Cumulative Particle Size Distribution Research Articles

Research on the Grinding Process of Superhard Particles in the Fluidized Bed Opposed Jet Mill Based on the CFD-DEM Methodology

The process of superhard particle breakage in the grinding zone of the fluidized bed opposed jet mill is investigated using the CFD-DEM (computational fluid dynamics-discrete element method) coupling method with the Tavares UFRJ Breakage Model in the present study. The effects of structural and operational parameters, such as target plate structure, nozzle position, air inlet velocity, and feed rate, on the equipment stress distribution, airflow velocity, pressure field, particle velocity, and cumulative particle size distribution are thoroughly studied to determine the optimal structural and operational parameters. Experimental validation is conducted, including scanning electron microscope (SEM) observation of particle morphology and analysis of particle size distribution of ground product particles. The simulation results indicate that the wear rate of the structure without a target plate is lower than that of the structure with a target plate in the grinding central zone. Therefore, the structure without a target plate is chosen for further investigation. The cumulative particle size distribution after grinding is influenced by nozzle position, air inlet velocity, and feed rate. The particle D50 is positively correlated with nozzle spacing and feed rate, while it is negatively correlated with air inlet velocity. The optimal grinding effect is achieved when the distance between the nozzle and the center of the grinding zone ranges from 52.5 mm to 72.55 mm, the air inlet velocity is 950 m/s, and the feed rate is 10.5 g/s. Through experimental investigation, it has been observed that when the feed rate is 10 g/s, the particle size distribution becomes more uniform. Furthermore, consistent trends in the cumulative particle size distribution in the experiment and simulation results can be found, which validates the present numerical model. It was observed that particles at low feed rates retain certain angular edges, while particle roundness increases at high feed rates.

Research on coal crushing behavior under supercritical CO2 transient high-pressure fracturing

CO2 fracturing enhances gas permeability by creating a complex network of fractures in coal seams. Crushing serves as the foundation of fracture development, and studying the coal crushing behavior under supercritical CO2 transient high-pressure fracturing is of great significance to understand fracture evolution and guide precise fracturing. This study utilized a self-built experimental platform for supercritical CO2 transient high-pressure fracturing to obtain fractured coals at different energy levels. Based on multifractal theory, the relationship between fracturing energy and crushing behavior was studied by laser particle analysis and scanning electron microscopy. The results showed that the volume average particle size (D4,3), and the particle sizes at which the cumulative particle size distribution reached 50% (D50), and 90% (D90) decreased significantly with the increase of fracturing energy. The converted diameter and the crushing work ratio exhibited an exponential relationship with the fracturing energy. The larger the fracturing energy, the smaller the values of the multifractal generalized dimension spectrum parameters (D0, D1, and ΔD(q)), the larger the values of the multifractal singular spectrum width (Δα (q)), and the denser and more even the particle size distribution of fractured coal. The multifractal parameters and shape coefficients exhibited phased change during the fracturing process. The coal particles progressed from an initial stage with numerous microcracks and fissures to a honeycomb structures with small pores. After the disintegration of the honeycomb structures, agglomerated ultrafine particles were formed. The findings provide a theoretical reference for optimizing the selection of fracturing parameters.

Using Dry Dispersion Laser Diffraction to Assess Dispersibility in Spheronized Agglomerate Formulations.

In this study, dry dispersion laser diffraction was used to study the dispersibility of spheronized agglomerate formulations and identify geometric particle size metrics that correlated well with aerodynamic particle size distribution (APSD). Eleven unique batches of agglomerates were prepared for both laser diffraction and cascade impaction testing. Correlations between the particle size distribution (PSD) and aerodynamic particle size distribution (APSD) metrics for the eleven agglomerate batches were determined in a semi-empirical manner. The strongest correlation between APSD and PSD was observed between the impactor-sized mass (%ISM) and the cumulative PSD fraction <14.5 µm. The strongest correlation with fine particle fraction (FPF) was observed with the cumulative PSD fraction <0.99 micron (R-squared = 0.974). In contrast to the other APSD metrics, good correlations were not found between the mass median aerodynamic diameter (MMAD) and the cumulative PSD fractions. Overall, the implementation of laser diffraction as a surrogate for cascade impaction has the potential to streamline product development. Laser diffraction measurements offer savings in labor and turnaround time compared to cascade impaction.

