891 resultados para POROUS ALUMINA
Resumo:
The paper industry is constantly looking for new ideas for improving paper products while competition and raw material prices are increasing. Many paper products are pigment coated. Coating layer is the top layer of paper, thus by modifying coating pigment also the paper itself can be altered and value added to the final product. In this thesis, synthesis of new plastic and hybrid pigments and their performance in paper and paperboard coating is reported. Two types of plastic pigments were studied: core-shell latexes and solid beads of maleimide copolymers. Core-shell latexes with partially crosslinked hydrophilic polymer core of poly(n-butyl acrylate-co-methacrylic acid) and a hard hydrophobic polystyrene shell were prepared to improve the optical properties of coated paper. In addition, the effect of different crosslinkers was analyzed and the best overall performance was achieved by the use of ethylene glycol dimethacrylate (EGDMA). Furthermore, the possibility to modify core-shell latex was investigated by introducing a new polymerizable optical brightening agent, 1-[(4-vinylphenoxy)methyl]-4-(2-henylethylenyl)benzene which gave promising results. The prepared core-shell latex pigments performed smoothly also in pilot coating and printing trials. The results demonstrated that by optimizing polymer composition, the optical and surface properties of coated paper can be significantly enhanced. The optimal reaction conditions were established for thermal imidization of poly(styrene-co-maleimide) (SMI) and poly(octadecene-co-maleimide) (OMI) from respective maleic anhydride copolymer precursors and ammonia in a solvent free process. The obtained aqueous dispersions of nanoparticle copolymers exhibited glass transition temperatures (Tg) between 140-170ºC and particle sizes from 50-230 nm. Furthermore, the maleimide copolymers were evaluated in paperboard coating as additional pigments. The maleimide copolymer nanoparticles were partly imbedded into the porous coating structure and therefore the full potential of optical property enhancement for paperboard was not achieved by this method. The possibility to modify maleimide copolymers was also studied. Modifications were carried out via N-substitution by replacing part of the ammonia in the imidization reaction with amines, such as triacetonediamine (TAD), aspartic acid (ASP) and fluorinated amines (2,2,2- trifluoroethylamine, TFEA and 2,2,3,3,4,4,4-heptafluorobuthylamine, HFBA). The obtained functional nanoparticles varied in size between 50-217 nm and their Tg from 150-180ºC. During the coating process the produced plastic pigments exhibited good runnability. No significant improvements were achieved in light stability with TAD modified copolymers whereas nanoparticles modified with aspartic acid and those containing fluorinated groups showed the desired changes in surface properties of the coated paperboard. Finally, reports on preliminary studies with organic-inorganic hybrids are presented. The hybrids prepared by an in situ polymerization reaction consisted of 30 wt% poly(styrene- co-maleimide) (SMI) and high levels of 70 wt% inorganic components of kaolin and/or alumina trihydrate. Scanning Electron Microscopy (SEM) images and characterization by Fourier Transform Infrared Spcetroscopy (FTIR) and X-Ray Diffraction (XRD) revealed that the hybrids had conventional composite structure and inorganic components were covered with precipitated SMI nanoparticles attached to the surface via hydrogen bonding. In paper coating, the hybrids had a beneficial effect on increasing gloss levels.
Resumo:
In this thesis, the gas sensing properties of porous silicon-based thin-film optical filters are explored. The effects of surface chemistry on the adsorption and desorption of various gases are studied in detail. Special emphasis is placed on investigating thermal carbonization as a stabilization method for optical sensing applications. Moreover, the possibility of utilizing the increased electrical conductivity of thermally carbonized porous silicon for implementing a multiparametric gas sensor, which would enable simultaneous monitoring of electrical and optical parameters, is investigated. In addition, different porous silicon-based optical filter-structures are prepared, and their properties in sensing applications are evaluated and compared. First and foremost, thermal carbonization is established as a viable method to stabilize porous silicon optical filters for chemical sensing applications. Furthermore, a multiparametric sensor, which can be used for increasing selectivity in gas sensing, is also demonstrated. Methods to improve spectral quality in multistopband mesoporous silicon rugate filters are studied, and structural effects to gas sorption kinetics are evaluated. Finally, the stability of thermally carbonized optical filters in basic environments is found to be superior in comparison to other surface chemistries currently available for porous silicon. The results presented in this thesis are of particular interest for developing novel reliable sensing systems based on porous silicon, e.g., label-free optical biosensors.
