Fractal Dimension Of Aggregates Research Articles

Fractal dimension in concrete and implementation for meso-simulation

A complete understanding of the geometrical structure of concrete is important. Based on the geometrical characteristics of concrete, hypothesizing that graded aggregates have a fractal effect is reasonable. In the framework of fractal theory, the fractal dimensions of aggregates and cement were clarified, and a mathematical model of the fractal dimension was formed to describe the geometrical characteristics of concrete. Two numerical meso-model groups generated by the random fractal and traditional generation method were measured and analyzed considering the gradation curve, coarse aggregate content, and weighted mean size as evaluation indices. It was verified that the evaluation indices of the numerical models with the fractal dimension of actual concrete and those of actual concrete were the same, and the numerical simulation results were consistent with theory. Based on sampling statistical analysis, the geometrical homogenization of the meso-model generated by the random fractal method was found to be satisfactory for meso-scale applications.

Influence of Aqueous Inorganic Anions on the Reactivity of Nanoparticles in TiO2 Photocatalysis.

The influence of inorganic anions on the photoreactivity and aggregation of titanium dioxide nanoparticles (NPs) was assessed by dosing carbonate, chloride, nitrate, phosphate, and sulfate as potassium salts at multiple concentrations. NP stability was monitored in terms of aggregate morphology and electrophoretic mobility (EPM). Aggregate size and fractal dimension were measured over time by laser diffraction, and the isoelectric point (IEP) as a function of anion and concentration was obtained by measuring EPM versus pH. Phosphate, carbonate, and to a lesser extent, sulfate decreased the IEP of TiO2 and stabilized NP suspensions owing to specific surface interactions, whereas this was not observed for nitrate and chloride. TiO2 NPs were exposed to UV-A radiation, and the photoreactivity was assessed by monitoring the production of reactive species over time both at the NP surface (photogenerated holes) and in the bulk solution (hydroxyl radicals) by observing their reactions with the selective probe compounds iodide and terephthalic acid, respectively. The generation of photogenerated holes and hydroxyl radicals was influenced by each inorganic anion to varying degrees. Carbonate and phosphate inhibited the oxidation of iodide, and this interaction was successfully described by a Langmuir-Hinshelwood mechanism and related to the characteristics of TiO2 aggregates. Chloride and nitrate do not specifically interact with TiO2, and sulfate creates relatively weak interactions with the TiO2 surface such that no decrease in photogenerated hole reactivity was observed. A decrease in hydroxyl radical generation was observed for all inorganic anions. Quenching rate constants for the reaction of hydroxyl radicals with each inorganic anion do not provide a comprehensive explanation for the magnitude of this decrease, which arises from the interplay of several physicochemical phenomena. This work shows that the reactivity of NPs will be strongly influenced by the makeup of the waters they are released into. The impact of anion species on hydroxyl radical inhibition was as follows: carbonate > chloride > phosphate > nitrate > sulfate.

Thermal activation in statistical clusters of magnetic nanoparticles

This article presents a kinetic Monte-Carlo study of thermally activated magnetisation dynamics in clusters of statistically distributed magnetic nanoparticles. The structure of clusters is assumed to be of fractal nature, consistently with recent observations of magnetic particle aggregation in cellular environments. The computed magnetisation relaxation decay and frequency-dependent hysteresis loops are seen to significantly depend on the fractal dimension of aggregates, leading to accelerated magnetisation relaxation and reduction in the size of hysteresis loops as the fractal dimension increases from one-dimensional-like to three-dimensional-like clusters. Discussed are implications for applications in nanomedicine, such as magnetic hyperthermia or magnetic particle imaging.

Reversible and irreversible aggregation of magnetic liposomes.

Understanding stabilization and aggregation in magnetic nanoparticle systems is crucial to optimizing the functionality of these systems in real physiological applications. Here we address this problem for a specific, yet representative, system. We present an experimental and analytical study on the aggregation of superparamagnetic liposomes in suspension in the presence of a controllable external magnetic field. We study the aggregation kinetics and report an intermediate time power law evolution and a long time stationary value for the average aggregate diffusion coefficient, both depending on the magnetic field intensity. We then show that the long time aggregate structure is fractal with a fractal dimension that decreases upon increasing the magnetic field intensity. By scaling arguments we also establish an analytical relation between the aggregate fractal dimension and the power law exponent controlling the aggregation kinetics. This relation is indeed independent on the magnetic field intensity. Despite the superparamagnetic character of our particles, we further prove the existence of a population of surviving aggregates able to maintain their integrity after switching off the external magnetic field. Finally, we suggest a schematic interaction scenario to rationalize the observed coexistence between reversible and irreversible aggregation.