Particle evolution mechanism of wide size distribution limestone under fluidized bed combustion conditions

The dynamic evolution of particles in limestone with a wide size distribution is significant for in-furnace desulfurization in circulating fluidized beds (CFB). In this study, air/SO2 mixtures were selected to simulate the flue gas combustion atmosphere, and the evolution on particle size of limestone with a wide size distribution was investigated using a self-built fluidized bed, with a focus on the evolution mechanism. The results show that the change in the cumulative particle size distribution (PSD) of limestone with a wide size distribution exhibited three stages as a function of reaction time. The cumulative PSD decreased continuously and reached 79.3% after 20 min during the first stage. The cumulative PSD was unchanged from 30 to 120 min in the second stage. The cumulative PSD increased from 81.9% to 88.3% in the range of 120–240 min during the third stage. The effects of attrition, heat stress, calcination, and sulfation on the changes in particle size were quantified and correlated with time. A novel method is proposed to predict the evolution mechanism of limestone with a wide size distribution. Calcination dominated in the time range of 0–60 min, and the predominant effect transformed from calcination to attrition at 240 min. However, the contribution of calcination was not negligible. The evolution of limestone with a wide size distribution can be promoted by the interactions of different effects.

Comparing integrated continuous process “LaVortex®” and conventional batch processes for the pharmaceutical manufacturing of acetaminophen oral dosage formulations: Challenges and pharmaceutical properties of the granular and tableted products

LaVortex® was developed as a novel free-flow continuous granulation/drying (CGD) system. In this study, we compared the advantages and disadvantages of granules prepared by continuous and batchwise manufacturing systems. Granules containing 30 % acetaminophen were manufactured under various operating conditions using CGD system, with comparison granules manufactured using conventional batch systems that involve a combination of fluid bed granulation (FG), agitation granulation (AG), continuous drying, fluid bed drying, and/or shelf drying, after which the pharmaceutical properties of each type of manufactured granule were evaluated. Cumulative particle-size distributions were determined by sieving, powder flowabilities were determined by angle of repose measurements, and scanning electron microscopy was employed to examine granule morphologies. The CGD system produced fine-to-large spherical or ellipsoidal granules that exhibited excellent powder fluidities and tabletabilities that are almost identical to those of AG granules. Moreover, the CGD granules exhibited better powder flowability than the FG granules. The addition of water promoted CGD-granule growth and improved significantly powder flowability, and did a little in tabletability. Small spherical granules with good fluidity suitable for fine-particle-coating core materials, or large granules with excellent fluidity and tabletability, were prepared by adjusting the values of the elemental parameters of the CGD process.

Equation for determining cumulative particle size distribution using the pressure of a sedimenting suspension

One of the basic properties of soil––its particle size distribution (PSD)––can be measured using several techniques, among which methods based on sedimentation have a prominent place. Many of these sedimentation methods use changes in the density of a suspension to produce a PSD curve. A certain group of these measure changes in suspension pressure during the ongoing sedimentation process. To date, conversion of the measured changes in suspension pressure to cumulative PSD (CPSD) has been performed using statistical methods and not a physical model of the phenomenon. Here, this gap is filled. Based on the assumptions similar to used at the Stokes equation, an equation was derived linking the CPSD function with the function describing the changes in suspension pressure and its derivative. The derived equation allows direct calculation of the CPSD function based on changes in the pressure of the suspension at a specific depth. In this work, it is shown that the calculation in the reverse direction––obtaining a function describing the pressure in the suspension at a certain depth, PL(D), depending on the soil CPSD function––is also possible, although it requires use of the finite-difference method. The use of the derived equation to interpret test results is shown through examples of six selected soils with different PSDs.

Equation for Determining Cumulative Particle Size Distribution Using the Pressure of a Sedimenting Suspension

Equation for Determining Cumulative Particle Size Distribution Using the Pressure of a Sedimenting Suspension

The Effect of Moisture on the Particle Size Characteristics of Knife-milled Beech Chips

The paper presents the effect of moisture on the particle size distribution of knife-milled beech chips. The beech chips of 0.5, 7.5, 15.9 and 30.9 wt % in moisture were milled by a knife mill equipped with a single-bladed rotor under the constant peripheral speed of revolution of 10.2 m·s-1 (1,500 min-1). It was found that the RRSB model precisely fits cumulative mass particle size distribution. The Rosin–Rammler size parameter 0.412 - 4.240 mm varies concerning biomass moisture and size of drum screen sieve. Assuming empiric modelling approaches, it was found that the Rosin–Rammler particle size exponentially decreases with a decrease in knife mill screen sizes and linearly increases with biomass moisture. The polydispersity index was independent of wood chips moisture and knife mill screen size, evincing the value of 2.224 ± 0.328.