Resumo:
Papper kan anses vara ett av de mest använda materialen i det dagliga livet. Tidskrifter, tidningar, böcker och diverse förpackningar är några exempel på pappersbaserade produkter. Papperets egenskaper måste anpassas till användningsändamålet. En tidskrift kräver t.ex. hög ljushet, opacitet och en slät yta hos papperet, medan dessa egenskaper är mindre viktiga för en dagstidning. Allt tryckpapper behöver vissa mekaniska egenskaper för att tåla vidarebearbetning såsom kalandrering, tryckning och vikning. Man kan bestryka papper för att förbättra dess optiska egenskaper och tryckbarhetsegenskaper. Vid bestrykning appliceras en dispersion av mineralpigment och polymerbindemedel som ett tunt lager på papperets yta. Bestrykningsskiktet kan ses som ett komplext, poröst kompositmaterial som även bidrar till papperets mekaniska egenskaper och dess processerbarhet i diverse konverteringsoperationer. Kravet på framställning av förmånligt papper med tillräckliga styrkeegenskaper ställer allt högre krav på optimeringen av pappersbestrykningsskiktets egenskaper och produktionskostnader. Målet med detta arbete var att förstå sambandet mellan pigmentbestrykningsskiktets mikrostruktur och dess makroskopiska, mekaniska egenskaper. Resultaten visar att adhesionen i gränsytan mellan pigment och bindemedel är kritisk för bestrykningsskiktets förmåga att bära mekanisk belastning. Polära vätskor är vanliga i tryckfärger och kan, eftersom de påverkar syra/bas-interaktionerna mellan pigment och latexbindemedel, försvaga denna adhesion. Resultaten tyder på att ytstyrkan hos bestruket papper kan höjas genom användning av bifunktionella dispergeringsmedel för mineralpigment. Detta medför inbesparingar i pappersproduktionen eftersom mängden bindemedel, den dyraste komponenten i bestrykningsskiktet, kan minskas.
Resumo:
Cranial bone reconstructions are necessary for correcting large skull bone defects due to trauma, tumors, infections and craniotomies. Traditional synthetic implant materials include solid or mesh titanium, various plastics and ceramics. Recently, biostable glass-fiber reinforced composites (FRC), which are based on bifunctional methacrylate resin, were introduced as novel implant solution. FRCs were originally developed and clinically used in dental applications. As a result of further in vitro and in vivo testing, these composites were also approved for clinical use in cranial surgery. To date, reconstructions of large bone defects were performed in 35 patients. This thesis is dedicated to the development of a novel FRC-based implant for cranial reconstructions. The proposed multi-component implant consists of three main parts: (i) porous FRC structure; (ii) bioactive glass granules embedded between FRC layers and (iii) a silver-polysaccharide nanocomposite coating. The porosity of the FRC structure should allow bone ingrowth. Bioactive glass as an osteopromotive material is expected to stimulate the formation of new bone. The polysaccharide coating is expected to prevent bacterial colonization of the implant. The FRC implants developed in this study are based on the porous network of randomly-oriented E-glass fibers bound together by non-resorbable photopolymerizable methacrylate resin. These structures had a total porosity of 10–70 volume %, of which > 70% were open pores. The pore sizes > 100 μm were in the biologically-relevant range (50-400 μm), which is essential for vascularization and bone ingrowth. Bone ingrowth into these structures was simulated by imbedding of porous FRC specimens in gypsum. Results of push-out tests indicated the increase in the shear strength and fracture toughness of the interface with the increase in the total porosity of FRC specimens. The osteopromotive effect of bioactive glass is based on its dissolution in the physiological environment. Here, calcium and phosphate ions, released from the glass, precipitated on the glass surface and its proximity (the FRC) and formed bone-like apatite. The biomineralization of the FRC structure, due to the bioactive glass reactions, was studied in Simulated Body Fluid (SBF) in static and dynamic conditions. An antimicrobial, non-cytotoxic polysaccharide coating, containing silver nanoparticles, was obtained through strong electrostatic interactions with the surface of FRC. In in vitro conditions the lactose-modified chitosan (chitlac) coating showed no signs of degradation within seven days of exposure to lysozyme or one day to hydrogen peroxide (H2O2). The antimicrobial efficacy of the coating was tested against Staphylococcus aureus and Pseudomonas aeruginosa. The contact-active coating had an excellent short time antimicrobial effect. The coating neither affected the initial adhesion of microorganisms to the implant surface nor the biofilm formation after 24 h and 72 h of incubation. Silver ions released to the aqueous environment led to a reduction of bacterial growth in the culture medium.
