Porous Spherical Particles Research Articles

Pore Network Modeling of Intraparticle Transport Phenomena Accompanied by Chemical Reactions.

In this work, a 3D pore network model (PNM) is introduced for modeling reaction-diffusion phenomena, with and without coupled heat transfer, in a spherical porous catalyst particle. The particle geometry is generated by packing thousands of microspheres inside a large sphere to represent the 3D geometry, porosity, and tortuosity of a spherical catalyst particle. A pore-network representation is extracted from this geometry, and a PNM for diffusion-reaction and heat conduction is constructed. This newly proposed particle-scale PNM allows for the application of realistic 3D nonuniform boundary conditions on the particle's surface, which is commonly encountered in slender packed-bed reactors. Concentration profiles inside the particle, and effectiveness of the reactions, is analyzed.

Correlation between phase composition and physicochemical properties in Cu-, Mo-, and W- doped bismuth vanadate

We report a detailed study about the correlation between the physicochemical properties of solvothermally synthesized pristine and 1 %, 2.5 %, and 5 % Cu, Mo, and W-doped bismuth vanadate (BiVO4, BVO) with its phase composition. The effect of the dopant and the duration of synthesis (8 h and 20 h) on the physicochemical properties of BVO allowed us to tune the ratio of monoclinic scheelite to tetragonal zircon phase in BVO powders. This approach helped us to establish the relationship between the presence of monoclinic scheelite or tetragonal zircon phase with structural, morphological and optical properties of BVO powders, obtained by different physicochemical methods (e.g. X-ray Diffraction (XRD), Scanning Electron Microscopy (SEM), Raman spectroscopy, X-ray Photoelectron Spectroscopy (XPS), Diffuse Reflectance Spectroscopy (DRS) and Photoluminescence spectroscopy (PL)). The results indicated that, in addition to XRD, Raman, and DRS, several other methods could distinguish between the two phases. For example, SEM analysis revealed that monoclinic scheelite BVO exhibits either elongated assemblies of cube-like particles or prismatic particles with sizes ∼500 nm. In contrast, tetragonal zircon BVO exclusively exhibited porous spherical particles with diameter ∼2 μm. DRS and Raman spectroscopy indicated that there is a possibility of distinguishing between the two phases if their shares are large enough. For instance, monoclinic BVO showed band gap values in the range of 2.35–2.52 eV, while tetragonal zircon BVO exhibited values in the range of 2.80–3.00 eV. XPS showed a correlation between phase composition and surface chemistry of BVO only for Cu-doped samples, revealing the presence of Cu+ in monoclinic BVO and the presence of both Cu+ and Cu2+ in tetragonal zircon BVO. PL showed that monoclinic scheelite BVO displayed decreased charge recombination compared to tetragonal zircon BVO. Deeper insight into the correlation between the physicochemical properties and phase composition of Cu, Mo, and W-doped bismuth vanadate (BiVO4, BVO) was based on water/pentanol medium (2:1 vol%) as a novel synthesis pathway. This may open new avenues for the broader methodological exploration of surface chemistry, particle size, and morphology of BVO particles through the use of diverse functionalization agents. Finally, the established links between phase composition and structural, morphological, and other physicochemical properties provide new and more predictable opportunities for further improvement of BVO properties for various applications.

A coupled point particle two-phase heat and mass transfer model for dispersed flows based on Boundary Element Methods

In dispersed multiphase flow processes we encounter coupled heat, mass and momentum transfer between the disoersed and the continuous phase. In the context of the subdomain Boundary Domain Integral Method (BDIM) solution of the Navier-Stokes equations a two-way coupling model is presented based on the use of the elliptic fundamental solution and the Dirac delta function properties which leads to accurate evaluation of the heat and mass point particle source impacts on the continuous (air) phase. In addition, the two-phase flow case under consideration is extended to the case of porous spherical particle drying with internal moving drying front, which is solved by the Boundary Element Method (BEM).