Effect of wall materials on the spray drying encapsulation of brown seaweed bioactive compounds obtained by subcritical water extraction

Incorporation of algae bioactive compounds in real food systems requires integrated extraction and encapsulation processes to ensure the stability of highly sensitive and perishable compounds of interest. This study presents the spray drying encapsulation of brown seaweed (Saccharina japonica) bioactive compounds obtained by subcritical water extraction using different coating materials. Polysaccharides (dextrin, maltodextrin, lactose, and gum arabic) and proteins (whey protein, gelatin, and sodium caseinate) were studied for S. japonica polyphenolic compounds (PCs) encapsulation efficiency (EE) and retention of antioxidant activities (AAs). Particles were characterized for the content in phenolic compounds, physicochemical properties for moisture content, solubility, bulk and tapped densities, particle size distribution, morphology (SEM), and infrared absorption spectroscopy (FT-IR). Whey protein and gelatin exhibited best EE (87.11% and 86.59%, respectively), and more than two-fold EE in polysaccharides coating materials. Smallest particles were observed in maltodextrin with a Cumulative particle size distribution (D90) of 9.4 μm while D90 was large in protein coating materials with 148.6 μm and 1290.8 μm for whey protein and gelatin, respectively. Lowest bulk and tapped densities were observed in gelatin coated microparticles with 0.10 and 0.17 g/cm3 and highest values in lactose with 0.33 and 0.56 g/cm3. p-Hydroxybenzoic acid (HA) was the most predominant phenolic acid recovered by subcritical water extraction with 23.58 mg/g, and well retained in gelatin coated microparticles (27.99 mg/g). Based on the EE whey protein and gelatin were more suitable for encapsulation of PCs from aqueous S. japonica extracts. The combined use of subcritical water extraction and spray drying encapsulation could be an effective approach toward the recovery and formulation of algae bioactive compounds with potential applications in functional food product development and cosmetics.

Experimental Study on the Generation, Coulomb split and Movement Characteristics of Charged Droplets

A discrete droplet's dynamic characteristics in another immiscible liquid under the actions of an electric field are widely encountered in many practical fields such as emulsification, transesterification, and spacecraft propulsion. An experimental study was carried out to investigate the generation, Coulomb split, and motion of charged methanol droplets with a typical nozzle-plate electrode apparatus by utilizing high-speed photography. Dynamic behavior of droplets with time-resolved characteristics at the ambient needle orifice was visualized at various electric field strengths and flow rates. The resulting phenomena were quantitatively analyzed with the image-processing software. The secondary Coulomb splitting mode of charged droplets, which could be divided into no-crushing deformation, one-side split, two-side split, and membrane breakup under the electric field, has been detailed. Besides, the average particle size and cumulative particle size distribution of broken droplets under different working conditions were obtained. When the electric field intensity reaches a specific range, the influence of electric field intensity and liquid flow rate on the size of broken droplets becomes negligible. Furthermore, the velocity magnitude of discrete droplets was discussed, and the cloud diagram of its velocity characteristics was presented. It could be found that increasing the electric field strength is more effective than the liquid flow rate in terms of enlarging the expansion angle of the atomized droplets and the velocity of the discrete phase droplets.

Three phase corrosion of pipeline steel: Size effects of deposited solids under water droplets and an oil diffusion barrier

Existing studies have examined either under deposit corrosion in bulk solutions or underoil droplet corrosion without deposits. Yet, neither of these scenarios represents the conditions existing within a diluted bitumen pipeline where underoil droplet corrosion occurs in tandem with under deposit corrosion. Herein, this industrially important 3-phase system – solid deposit, aqueous droplet, oil cover – is studied for the first time. In particular, the relationship between varying deposit particle size and underoil droplet corrosion is established. Scanning electron microscopy coupled with profilometry was used to monitor droplet corrosion over time for API-X100 pipeline steel covered with different sized silica particles underneath simulated diluted bitumen. A zero resistance ammeter was used to validate the observed corrosion from the immersion experiments. The data indicate that localized corrosion coupled with uniform corrosion occurred beneath the large (80% of the cumulative particle size distribution less than 540 µm) and small (80% of the cumulative particle size distribution less than 43 µm) silica covered underoil droplets on API-X100 pipeline steels after 24 h of exposure. The underoil droplet corrosion of silica covered steel has maximum localized penetration predominantly around the silica pile perimeter. With continued exposure, up to 240 h, the corrosion beneath the two sizes of silica continues to develop with a difference in rate. The maximum penetration rate (13.58±0.76 mm/year) of localized corrosion under the large silica particles was higher than that (10.02±0.87 mm/year) of the localized corrosion beneath the small silica particles.