Resumo:
Mixed convection on the flow past a heated length and past a porous cavity located in a horizontal wall bounding a saturated porous medium is numerically simulated. The cavity is heated from below. The steady-state regime is studied for several intensities of the buoyancy effects due to temperature variations. The influences of Péclet and Rayleigh numbers on the flow pattern and the temperature distributions are examined. Local and global Nusselt numbers are reported for the heated surface. The convective-diffusive fluxes at the volume boundaries are represented using the UNIFAES, Unified Finite Approach Exponential-type Scheme, with the Power-Law approximation to reduce the computing time. The conditions established by Rivas for the quadratic order of accuracy of the central differencing to be maintained in irregular grids are shown to be extensible to other quadratic schemes, including UNIFAES, so that accuracy estimates could be obtained.
Resumo:
The flow of Bingham liquids through porous media has been studied. Experiments have been performed to determine the flow rate / pressure drop relationship for the flow of a grease of Binghamian rheological behavior through an array of rods of circular cross section. The yield stress and plastic viscosity of the grease have been determined with the aid of a controlled stress rotational rheometer. To investigate a wider range of the flow parameters, the mass and momentum conservation equations have been solved numerically, in conjunction with the generalized Newtonian constitutive law and the bi-viscosity model. The finite volume method has been employed to obtain the numerical solution. These numerical results also yielded a flow rate / pressure drop relationship, which is in very good agreement with the experimental results. A capillaric theory has been developed to determine an analytical relationship between the flow rate and pressure drop for flows of Bingham liquids through porous media. It is shown that the predictions of this theory are in good agreement with the experimental and numerical results.
Resumo:
In two-phase miniature and microchannel flows, the meniscus shape must be considered due to effects that are affected by condensation and/or evaporation and coupled with the transport phenomena in the thin film on the microchannel wall, when capillary forces drive the working fluid. This investigation presents an analytical model for microchannel condensers with a porous boundary, where capillary forces pump the fluid. Methanol was selected as the working fluid. Very low liquid Reynolds numbers were obtained (Re~6), but very high Nusselt numbers (Nu~150) could be found due to the channel size (1.5 mm) and the presence of the porous boundary. The meniscus calculation provided consistent results for the vapor interface temperature and pressure, as well as the meniscus curvature. The obtained results show that microchannel condensers with a porous boundary can be used for heat dissipation with reduced heat transfer area and very high heat dissipation capabilities.
Resumo:
Hydraulic head is distributed through a medium with porous aspect. The analysis of hydraulic head from one point to another is used by the Richard's equation. This equation is equivalent to the groundwater ow equation that predicts the volumetric water contents. COMSOL 3.5 is used for computation applying Richard's equation. A rectangle of 100 meters of length and 10 meters of large (depth) with 0,1 m/s fl ux of inlet as source of our fl uid is simulated. The domain have Richards' equation model in two dimension (2D). Hydraulic head increases proportional with moisture content.
Resumo:
Bio-ethanol has been used as a fuel additive in modern society aimed at reducing CO2-emissions and dependence on oil. However, ethanol is unsuitable as fuel supplement in higher proportions due to its physico-chemical properties. One option to counteract the negative effects is to upgrade ethanol in a continuous fixed bed reactor to more valuable C4 products such as 1-butanol providing chemical similarity with traditional gasoline components. Bio-ethanol based valorization products also have other end-uses than just fuel additives. E.g. 1-butanol and ethyl acetate are well characterised industrial solvents and platform chemicals providing greener alternatives. The modern approach is to apply heterogeneous catalysts in the investigated reactions. The research was concentrated on aluminium oxide (Al2O3) and zeolites that were used as catalysts and catalyst supports. The metals supported (Cu, Ni, Co) gave very different product profiles and, thus, a profound view of different catalyst preparation methods and characterisation techniques was necessary. Additionally, acidity and basicity of the catalyst surface have an important role in determining the product profile. It was observed that ordinary determination of acid strength was not enough to explain all the phenomena e.g. the reaction mechanism. One of the main findings of the thesis is based on the catalytically active site which originates from crystallite structure. As a consequence, the overall evaluation of different by-products and intermediates was carried out by combining the information. Further kinetic analysis was carried out on metal (Cu, Ni, Co) supported self-prepared alumina catalysts. The thesis gives information for further catalyst developments aimed to scale-up towards industrially feasible operations.
Resumo:
Methyl chloride is an important chemical intermediate with a variety of applications. It is produced today in large units and shipped to the endusers. Most of the derived products are harmless, as silicones, butyl rubber and methyl cellulose. However, methyl chloride is highly toxic and flammable. On-site production in the required quantities is desirable to reduce the risks involved in transportation and storage. Ethyl chloride is a smaller-scale chemical intermediate that is mainly used in the production of cellulose derivatives. Thus, the combination of onsite production of methyl and ethyl chloride is attractive for the cellulose processing industry, e.g. current and future biorefineries. Both alkyl chlorides can be produced by hydrochlorination of the corresponding alcohol, ethanol or methanol. Microreactors are attractive for the on-site production as the reactions are very fast and involve toxic chemicals. In microreactors, the diffusion limitations can be suppressed and the process safety can be improved. The modular setup of microreactors is flexible to adjust the production capacity as needed. Although methyl and ethyl chloride are important chemical intermediates, the literature available on potential catalysts and reaction kinetics is limited. Thus the thesis includes an extensive catalyst screening and characterization, along with kinetic studies and engineering the hydrochlorination process in microreactors. A range of zeolite and alumina based catalysts, neat and impregnated with ZnCl2, were screened for the methanol hydrochlorination. The influence of zinc loading, support, zinc precursor and pH was investigated. The catalysts were characterized with FTIR, TEM, XPS, nitrogen physisorption, XRD and EDX to identify the relationship between the catalyst characteristics and the activity and selectivity in the methyl chloride synthesis. The acidic properties of the catalyst were strongly influenced upon the ZnCl2 modification. In both cases, alumina and zeolite supports, zinc reacted to a certain amount with specific surface sites, which resulted in a decrease of strong and medium Brønsted and Lewis acid sites and the formation of zinc-based weak Lewis acid sites. The latter are highly active and selective in methanol hydrochlorination. Along with the molecular zinc sites, bulk zinc species are present on the support material. Zinc modified zeolite catalysts exhibited the highest activity also at low temperatures (ca 200 °C), however, showing deactivation with time-onstream. Zn/H-ZSM-5 zeolite catalysts had a higher stability than ZnCl2 modified H-Beta and they could be regenerated by burning the coke in air at 400 °C. Neat alumina and zinc modified alumina catalysts were active and selective at 300 °C and higher temperatures. However, zeolite catalysts can be suitable for methyl chloride synthesis at lower temperatures, i.e. 200 °C. Neat γ-alumina was found to be the most stable catalyst when coated in a microreactor channel and it was thus used as the catalyst for systematic kinetic studies in the microreactor. A binder-free and reproducible catalyst coating technique was developed. The uniformity, thickness and stability of the coatings were extensively characterized by SEM, confocal microscopy and EDX analysis. A stable coating could be obtained by thermally pretreating the microreactor platelets and ball milling the alumina to obtain a small particle size. Slurry aging and slow drying improved the coating uniformity. Methyl chloride synthesis from methanol and hydrochloric acid was performed in an alumina-coated microreactor. Conversions from 4% to 83% were achieved in the investigated temperature range of 280-340 °C. This demonstrated that the reaction is fast enough to be successfully performed in a microreactor system. The performance of the microreactor was compared with a tubular fixed bed reactor. The results obtained with both reactors were comparable, but the microreactor allows a rapid catalytic screening with low consumption of chemicals. As a complete conversion of methanol could not be reached in a single microreactor, a second microreactor was coupled in series. A maximum conversion of 97.6 % and a selectivity of 98.8 % were reached at 340°C, which is close to the calculated values at a thermodynamic equilibrium. A kinetic model based on kinetic experiments and thermodynamic calculations was developed. The model was based on a Langmuir Hinshelwood-type mechanism and a plug flow model for the microreactor. The influence of the reactant adsorption on the catalyst surface was investigated by performing transient experiments and comparing different kinetic models. The obtained activation energy for methyl chloride was ca. two fold higher than the previously published, indicating diffusion limitations in the previous studies. A detailed modeling of the diffusion in the porous catalyst layer revealed that severe diffusion limitations occur starting from catalyst coating thicknesses of 50 μm. At a catalyst coating thickness of ca 15 μm as in the microreactor, the conditions of intrinsic kinetics prevail. Ethanol hydrochlorination was performed successfully in the microreactor system. The reaction temperature was 240-340°C. An almost complete conversion of ethanol was achieved at 340°C. The product distribution was broader than for methanol hydrochlorination. Ethylene, diethyl ether and acetaldehyde were detected as by-products, ethylene being the most dominant by-product. A kinetic model including a thorough thermodynamic analysis was developed and the influence of adsorbed HCl on the reaction rate of ethanol dehydration reactions was demonstrated. The separation of methyl chloride using condensers was investigated. The proposed microreactor-condenser concept enables the production of methyl chloride with a high purity of 99%.