Scale-up of dry impregnation processes for porous spherical catalyst particles in a rotating drum: experiments and simulations

Catalyst impregnation is the first step and one of the most crucial steps for preparing industrial catalysts. The process is typically performed in rotating vessels with a spray-nozzle to distribute the liquid onto porous catalyst supports until the pore volume is reached. The inter-particle variability of the impregnated liquid inside the particles significantly affects the activity and selectivity of the resulting catalyst. Current scale-up practices lead to poor fluid distribution and inhomogeneity in the liquid content. The aim of this work is to understand the dynamic behavior of the particles under the spray nozzle, which is essential for desired content uniformity, and to develop a scale-up model for the dry impregnation process. In this work, we considered four dimensionless numbers in the scaling analysis. The scale-up rules require that the dimensionless numbers are kept constant for different scales. Both DEM simulations and matching experiments of dry impregnation inside the porous particles were performed for different vessel sizes. The water content of the particles was compared for different times and locations, and the relative standard deviation is calculated from the axial water content. Simulation and experimental results show that particles achieve similar content uniformity at the end of impregnation, confirming that the scale-up rules are applicable to all vessel sizes. The dimensionless numbers give very good scale-up performance since curves collapse indicating similarity in the processes. In addition, the scale-up method is validated for different particle sizes in simulations.Graphical abstract

Numerical investigation on the densification of granulated porous indium tin oxide powders before compaction

Dense and uniform initial packing structures of powders are of key significance in powder metallurgy process, which can provide the precondition for the fabrication of high-performance components with low cost and high efficiency. In this paper, the packing densification of indium tin oxide (ITO) granulated micro powders with continuous size distributions and internal porosity under three-dimensional vibrations was numerically investigated by discrete element method (DEM). Firstly, the DEM model was validated by physical experiments, and the contact parameters between particles and the porosity therein were determined. Then the effects of operating parameters on the macro/micro properties (e.g., packing density, coordination number (CN), pores, and forces) of the packing structures were analyzed. Results show that the mean CN cannot intuitively reflect the packing structure due to the complex and varied inter-particle contacts caused by the inhomogeneity of the particle size in a multi-sized granular system. Additionally, the excellent packing structure of porous ITO particles is always obtained from low amplitude when the vibration intensity is the same. Corresponding mechanism analyses reveal that higher amplitude normally causes strong convective diffusion, leading to more pores in the packing. This increases the probability of wedging effect occurring during settling, thereby reducing the packing density. However, optimal packing quality with low amplitude can only be achieved when coupled with high frequency. Therefore, applying vibration is an effective way to achieve dense packing of porous spherical particles, especially at low amplitude and high-frequency operating conditions.

Transient slow motion of a porous sphere

The start-up creeping motion of a porous spherical particle, which models a permeable polymer coil or floc of nanoparticles, in an incompressible Newtonian fluid generated by the sudden application of a body force is investigated for the first time. The transient Stokes and Brinkman equations governing the fluid velocities outside and inside the porous sphere, respectively, are solved by using the Laplace transform. An analytical formula for the transient velocity of the particle as a function of relevant parameters is obtained. As expected, the particle velocity increases over time, and a particle with greater mass density lags behind a corresponding less dense particle in the growth of the particle velocity. In general, the transient velocity is an increasing function of the porosity of the particle. On the other hand, a porous particle with a higher fluid permeability will have a greater transient velocity than the same particle with a lower permeability, but may trail behind the less permeable particle in the percentage growth of the velocity. The acceleration of the porous particle is a monotonic decreasing function of the elapsed time and a monotonic increasing function of its fluid permeability. In particular, the transient behavior of creeping motions of porous particles may be much more important than that of impermeable particles.