Particle size analysis of pristine food-grade titanium dioxide and E 171 in confectionery products: Interlaboratory testing of a single-particle inductively coupled plasma mass spectrometry screening method and confirmation with transmission electron microscopy

Titanium dioxide is a white colourant authorised as food additive E 171 in the EU, where it is used in a range of alimentary products. As these materials may contain a fraction of particulates with sizes below 100 nm and current EU regulation requires specific labelling of food ingredient to indicate the presence of engineered nanomaterials there is now a need for standardised and validated methods to appropriately size and quantify (nano)particles in food matrices.A single-particle inductively coupled plasma mass spectrometry (spICP-MS) screening method for the determination of the size distribution and concentration of titanium dioxide particles in sugar-coated confectionery and pristine food-grade titanium dioxide was developed. Special emphasis was placed on the sample preparation procedure, crucial to reproducibly disperse the particles before analysis. The transferability of this method was tested in an interlaboratory comparison study among seven experienced European food control and food research laboratories equipped with various ICP-MS instruments and using different software packages. The assessed measurands included the particle mean diameter, the most frequent diameter, the percentage of particles (in number) with a diameter below 100 nm, the particles' number concentration and a number of cumulative particle size distribution parameters (D0, D10, D50, D99.5, D99.8 and D100). The evaluated method's performance characteristics were, the within-laboratory precision, expressed as the relative repeatability standard deviation (RSDr), and the between-laboratory precision, expressed as the relative reproducibility standard deviation (RSDR). Transmission electron microscopy (TEM) was used as a confirmatory technique and served as the basis for bias estimation.The optimisation of the sample preparation step showed that when this protocol was applied to the relatively simple sample food matrices used in this study, bath sonication turned out to be sufficient to reach the highest, achievable degree of dispersed constituent particles. For the pristine material, probe sonication was required. Repeatability and reproducibility were below 10% and 25% respectively for most measurands except for the lower (D0) and the upper (D100) bound of the particle size distribution and the particle number concentration. The broader distribution of the lower and the upper bounds could be attributed to instrument-specific settings/setups (e.g. the timing parameters, the transport efficiency, type of mass-spectrometer) and software-specific data treatment algorithms. Differences in the upper bound were identified as being due to the non-harmonised application of the upper counting limit. Reporting D99.5 or D99.8 instead of the effectively largest particle diameter (D100) excluded isolated large particles and considerably improved the reproducibility. The particle number-concentration was found to be influenced by small differences in the sample preparation procedure. The comparison of these results with those obtained using electron microscopy showed that the mean and median particle diameter was, in all cases, higher when using spICP-MS. The main reason for this was the higher size detection limit for spICP-MS plus the fact that some of the analysed particles remained agglomerated/aggregated after sonication.Single particle ICP-MS is a powerful screening technique, which in many cases provides sufficient evidence to confirm the need to label a food product as containing (engineered) titanium dioxide nanomaterial according to the current EU regulatory requirements. The overall positive outcome of the method performance evaluation and the current lack of alternative standardised procedures, would indicate this method as being a promising candidate for a full validation study.

Window of deposition description and prediction of deposition efficiency via machine learning techniques in cold spraying

In this work we describe an energy-based window of deposition, and predict the deposition efficiency for different cold-sprayed powder/substrate systems, using machine learning techniques. We implement several machine learning models to predict whether particles adhere or bounce off during cold spraying. The models are trained using data extracted from several experimental runs taking into account the cumulative particle size distribution and the deposition efficiency of the process. The classification models infer a critical total energy threshold above which deposition occurs. Based on this threshold, we describe an energy-based window of deposition for the powder/substrate systems studied. These models predict the deposition efficiency of different spraying operations for different powder materials with acceptable accuracy. Machine learning techniques provide better understanding of the particle deposition process and enable a more comprehensive exploration of the scope of cold spraying. The use of these techniques opens up new possibilities for the pursuit of links between the spraying process, the structure and different properties for novel cold-sprayed materials.