Resumo:
In my PhD Thesis, I study the conceptions and representation of emotions in medieval 13th and 14th-century Iceland. I have used Icelandic saga literature as my source material and Icelandic Family sagas (Íslendingasögur) as my main sources. Firstly, I wished to explore in my study the medieval Icelandic folk theory of emotions: what emotions were thought to be, from what they originated and how they operated? Secondly, in earlier research it has been shown that emotions were seldom described in Íslendingasögur. They were mostly represented in dialogue, poetry or in somatic changes (e.g. turning pale). Consequently, I examined whether medieval Icelanders had alternative emotion discourses in literature, in addition to the usual manner of representation. My study consists of qualitative case studies, and I have analysed the sources intertextually. I suggest that medieval Icelanders regarded emotions as movements of the mind. The mind existed in the heart. As a consequence, emotions were considered physical in nature. The human body and therefore also the human mind was considered porous: if the mind of the person was not strong enough, supernatural agents and forces could penetrate theboundaries of his/her body as winds or sharp projectiles. Correspondingly, minds of strong-willed people could penetrate the minds of others. As a result, illness and emotions could upspring. People did not always distinguish between emotions and physical illnesses. Excessive emotions could cause illness, even death. Especially fear, grief and emotions of moral responsibility (e.g. guilt) made people vulnerable to the supernatural influence. Guilt was considered part of the emotional experience of misfortune (ógæfa), and in literature guilt could also be represented as eye pain that was inflicted upon the sufferer by a supernatural agent in a dream. Consequently, supernatural forces and beings were part of the upspring of emotions, but also part of the representation of emotions in literature: They caused the emotion but their presence also represented the emotional turmoil in the lives of the people that the supernatural agents harassed; emotions that had followed from norm transgressions, betrayal and other forms of social disequilibrium. Medieval readers and listeners of the Íslendingasögur were used to interpreting such different layers of meaning in texts.
Resumo:
In this thesis properties and influence of modification techniques of porous silicon were studied by Atomic Force Microscope (AFM). This device permits to visualize the surface topography and to study properties of the samples on atomic scale, which was necessary for recent investigation. Samples of porous silicon were obtained by electrochemical etching. Nickel particles were deposited by two methods: electrochemical deposition and extracting from NiCl2 ethanol solution. Sample growth was conducted in Saint-Petersburg State Electrotechnical University, LETI. Kelvin probe force microscopy (KPFM) and Magnetic force microscopy (MFM) were utilized for detailed information about surface properties of the samples. Measurements showed the difference in morphology correlating with initial growth conditions. Submicron size particles were clearly visible on surfaces of the treated samples. Although their nature was not clarified due to limitations of AFM technique. It is expected that surfaces were covered by nanometer scale Ni particles, which can be verified by implication of RAMAN device.