Comparison of multiple diagnostic techniques to study soot formation and morphology in a diffusion flame

Different non-intrusive optical and intrusive non optical diagnostic methods are used to measure flame and soot properties in a laminar coflow diffusion flame in order to compare and analyze the sensitivity of each technique to soot particles with different age and morphology. Flame temperature is measured using rapid thermocouple insertion (RTI) method and also by measuring soot spectral emissions (SSE). Soot volume fraction (fv) is measured quantitatively with laser extinction (LE), time resolved laser induced incandescent (TiRe-LII) and SSE methods and qualitatively from the transmission electron microscope (TEM) images of the thermophoretically sampled soot particles. Particle internal/aggregate nanostructure, and primary particle diameter are also analyzed based on TEM images from the sampled particles and TiRe-LII. It is shown that the optical methods are only sensitive to mature soot particles with solid appearance and cannot detect either temperature or fv in regions where liquid like nascent soot particles are dominant. fv measured by LE and TiRe-LII agree well while the values measured by SSE are lower. This discrepancy is attributed to the high sensitivity of fv measured by SSE to the measured temperature values. Temperature profiles measured by SSE are considerably higher than the values measured by RTI. It is shown that not considering the change of the surface emissivity of the thermocouple junction due to particle deposition for estimating radiation loss in regions where nascent or mature soot particles are dominant contributes to this discrepancy. Primary particle sizes measured based on TEM images and TiRe-LII agree reasonably well. Soot aggregate fractal dimension is shown to decrease as the soot particles age and become more mature.

Aggregation and breakup of acrylic latex particles inside millimetric scale reactors

Aggregation of acrylic latex is investigated inside tubular millireactors working under laminar hydrodynamic conditions. The size distribution and fractal dimension of aggregates are measured using light scattering. Results show that the equilibrium between rupture and aggregation is achieved quickly, allowing the study of cluster size distribution and shape at the aggregation/rupture steady state. Both laminar hydrodynamic conditions and high shear rate are suspected to promote the formation of aggregates with a high fractal dimension, which means that the particles are almost spherical, thereby offering an interesting alternative to conventional batch processes. These results can provide useful information for industries aiming at producing aggregates at specified size and quality.

A mobile system for a comprehensive online-characterization of nanoparticle aggregates based on wide-angle light scattering and laser-induced incandescence.

A mobile demonstrator for the comprehensive online-characterization of gas-borne nanoparticle aggregates is presented. Two optical measurement techniques are combined, both utilizing a pulsed Nd:YAG laser as light source. Aggregate size and fractal dimension are measured by Wide-Angle Light Scattering (WALS). An ellipsoidal mirror images elastically scattered light from scattering angles between 10° and 165° onto a CCD-camera chip resulting in an almost complete scattering diagram with high angular resolution. Primary particle size and volume fraction are measured by time-resolved Laser-Induced Incandescence (TiRe-LII). Here, particles are heated up to about 3000 K by the short laser pulse, the enhanced thermal radiation signal is detected with gated photomultiplier tubes. Analysis of the signal decay time and maximum LII-signal allows for the determination of primary particle diameter and volume fraction. The performance of the system is demonstrated by combined measurements on soot nanoparticle aggregates from a soot aerosol generator. Particle and aggregate sizes are varied by using different equivalence ratios of the combustion in the generator. Soot volume fraction can be adjusted by different levels of dilution with air. Online-measurements were carried out demonstrating the favorable performance of the system and the potential for industrial applications such as process control and product development. The particle properties obtained are confirmed through transmission electron microscopy analysis on representative samples.

Effects of vegetation restoration on the aggregate stability and distribution of aggregate-associated organic carbon in a typical karst gorge region