Analytical expression for the model that describes the heterogeneous reaction-diffusion process with immobilized enzyme (penicillin G acylase)

This research article examines the reaction-diffusion process in an immobilized enzyme batch reactor. The model incorporates strongly non-linear factors that are associated with standard Michaelis-Menten kinetics. The non-linear reaction-diffusion equations for substrate and product concentrations have been approximated analytically. Employing two different semi-analytical methods, Akbari-Ganji's method (AGM) and the modified Adomian decomposition method (MADM), to compute the dimensionless steady-state solutions to the system of non-linear differential equations for all values of reaction parameters. In addition, the dynamics of the mean integrated effectiveness factor of penicillin acylase in porous spherical particles have been presented for the determination of the local effectiveness factor. In order to gauge the potency of our proposed solution, we compare two semi-analytical results with a numerical result that are in good agreement across the whole concentration range. The proposed formulation aims to simulate the dynamic performance of the system utilizing the parameters and would enhance the determination of the optimum particle size for enzyme catalysts.

Corrections to “Morphology Controlled Synthesis of Heteroatom-Doped Spherical Porous Carbon Particles Retaining High Specific Capacitance at High Current Density”

Corrections to “Morphology Controlled Synthesis of Heteroatom-Doped Spherical Porous Carbon Particles Retaining High Specific Capacitance at High Current Density”

Approximation of intra-particle reaction/diffusion effects of immobilized enzyme system following reverse Michaelis–Menten (rMM) mechanism: third degree polynomial and Akbari–Ganji methods

Two approximate analytical expressions based on third degree polynomial and Akbari–Ganji’s method (AGM) were derived for the reaction/diffusion controlled kinetics of an immobilized enzyme (IE) systems. The approximation methods predict substrate concentration profile and effectiveness factor (eta) in a porous spherical particle. The reaction is assumed to follow reverse Michaelis–Menten (rMM) kinetics. The approximate methods predictions were comparable to that of numerical solution (using the Matlab finite difference function, bvp4c) at wide range of {phi }^{2} and {y}_{o} especially at low {phi }^{2} and high {y}_{o} (polynomial equation) and low {phi }^{2} and low {y}_{o} (AGM equation). Although the approximate solution was derived for rMM kinetics, the results can be used to describe other important enzymatic reaction kinetics such as simple Michaelis–Menten (MM) kinetics and MM with competitive product inhibition kinetics. A necessary design equation should be satisfied when using polynomial or AGM approximation for different enzyme kinetic equations. In this work, two examples of enzymatic reactions of industrial interest were studied, namely glucose-fructose isomerization follows rMM kinetics and hydrolysis of lactose follows Michaelis–Menten (MM) equation with competitive product (galactose) inhibition. Predictions of the developed third degree polynomial and AGM approximation equations agree with that of numerical solution, the percentage relative error for the effectiveness factor was less than 11 in comparison with the numerical solution. Good agreement between approximate and numerical estimations demonstrates the validity of these approximation methods.

Degradation of Sodium Acetate by Catalytic Ozonation Coupled with a Mn-Functionalized Fly Ash: Reaction Parameters and Mechanism.

Supported ozone catalysts usually take alumina, activated carbon, mesoporous molecular sieve, graphene, etc. as the carrier for loading metal oxide via the impregnation method, sol-gel method and precipitation method. In this work, a Mn-modified fly ash catalyst was synthesized to reduce the consumption and high unit price of traditional catalyst carriers like alumina. As a solid waste discharged from coal-fired power plants fueled by coal, fly ash also has porous spherical fine particles with constant surface area and activity, abd is expected to be applied as the main component in the synthesis of ozone catalyst. After the pretreatment process and modification with MnOx, the obtained Mn-modified fly ash exhibited stronger specific surface area and porosity combined with considerable ozone catalytic performance. We used sodium acetate as the contaminant probe, which is difficult to directly decompose with ozone as the end product of ozone oxidation, to evaluate the performance of this Mn-modified fly. It was found that ozone molecules can be transformed to generate ·OH, ·O2- and 1O2 for the further oxidation of sodium acetate. The oxygen vacancy produced via Mn modification plays a crucial role in the adsorption and excitation of ozone. This work demonstrates that fly ash, as an industrial waste, can be synthesized as a potential industrial catalyst with stable physical and chemical properties, a simple preparation method and low costs.