Resumo:
Our objective was to observe the biodegradable and osteogenic properties of magnesium scaffolding under in vivo conditions. Twelve 6-month-old male New Zealand white rabbits were randomly divided into two groups. The chosen operation site was the femoral condyle on the right side. The experimental group was implanted with porous magnesium scaffolds, while the control group was implanted with hydroxyapatite scaffolds. X-ray and blood tests, which included serum magnesium, alanine aminotransferase (ALT), creatinine (CREA), and blood urea nitrogen (BUN) were performed serially at 1, 2, and 3 weeks, and 1, 2, and 3 months. All rabbits were killed 3 months postoperatively, and the heart, kidney, spleen, and liver were analyzed with hematoxylin and eosin (HE) staining. The bone samples were subjected to microcomputed tomography scanning (micro-CT) and hard tissue biopsy. SPSS 13.0 (USA) was used for data analysis, and values of P<0.05 were considered to be significant. Bubbles appeared in the X-ray of the experimental group after 2 weeks, whereas there was no gas in the control group. There were no statistical differences for the serum magnesium concentrations, ALT, BUN, and CREA between the two groups (P>0.05). All HE-stained slices were normal, which suggested good biocompatibility of the scaffold. Micro-CT showed that magnesium scaffolds degraded mainly from the outside to inside, and new bone was ingrown following the degradation of magnesium scaffolds. The hydroxyapatite scaffold was not degraded and had fewer osteoblasts scattered on its surface. There was a significant difference in the new bone formation and scaffold bioabsorption between the two groups (9.29±1.27 vs 1.40±0.49 and 7.80±0.50 vs 0.00±0.00 mm3, respectively; P<0.05). The magnesium scaffold performed well in degradation and osteogenesis, and is a promising material for orthopedics.
Resumo:
Fluid flow behaviour in porous media is a conundrum. Therefore, this research is focused on filtration-volumetric characterisation of fractured-carbonate sediments, coupled with their proper simulation. For this reason, at laboratory rock properties such as pore volume, permeability and porosity are measured, later phase permeabilities and oil recovery in function of flow rate are assessed. Furthermore, the rheological properties of three oils are measured and analysed. Finally based on rock and fluid properties, a model using COMSOL Multiphysics is built in order to compare the experimental and simulated results. The rock analyses show linear relation between flow rate and differential pressure, from which phase permeabilities and pressure gradient are determined, eventually the oil recovery under low and high flow rate is established. In addition, the oils reveal thixotropic properties as well as non-Newtonian behaviour described by Bingham model, consequently Carreau viscosity model for the used oil is given. Given these points, the model for oil and water is built in COMSOL Multiphysics, whereupon successfully the reciprocity between experimental and simulated results is analysed and compared. Finally, a two-phase displacement model is elaborated.
Resumo:
This thesis addresses the coolability of porous debris beds in the context of severe accident management of nuclear power reactors. In a hypothetical severe accident at a Nordic-type boiling water reactor, the lower drywell of the containment is flooded, for the purpose of cooling the core melt discharged from the reactor pressure vessel in a water pool. The melt is fragmented and solidified in the pool, ultimately forming a porous debris bed that generates decay heat. The properties of the bed determine the limiting value for the heat flux that can be removed from the debris to the surrounding water without the risk of re-melting. The coolability of porous debris beds has been investigated experimentally by measuring the dryout power in electrically heated test beds that have different geometries. The geometries represent the debris bed shapes that may form in an accident scenario. The focus is especially on heap-like, realistic geometries which facilitate the multi-dimensional infiltration (flooding) of coolant into the bed. Spherical and irregular particles have been used to simulate the debris. The experiments have been modeled using 2D and 3D simulation codes applicable to fluid flow and heat transfer in porous media. Based on the experimental and simulation results, an interpretation of the dryout behavior in complex debris bed geometries is presented, and the validity of the codes and models for dryout predictions is evaluated. According to the experimental and simulation results, the coolability of the debris bed depends on both the flooding mode and the height of the bed. In the experiments, it was found that multi-dimensional flooding increases the dryout heat flux and coolability in a heap-shaped debris bed by 47–58% compared to the dryout heat flux of a classical, top-flooded bed of the same height. However, heap-like beds are higher than flat, top-flooded beds, which results in the formation of larger steam flux at the top of the bed. This counteracts the effect of the multi-dimensional flooding. Based on the measured dryout heat fluxes, the maximum height of a heap-like bed can only be about 1.5 times the height of a top-flooded, cylindrical bed in order to preserve the direct benefit from the multi-dimensional flooding. In addition, studies were conducted to evaluate the hydrodynamically representative effective particle diameter, which is applied in simulation models to describe debris beds that consist of irregular particles with considerable size variation. The results suggest that the effective diameter is small, closest to the mean diameter based on the number or length of particles.