Abstract. Land use changes have a major impact on soil structure and soil nutrients. The influences of vegetation restoration on aggregate stability and soil carbon storage have been studied extensively, but the distribution of aggregate-associated carbon is not yet understood. The objective of this work was to study the influences of vegetation restoration on aggregate stability and distribution of soil organic carbon (SOC) associated with water-stable aggregates (WSAs) in a karst gorge region. The experiment was carried out in 2012 and included four land use types: bare land (BL), grassland (GL), shrubland (SL), and woodland (WL). Soil samples were collected from the 0–20, 20–40, and 40–60 cm depths, and aggregates were separated by a wet-sieving method. Aggregate stability and aggregated-associated SOC were determined, and the relationships between water-stable aggregation with SOC were examined. The results showed that total SOC and SOC associated with WSAs of various sizes were the highest at a soil depth of 0–20 cm. In addition, the SOC contents of the WSAs increased as the soil aggregate sizes decreased. The SOC contents of the WSAs < 0.25 mm were highest except in the bare land, and the SOC contents of the aggregates < 0.25 mm comprised the majority of the total aggregate SOC contents. The aggregates were dominated by particles with sizes > 5 mm under dry-sieving treatment, while aggregates were predominantly comprised of WSAs < 0.25 mm under wet-sieving treatment. At a soil depth of 0–60 cm, the mean weight diameter (MWD), geometrical mean diameter (GMD), and fractal dimensions (D) of the dry aggregates and water-stable aggregates in the different types of land were ranked, in descending order, as WL > GL > SL > BL. The contents of WSAs > 0.25 mm, MWD, and GMD increased significantly, in that order, and the percentage of aggregate destruction (PAD) and fractal dimensions decreased significantly as the soil aggregate stability improved. SOC contents increased after vegetation restoration, and the average SOC content of WL was 2.35, 1.37, and 1.26 times greater than that in the BL, GL, and SL, respectively. We conclude that woodland and grassland facilitated WSA stability and SOC protection; thus, promoting the natural restoration of vegetation by reducing artificial disturbances could effectively restore the ecology and prevent soil erosion in karst regions.

A refined algorithm to simulate latex colloid agglomeration at high ionic strength

This study is focussed on the simulation of particle agglomeration at relatively high ionic strength using a refined stochastic algorithm developed in the context of parcel-tracking approaches. For that purpose, experimental data of both diffusion-limited and reaction-limited aggregation of latex particles were obtained using dynamic light scattering techniques for different initial particle sizes (diameters ranging from 24 to 495 nm) and at various chemical conditions (ionic strength between 0.5 and 2 M with NaCl or CaCl\(_2\) solutions). The experimental data collected have been compared to numerical results obtained with the refined parcel-tracking algorithm for particle agglomeration which has been developed. Results show that the evolution of the aggregate diameters over time can be properly captured by the present model with the value of the aggregate fractal dimension that is extracted from experimental data.

Effects of aggregate morphology and size on laser-induced incandescence and scattering from black carbon (mature soot)

We have used a Single-Particle Soot Photometer (SP2) to measure time-resolved laser-induced incandescence (LII) and laser scatter from combustion-generated mature soot with a fractal dimension of 1.88 extracted from a burner. We have also made measurements on restructured mature-soot particles with a fractal dimension of 2.3–2.4. We reproduced the LII and laser-scatter temporal profiles with an energy- and mass-balance model, which accounted for heating of particles passed through a CW-laser beam over laser–particle interaction times of ~10μs. The results demonstrate a strong influence of aggregate size and morphology on LII and scattering signals. Conductive cooling competes with absorptive heating on these time scales; the effects are reduced with increasing aggregate size and fractal dimension. These effects can lead to a significant delay in the onset of the LII signal and may explain an apparent low bias in the SP2 measurements for small particle sizes, particularly for fresh, mature soot. The results also reveal significant perturbations to the measured scattering signal from LII interference and suggest rapid expansion of the aggregates during sublimation.

Aggregation and resuspension of graphene oxide in simulated natural surface aquatic environments

A series of experiments were performed to simulate the environmental behavior and fate of graphene oxide nanoparticles (GONPs) involved in the surface environment relating to divalent cations, natural organic matter (NOM), and hydraulics. The electrokinetic properties and hydrodynamic diameters of GONPs was systematically determined to characterize GONPs stability and the results indicated Ca2+ (Mg2+) significantly destabilized GONPs with high aggregate strength factors (SF) and fractal dimension (FD), whereas NOM decreased aggregate SF with lower FD and improved GONPs stability primarily because of increasing steric repulsion and electrostatic repulsion. Furthermore, the GONPs resuspension from the sand bed into overlying water with shear flow confirmed that the release would be restricted by Ca2+ (Mg2+), however, enhanced by NOM. The interaction energy based on Derjaguin–Landau–Verwey–Overbeek theory verifies the aggregation and resuspension well. Overall, these experiments provide an innovative look and more details to study the behavior and fate of GONPs.