Evaluation of models for fitting soil particle-size distribution using UNSODA and a Brazilian dataset

The mineral soil Particle Size Distribution (PSD) is a fundamental and very useful soil characteristic widely used to support soil classification, soil management and soil processes modeling. An important limitation of PSD is the lack of standardization for granulometric fractions obtained from different soil classification systems, making difficult to compare and combine data. To overcome this drawback several attempts have been made to mathematically fit PSD data in order to allow soil texture data conversion among soil databases. Parametric equations have been proposed and/or evaluated for particular systems, but none of them has been studied, compared and proved being effective for soils of different types, regions and textural classes. Thus, the purpose of this work was evaluating and comparing performances of several PSD equations on a more comprehensive soil database as well as providing a method capable of fitting a general model for any soil texture. Cumulative PSD data of 221 soil samples, carefully selected from UNSODA and Brazilian/Embrapa datasets to include 12 soil textural classes mapped in the texture triangle, were used in this study to evaluate the fitting performance of commonly applied PSD equations with three and four parameters for unimodal data (SKAG-3p, ANDE-4p, BEST-3p, FRED-4p) and a seven-parameters equation (FRED-7p) used for gap-graded bimodal shaped data. The FRED-7p equation showed outstanding fittings accuracies with average RMSE (100*g g−1) of 0.53 for all soils, about twice as low as the second best fitted equation (ANDE-4p). FRED-7p fitting accuracy was slightly influenced by soil texture, showing a small increase as sand content increases and a decrease as silt content increases. The FRED-7p equation, originally proposed to fit cumulative gap-graded bimodal PSD, performed properly and accurately for all textural classes, including both unimodal and bimodal shaped PSDs. As a result of that, it is strongly recommended as a general model for any kind of soil PSD.

Particle size analysis by an automated dynamometer method integrated with an x-y sample changer

Methods for determining the particle size distribution (PSD) of soils have been developed for many years and we now have a wide range at our disposal. Despite this, the question of their usefulness and the quality of the results obtained by using particular methods is still open. Among them, historically, the oldest sedimentation methods are still very much employed. The paper presents, developed and consistently modernized by the authors, a method of determining the PSD based on changes in the apparent weight of the float submerged in sedimenting suspension. The apparent weight measurement is performed using a sensitive dynamometer with the piezoelectric effect. Then, it is recalculated into cumulative PSD (CPSD) on the basis of Stoke’s law. The method allows the measurement of PSD in a range of grain diameters from 2 µm to 120–130 µm. The integration of the vertically displacing dynamometer and float with the mixer made it possible to automate. Moving the measuring head in the horizontal plane permitted automatic examination of several samples in one measuring cycle. The device works independently after starting. Of note, the method allows for the determination of many different fractions selected by the user. The results of the tests are saved in the form of a report in pdf or xls format. Verification of the method was carried out by comparing the measured and calculated CPSD values of soils, created by mixing in specified proportions of two components with known particle size distribution. The results obtained by this method show a high repeatability and accuracy. Good agreement with the reference method (pipette) is expressed by the RMSE value of 3.36%.

Wet and dry grinding of coal in a laboratory-scale ball mill: Particle-size distributions

In this study, experimental data for wet- and dry-ground coal samples under wet and dry grinding are characterized by commonly used distribution functions. First, both the R-R and Swrebec functions have superior fitting performances for cumulative particle size curves compared to the other studied functions. On this basis, a time-dependent expression is drawn to describe the cumulative particle size distribution. Second, the R-R function produces a significantly superior fit to the relative mass distributions of the ground products compared to those of the others at a short grinding time. The goodness of fit for all distribution functions studied performs marginally worse at approximately 3min, which can be associated with a change in the dominant breakage mechanisms from impact to abrasion-chipping. With an increase in the grinding time, the G-G-S function is the optimal function for characterizing the particle size probability mass distributions of wet grinding, whereas the G-M function provides the best fitting performance when applied to the experimental dry-grinding data. Further, the optimal particle size probability density functions are associated with the difference in breakage mechanisms between wet and dry grinding.