Biopolymer-Capped Pyrazinamide-Loaded Colloidosomes: In Vitro Characterization and Bioavailability Studies.

This study aimed to prepare colloidosome particles loaded with pyrazinamide (PZA). These drug-loaded colloidosomes were prepared using an in situ gelation technique using a central composite design with a shell made of calcium carbonate (CaCO3) particles. Optimal amounts of 150 mg of CaCO3, sodium alginate (2%), and 400 mg of poly(3-hydroxybutyrate-co-3-hydroxy valerate) (PHBV) concentration resulted in the maximum drug loading and efficient release profile. Field emission scanning electron microscopy results showed spherical porous particles with a good coating of the PHBV polymer. Additionally, Fourier transform infrared (FTIR) spectroscopy, differential scanning calorimetry (DSC), thermogravimetric and differential thermal analysis (TGA-DTA), and X-ray diffraction (XRD) analysis showed good compatibility between the drug and excipients. The pharmacokinetic studies demonstrated that the drug-loaded colloidosomes resulted in 4.26 times higher plasma drug concentrations with Cmax values of 32.386 ± 2.744 mcg/mL (PZA solution) and 115.868 ± 53.581 mcg/mL (PZA-loaded colloidosomes) and AUC0-t values of 61.24 mcg-h/mL (PZA solution) and 260.9 mcg-h/mL (PZA-loaded colloidosomes), indicating that colloidosomes have the potential to be effective drug carriers for delivering PZA to the target site.

Influence of the nanostructural characteristics of inorganic fillers on the physical properties of resin cements.

Light-curing resin cements, each comprising one of five different inorganic fillers (non-porous and porous spherical SiO2 particles, irregularly shaped glass and ZrO2 particles, and porous ZrO2 spheres), monomers, and polymerization initiators were prepared to determine the effect of filler morphology on the adhesive strength of the resin cement. The strength of adhesion to a computer-aided design/computer-aided manufacturing (CAD/CAM) resin block was investigated mechanically by measuring the tensile bond strength, flexural strength, and elastic modulus. The resin cement containing sub-micron porous ZrO2 spheres had significantly higher tensile bond strength than the other resin cements. The resin cement containing the porous ZrO2 spheres had markedly lower flexural strength and elastic modulus values than the resin cements containing SiO2 and glass fillers.

Combined granulation–alkali activation–direct foaming process: A novel route to porous geopolymer granules with enhanced adsorption properties

High-value applications, such as adsorbents, have drawn attention to geopolymers. In several of those applications, having the geopolymer as porous spherical particles is beneficial. This study presents a novel process for fabricating porous metakaolin-based geopolymer granules using a combination of direct foaming, one-part alkali activation, and granulation. In short, the precursor (e.g., metakaolin) and solid activator (e.g., sodium silicate) are loaded in a granulator, in which an aqueous blowing agent (e.g., H2O2) is added while the granulator is running, and the obtained granules are cured at 60 °C. Characterization of the granules for physico-chemical and morphological properties indicated an increase in overall porosity, especially in the µm-scale pores. Also specific surface area (+50%) and nanoscale pore volume (+102%) increased when using more concentrated H2O2 (20 or 30%) compared to nonporous granules. The use of porous granules was also demonstrated in dynamic adsorption experiments for ammonium (NH4+) uptake, which showed up to ∼126% increase in cumulative adsorption amount compared to nonporous granules. The highest NH4+ uptake was obtained with 10% H2O2 solution as the granulation fluid. The results confirmed the feasibility of the method for introducing porosity to geopolymer granules, which enhances the adsorption properties of the granules.