A simple semi-empirical model for effective density measurements of fractal aggregates

Effective density measurements are used extensively to convert submicron particle sizes based on a particle׳s mobility diameter into mass. Measurements of the effective density also provide information concerning the particle morphology. For example, the effective density curves of fractal aggregates reveal a scaling factor that seems to correlate with the fractal dimension of the particles. The present paper proposes a simple semi-empirical model that permits the quantitative interpretation of these measurements to determine parameters such as the fractal dimension, the primary particle size, and the bulk density of an aggregate particle. The proposed model is based on the assumption that the hydrodynamic drag force of an aggregate is proportional to the drag force applied to isolated primary spheres and to the number of primary spheres in the aggregate at power α. The model was applied to soot particles produced by either a spark discharge (PALAS GFG1000) or by combustion (miniCAST 5206)—both mechanisms enable the generation of aggregates or agglomerates with very different primary sphere diameters. The proposed model showed a good fit for all of the effective density measurements obtained in this study; the α parameter was driven by the aggregate fractal dimension and by the Knudsen number that was determined based on the primary particle diameter. Finally, for a known primary particle diameter, the fractal dimension and the bulk density were determined successfully with the proposed model.

Simultaneous measurement of internal and external properties of nanoparticles in flame based on thermophoresis

The mechanism of nanoparticles processed in flame aerosol reactors involves vapor to solid reaction, nucleation, coalescence, agglomeration, diffusion and other processes. Determination of internal (e.g., particle size distribution (PSD), aggregate fractal dimension (AFD), and particle volume fraction (PVF)) and external (e.g., temperature and flow velocity) properties of nanoparticles through numerical simulations or experimental measurements is critical to understanding the underlying particle dynamics, which still remains a major challenge. Multiple key internal and external properties of nanoparticles in flame were measured and characterized simultaneously in this study by a simple and novel dual time-interval thermophoretic sampling (DTTS) method. A tailor-made fine-wire thermocouple was first used to measure flame temperature, with a sufficiently short residence time to reduce the effects of radiation losses and nanoparticles deposition as possible and thereby the thermocouple response met the first-order dynamic equation where only heat convection was considered. Two TEM grids were used for nanoparticle sampling at a position and were exposed to flame for two different time intervals. As the amount of particles deposited on the probe surface by the thermophoretic force is a function of gas temperature, flow velocity, PVF and the probe exposure time in the flame, we proposed an integrative solution for these multiple parameters using the two samples by accounting for the effects of the unsteady temperature gradient of the probe. The effects of flow velocity on convection heat transfer of flame and TEM grids were considered by analyzing the visible microscopic state of thermophoretic-deposited particles. A co-flow diffusion CH4 flame for TiO2 nanoparticle synthesis by feeding TiCl4 vapor was measured via the DTTS method. The experimental measurements of flame temperature, flow velocity and PVF at the different flame heights agree well with the simulation results by coupled computational fluid dynamics with population balance modeling (CFD-PBM).

Effect of manure on organic carbon content and fractal dimensions of aggregates

Effects of farmyard manure treatments on some soil structural parameters such as, aggregate stability (AS), geometric mean weight (GMWD) and mean weight (MWD) diameters, fragmentation (D) and mass (D m ) fractal dimensions, bulk density (BD) and organic C (OC) contents of aggregates were determined in a clay soil. Application of 67 Mg ha -1 farmyard manure to Vertic Haplustoll soil decreased AS 12.14% compared with the control. Manure treatment increased the proportion of microaggregates in the fractions 1.00 mm in size. While OC contents of aggregates increased between 22.8% and 123.4%, BD values decreased between 0.8% and 16.6% with the manure treatment. Fragmentation (D) and mass (D m ) fractal dimensions were increased with decreasing numbers of macroaggregates of the clay soil. GMWD (1.16 mm) and MWD (1.86 mm) obtained in the manure treatment were lower than that in the control treatment (1.20 mm and 1.95 mm, respectively). Although OC content of the aggregates increased with the manure treatment, the number of macroaggregates of clay soil decreased with decreasing AS..

Modelling of deposition of flexible fractal-like aggregates on cylindrical fibre in continuum regime

A new mathematical model of aggregate composed of N primary spherical particles has been created. The aggregate structure is modelled as an elastic body, capable of undergoing stretching, bending and twisting, during its movement in fluid. An aggregate is defined as a system of spherical particles joined together by springs, and the stiffness of structure is maintained by potential energy functions. Aggregate movement has been tracked in a Kuwabara cell model for three different values of velocity in continuum regime. The deposition efficiency of aggregates on a cylindrical collector has been related to the fractal dimension of aggregates, velocity of air and spring constant, which determine the magnitude of deformation of the aggregate structure. It was found that fractal dimension, velocity of air and imposed parameters of oscillations constants, strongly influence the deposition efficiency of aggregates.

Comments on paper: “Evolution of aggregate size and fractal dimension during Brownian coagulation” by Margaritis Kostoglou, Athanasios G. Konstandopoulos

The paper proposed a simple constitutive law and combined it with a Monte Carlo method to describe the evolution of size and fractal dimension of aggregates with different fractal dimensions in coagulation. Their formula for determining the fractal dimension of an aggregate in coagulation is formulated under a condition that the size of primary particles consisting of aggregate is kept constant in the course of coagulation process. This comment shows that a more general expression for determining the fractal dimension can be derived by the use of a variable size of primary particles and mass conservation law.

Biological and physicochemical properties of bovine sodium caseinate hydrolysates obtained by a bacterial protease preparation

In this work, we aimed at the production of bovine sodium caseinate (NaCAS) hydrolysates by means of an extracellular protease from Bacillus sp. P7. Mass spectrometry was carried out to evaluate peptide mass distribution and identified sequences of peptides with a signal/noise ratio higher than 10. Antioxidant and antimicrobial properties of hydrolysates were evaluated. An acid-induced aggregation process of the hydrolysates and their corresponding mixtures with NaCAS were also analyzed. The results showed that the enzymatic hydrolysis produced peptides, mostly lower than 3 kDa, with different bioactivities depending on the time of hydrolysis (ti). These hydrolysates lost their ability to aggregate by addition of glucono-δ-lactone, and their incorporation into NaCAS solutions alter the kinetics of the process. Also, the degree of compactness of the NaCAS aggregates, estimated by the fractal dimension of aggregates, was not significantly altered by the incorporation of hydrolysates. However, at higher protein concentrations, when the decrease in pH leads to the formation of NaCAS acid gels, the presence of hydrolysates alters the microstructure and rheological behavior of these gels.

A comparative study of the physical properties of in-cylinder soot generated from the combustion of n-heptane and toluene/n-heptane in a diesel engine

This study examines the similarities and dissimilarities in the physical properties of in-cylinder soot obtained during combustion of n-heptane and a toluene/n-heptane mixture (TRF20, 20% toluene by volume) in a heavy-duty diesel engine. A total cylinder sampling system was used to sample the in-cylinder soot during different combustion phases. For each sample, the morphology, size, fractal dimension and nanostructure of the soot particles were analyzed using high-resolution transmission electron microscopy and Raman scattering spectrometry. The oxidation reactivity of soot particles was also evaluated in terms of apparent activation energy using thermogravimetric analysis. Throughout the combustion process, soot aggregates from the combustion of TRF20 generally exhibited more primary particles and larger-sized clusters than the n-heptane soot aggregates. Despite the different fuel formulations, both n-heptane and TRF20 showed similar trends during the combustion process in terms of changes in fractal dimension of soot aggregates, mean primary particle size and nanostructure (as characterized by fringe length, separation distance and tortuosity). The presence of toluene, however, led to a decrease in the fractal dimensions of the aggregates and a concurrent increase in the mean size of primary particles. Moreover, in the same combustion stages, the mean fringe length for the TRF20 soot was smaller than that for the n-heptane soot, while the mean separation distance and tortuosity for the TRF20 soot were both larger than those for the n-heptane soot. Relative to the n-heptane soot, the TRF20 soot had less graphitic organization and lower resistance to oxidation.

Research on the AC-13 Skeleton Dense-Graded Asphalt Mixtures by Fractal Theory

This paper study on AC-13 skeleton dense-graded asphalt mixtures by fractal theory, obtaining that both aggregate size and gradation have fractal character. Compared three kinds of asphalt mixture, we found that there was a strong correlation between fractal dimension of aggregate and aggregate size distribution. AC-13 skeleton dense-graded asphalt mixtures were tested. The results show that the aggregate fractal dimension has a good correlation with mixture’s bulk density, mineral aggregate gap rate, percentage of voids and asphalt degree of saturation too. The study is useful for reference to the readers who engage in further study of the fractal theory’s application to asphalt mixtures.

Adsorption of Superparamagnetic Iron Oxide Nanoparticles on Silica and Calcium Carbonate Sand

Superparamagnetic iron oxide (SPIO) nanoparticles have the potential to be used in the characterization of porous rock formations in oil fields as a contrast agent for NMR logging because they are small enough to traverse through nanopores and enhance contrast by shortening NMR T2 relaxation time. However, successful development and application require detailed knowledge of particle stability and mobility in reservoir rocks. