of distances between its surface and its interior, with shorter diffusion path lengths along the minor axis and longer ones along the major axis. As a result, the characteristic time for gas to escape from, or enter, an ellipsoidal particle differs from that of a sphere of equivalent volume, and the magnitude of that difference scales with how elongated the particle actually is.

The researchers coupled this geometric insight with a rigorous experimental and computational pipeline. They performed gas desorption experiments on coal particles and then used numerical forward modeling together with parameter optimization to infer the diffusion coefficients that best explained the observed desorption data. Crucially, they ran this inversion twice, once with a spherical model and once with an ellipsoidal model, so that the two geometric frameworks could be compared head to head against identical experimental evidence. This design isolates the effect of particle shape on the estimated diffusion coefficient, which is precisely the quantity that previous studies had left insufficiently quantified.

The evolution laws of the diffusion coefficients and gas pressures were then analyzed across varying particle sizes and adsorption pressures, revealing a consistent pattern. The spherical model generally overestimates gas diffusion coefficients and diffusion rates relative to the ellipsoidal model. More importantly, the deviation is not constant. It grows under lower adsorption pressures and for larger particle sizes, and in the most extreme case examined, the difference between the two models reached 8.94 × 10⁻¹³ m²/s. This means that engineers using spherical assumptions in low-pressure or coarse-particle conditions, which are common in field-relevant scenarios, would systematically misjudge how fast methane is released from the coal matrix.

Why does this systematic bias arise? Physically, the elongation of coal particles changes the effective diffusion path network within each grain. A sphere of equivalent volume concentrates its interior points at larger average distances from the surface than an ellipsoid does along its short axes, and the inversion of desorption data compensates for the mismatched geometry by inflating the fitted diffusion coefficient. In practical terms, a spherical model forces the data to fit a shape the particles do not have, so the estimated diffusivity absorbs the geometric error. The ellipsoidal model, by encoding the measured axial ratios, removes much of this compensating distortion and yields diffusion coefficients that better reflect the intrinsic transport properties of the coal matrix itself rather than artifacts of the assumed shape.

The implications ripple outward across the coal gas research community. Diffusion coefficients measured in the laboratory are routinely embedded into larger reservoir-scale simulations of coalbed methane recovery, into models of gas emission from mine working faces, and into indices used to assess the risk of coal and gas outbursts. If the input diffusivities are systematically inflated by spherical assumptions, reservoir productivity predictions may be overly optimistic, gas drainage designs may be misconfigured, and safety margins in mines may be thinner than intended. The authors argue that incorporating nonspherical morphology is essential for accurately characterizing gas diffusion in coal particles and that their ellipsoidal model offers improved theoretical rationality and engineering applicability compared with the entrenched spherical convention.

The study also fits into a broader movement toward geometric realism in porous media science. Related work has documented how grinding methods alter coal particle morphology, how three-dimensional X-ray computed tomography reveals the complex shapes of micron-sized coal grains, and how particle shape influences processes from flotation kinetics to sorption behavior. What sets this research apart is that it quantifies, with specific numbers, the price of ignoring shape in gas diffusion analysis, and then demonstrates a practical remedy. By first measuring roundness and axial ratios, then building forward and inverse numerical models on that measured geometry, the team provides a reproducible workflow that other laboratories can adopt without exotic instrumentation.

For an industry that depends on precise predictions of how methane behaves in coal, the message is straightforward. The sphere has been a useful fiction, but it is a fiction nonetheless. As coalbed methane development expands and gas disaster prevention remains a life-or-death concern in mining regions worldwide, models that respect the true, irregular, ellipsoid-like character of coal particles offer a path to more trustworthy science and, ultimately, safer and more efficient operations. The new results make clear that when it comes to gas moving through coal, shape is not a detail. It is part of the physics.

The findings also connect to a persistent puzzle in coal gas research: the observation that diffusion in coal powders behaves as a multi-rate process rather than a single, constant-coefficient phenomenon. Because coal contains pore systems spanning multiple scales, gas molecules encounter different transport regimes as they migrate through the matrix. Geometry adds another layer to this complexity, since the distribution of path lengths within an elongated particle naturally produces a spread of diffusion timescales. An ellipsoidal framework therefore aligns more naturally with the heterogeneous character of coal’s pore architecture than a sphere does.

The methodological approach deserves attention as well. Rather than deriving a closed-form analytical solution, the team relied on forward modeling paired with parameter optimization, an inverse-problem strategy in which model outputs are iteratively adjusted until they match measured desorption data. This approach has become increasingly common in coal permeability and diffusion studies, and it allows researchers to work with geometries that lack elegant analytical expressions. The trade-off is that results depend on the quality of the optimization, which makes the careful quantification of particle shape parameters a necessary foundation rather than an optional refinement.

Pressure dependence is another thread worth noting. Earlier experimental work has shown that gas diffusion coefficients in coal vary with adsorption pressure, and the present results indicate that the error introduced by spherical assumptions is itself pressure-dependent, growing as pressure falls. This coupling of geometric and pressure effects suggests that laboratory conditions must be matched carefully to field conditions when transferring measured diffusivities into reservoir or mine-safety models, since a coefficient calibrated at one pressure may mislead at another even before shape effects are considered.

Subject of Research: Effects of nonspherical coal particle morphology on gas diffusion behavior, quantified through desorption experiments and numerical modeling

Article Title: Effects of Nonspherical Morphology on Gas Diffusion in Coal Particles: Experiments and Numerical Modeling

Article References: Liu, Q., Li, Z., Wang, E., Sang, S., Mao, Z., Liu, X., Feng, X., Deng, S., Wang, D., & Zhang, X. (2026). Effects of Nonspherical Morphology on Gas Diffusion in Coal Particles: Experiments and Numerical Modeling. Natural Resources Research. https://doi.org/10.1007/s11053-026-10769-x

Image Credits: AI Generated

DOI: 10.1007/s11053-026-10769-x

Keywords: gas diffusion, coal particles, particle morphology, ellipsoidal model, diffusion coefficient, gas desorption, coalbed methane, numerical modeling, spherical model, adsorption pressure, particle size, mine safety