A point particle source model for conjugate heat and mass transfer in dispersed two-phase flows by BEM based methods

The paper reports on development of a Boundary Element Method (BEM) based two phase dispersed flow model, that allows an accurate and efficient heat and mass transfer coupling by using a moving point source model to account for particle–fluid interaction. The two-way coupling model highlights the efficient use of the elliptic fundamental solution and the Dirac delta distribution properties to accurately evaluate the heat and mass point particle source impact on the continuous phase, solved by the Boundary Domain Integral Method (BDIM). In addition to the BDIM model of the particle–fluid heat and mass transfer interaction, the two-phase flow case under consideration is extended to the case of porous spherical particle drying with internal moving drying front, which is solved by the Boundary Element Method. As the two-phase flow is considered to be dilute, the particle–fluid momentum exchange is covered by a one-way coupling algorithm, with Lagrangian particle tracking used for determination of particle positions and velocities in the flow. Two computational cases are presented, where 1000 and 10000 particles are dried in a stream of hot air. Comparison between the obtained drying times for the cases of the one-way and the two-way heat and mass transfer coupling results shows, that the developed two-way coupling model accurately captures the effect of moisture accumulation and temperature decrease in the fluid phase, leading to realistic computations of drying rates of particles in the flow.

Enhanced Pharmacokinetics and Anti-inflammatory Activity of Curcumin Using Dry Emulsion as Drug Delivery Vehicle.

Many naturally available dietary molecules such as curcumin have not seen the market due to poor solubility, bioavailability, and photodegradability. Successful development of a lipid-based dry emulsion may overcome these issues and help in reaching the markets for natural dietary molecules such as curcumin. The current study aims to develop a dry emulsion formulation of curcumin using natural oil and evaluate its dissolution, photostability, pharmacokinetics, and anti-inflammatory activity. Dry emulsions were prepared using emu oil and corn oil as the lipid phase, Caproyl 90 and Cremophor RH 40 as surfactants, and dextrin as a hydrophilic carrier. Microscopic studies showed the formation of spherical porous particles, and solid-state characterization using differential scanning calorimetry and powder X-ray diffraction showed the conversion of curcumin to an amorphous form. About 80% drug release was observed from formulation, whereas pure drug showed only 50% drug release in 30min. Invivo pharmacokinetic studies showed fivefold improvement in the maximum concentration of curcumin in plasma (Cmax) and sevenfold improvement in the area under the concentration-timecurve of curcumin from emu oil formulation compared with pure curcumin. Significant differences were observed in the anti-inflammatory activity of curcumin dry emulsion and plain curcumin. Emu-oil-based formulations showed synergistic anti-inflammatory activity over corn-oil-based formulations with improved photostability. The present study suggests that the dry emulsion may enhance the bioavailability with synergistic anti-inflammatory activity and photostability of curcumin when given orally.

DRUG RELEASE FROM POROUS SPHERICAL PARTICLE: DIFFUSION MODEL WITH AN INTERMEDIATE COMPLEX FORMATION

This publication proposes a new model of drug release from a spherical particle that takes into account the transfer of the drug and the porous particle into the solution by forming an intermediate complex with the bio carrier, one of the components of the solution. The mathematical model is reduced to a dimension-less form that is convenient for qualitative analysis of the process. The problem is realized numerically. The initial stage of filling a porous particle with a bio carrier and stage of drug release into environment were analyzed. Two main types of kinetic curves corresponding to diffusive and convective modes were revealed. The kinetic curves with the initial stage of drug release delay were revealed. The model was in effects (unobvious at first glance) related to the interaction of opposite factors affecting the drug release. The different types of kinetic curves obtained on its basis correspond to different observational conditions, types of particles, and properties of bio fluids. This model can be improved to describe and predict drug release kinetics not only from single porous particles, but also from containers of more complex shape.

Preparation of Porous Silica Particles with a Controlled Mesopore Size by Ultrasonic Spray Drying for High-Performance Liquid Chromatography (HPLC)

Highly spherical porous silica particles (PSPs) with a controlled pore size were prepared by ultrasonic spray drying and were used as a packing material for high-performance liquid chromatography (HPLC). By using organic additives added to the silica sol as porogens instead of low-melting salts, choosing the size of the colloidal SiO2 particles, and varying the type and the ratio of additives, the pore size of the PSPs was finely tuned from 2.9 to 34.4 nm. Subsequently, PSPs having pore sizes of 7.4, 13.5, and 29.0 nm were modified by chlorodimethyloctadecylsilane (PSPs-C18), and HPLC columns packed with the different PSPs-C18 were evaluated systematically using aromatic compounds and alkylbenzene derivatives as probes. A plate number of 81,000/m and the relative standard deviation of less than 1% in the retention time were obtained for pentylbenzene over 100 injection and HPLC separation cycles for the 7.4-PSPs-C18 column. Five proteins were also separated within 25 min using the 29.0-PSPs-C18 column.