Exploring the effect of the geological texture at meso and micro scale on grinding performance

Comminution indices are used to represent the grindability of a combination of minerals treated by specific processes. If two rock samples with similar values for an index are treated in the same comminution process, they are expected to have a similar behavior during grinding. However, indices are obtained assuming the breakage of homogeneous and continuous materials without considering minor scale mineral and geological textural characteristics. Eventual differences in the process could be related to those properties and may not be explained by comminution indices by itself. In the present study, two different copper ores samples with similar Bond Work index were used to evaluate the influence of mineralogy and geological texture at meso and micro scale in a ball grinding process at laboratory scale. Samples were characterized through geological texture analysis at micro-scale using petrographic microscopy, hyperspectral characterization, X-ray diffraction, and X-ray fluorescence. The effect of mineral properties on grinding was assessed through controlled grinding kinetics performed in a Magotteaux Mill®. Results show that the BWi allows to describe the transition between initial and final states at long grinding times, but it cannot reproduce the entire grinding kinetic, while textural properties, such as grain size and matrix-grain mineralogical composition, may be linked to P80 variation over time and the variation of cumulative particle size distributions at different grinding times. Results suggest that geological texture may be considered as a complement to traditional grindability indices to evaluate the grinding performance.

VOLUME BASED CLOSED-CYCLE HARDGROVE GRINDABILITY METHOD

This paper deals with the development of a volume based closed-cycle grindability test method based on the recently introduced Universal Hardgrove mill and procedure. Five model materials with various origin and material characteris- tics (hardness, grindability, heterogeneity) were chosen for the experiments, i.e. limestone, quartz, andesite, basalt and cement clinker. The grindability of the material was characterized simultaneously in four various ways: 1) the standard Hardgrove Grindability test (HGI), 2) Bond work index calculated from HGI, 3) the conventional Bond test and 4) the closed-cycle volume based grindability test in the Universal Hardgrove mill. The grindability coefficient (G), and the cumulative particle size distribution of 80% passing size (x80) of the product of the closed-cycle Hardgrove test were determined. Relative deviation of the above parameters was very good (in most cases lower than 3%) which indicates the new proposed method as a robust procedure for rapid determination of specific grinding energy of closed cycle grinding in ring mills. Therefore, this test is able to ease the optimization of grinding conditions relatively fast and reliably.

Process control and in vitro/in vivo evaluation of aripiprazole sustained-release microcrystals for intramuscular injection

This work describes the preparation of aripiprazole sustained-release microcrystals for intramuscular injection, through recrystallization, drying, wet grinding, and solidification steps, which had a great impact on the product quality. Here, we evaluated the crystal form of the drug in each step by differential scanning calorimetry (DSC), powder X-ray diffraction (PXRD), and fourier transform infrared spectroscopy (FT-IR), demonstrating that there is no change in the crystal form of aripiprazole monohydrate (H1) during grinding and freeze-drying. Microscopy and scanning electron microscopy (SEM) data showed that freeze-drying had no effect on the morphology of milled H1, and thermal gravimetric analysis (TGA) results showed that the freeze-dried formulation had acceptable water content. In particular, in this study, a similarity factor fitting was applied to determine the similarity of the particle size cumulative distribution curve, and the similarity factor value (99.00) showed that there was no change in the particle size distribution before and after freeze-drying. A two-chamber transmembrane method was used to investigate the in vitro release of the aripiprazole sustained-release microcrystal (ALSI) and commercial preparations (Abilify Maintena®). The similarity factor fitting of in vitro release profiles and drug cumulative release curves in vivo yielded similarity factor values of 98.00 and 95.43, respectively, indicating similar in vitro release and in vivo bioavailability of rats between the ALSI and Abilify Maintena®. A single-dose administration could produce long-term effects for a month. For a microcrystalline suspension, in addition to the conventional quality control indicators, the similarity of the cumulative particle size distribution, the in vitro release profile, and the similarity of the drug release percentage in vivo can be used to reflect product quality and process control.

Particle size effects on soil reflectance explained by an analytical radiative transfer model

Experimental evidence points to an intimate link between soil reflectance, R, and particle/aggregate diameter, D. Based on this strong correlation, various statistical methods for remote and proximal sensing of soil texture and hydraulic properties have been developed. In this paper, we derive a more fundamental and physically-based analytical radiative transfer model that yields a closed-form functional R(D) relationship for dry soils. Despite several simplifying assumptions, the proposed model shows good agreement with measured spectral reflectance (350–2500 nm) data of six soils covering a broad range of textures, colors, and mineralogies. The proposed S-shaped R(D) function resembles cumulative particle and pore size distributions as well as the soil water characteristic function. These analogies may potentially lead to new avenues for developing novel physical models for extracting important soil properties from remotely sensed reflectance data.