Theory of two-component irreversible adsorption with pore diffusion control

• Theory of pore-diffusion controlled multi-component irreversible adsorption. • Shrinking core model for multi-component irreversible binding. • Closed-form expressions for batch uptake and column breakthrough. • Solutions validated by numerical simulation with the general rate model. This paper provides a theoretical analysis of the kinetics of two-component irreversible adsorption in porous spherical particles for conditions where pore diffusion is limiting. The two components are assumed to have the same binding capacity without the possibility of displacement of one component by the other but with different effective pore diffusivities. As a result, the amounts of each component adsorbed depend on the relative rates of mass transfer within the particles. Closed-form analytical expressions derived by solving the relevant conservation equations are obtained to describe adsorption from an infinite bath with constant concentrations at the particle surface, batch adsorption in a finite bath, and adsorption in packed columns, both under constant pattern and non-constant pattern conditions. In each case, the expression derived reduces to a single integral. These expressions are in good agreement with the numerical solutions of the corresponding general rate model for conditions where the kinetics of binding is fast and provide a simple means to predict two-component adsorption in many practical cases where strong adsorption conditions prevail. Generalizations to systems with more than two components, to cases where the external mass transfer resistance is important, and to unequal capacities are also provided.

Porous soluble dialdehyde cellulose beads: A new carrier for the formulation of poorly water-soluble drugs

Cellulose beads are porous spherical particles with promising futures for drug delivery applications. In this study, novel dialdehyde cellulose (DAC) beads are developed by periodate oxidation of pristine cellulose for oral delivery of weakly basic poorly water-soluble drugs. Diazepam and itraconazole were studied as model drugs. Drug loadings in DAC beads up to 40% were obtained. Depending on the drug loading, complete or partial amorphization of drugs in DAC beads was observed. Drugs in the amorphous state not only presented a higher extent of dissolution from the DAC beads compared to the crystalline model drug, but the obtained concentration was also supersaturated. This supersaturation is attributed to the amorphization of the drugs in the beads in conjunction with the dissolution of the DAC beads at a neutral pH of the dissolution medium. Further, the effects of two different solvent systems used in the lyophilization step during the preparation of the DAC beads (100% water and 90/10% tert-butanol/water mixture) on their structure were investigated. Interestingly, the selection of the solvent system greatly impacted the bead structure, resulting in radically different drug loading capacity, physical properties, and release behavior of the model drugs. In summary, this is the first study that reports on exploiting soluble, porous, dialdehyde cellulose beads, showing great potential as a carrier for improving the rate and extent of dissolution of poorly soluble drugs and maintaining supersaturation.

Study and comparison of different drying processes of porous particle at high temperature

This work presents a comparative study of four drying processes of a porous media: superheated steam drying at atmospheric pressure (APSSD), humid air (HA), low pressure superheated steam drying (LPSSD) and vacuum drying (VD). A single porous particle model has been developed to simulate the four drying processes. The model is based on the method of averaging volume. Spherical porous particles of coal are used as the model material in this paper. The evaporation rates are equal for these processes in point called the inversion temperature. This temperature was calculated during the constant rate period (CRP) and the falling rate period (FRP). A variation in the values of inversion temperature was observed (363-503 K). The effect of drying parameters such as: particle radius, gas mass flux, permeability, porosity and operating pressure were investigated. Several researchers have reported the noticeable variation of the inversion temperature values according to the drying period used to calculate this key parameter. Our results are compared with those obtained from a front model reported in the literature. A good agreement is found.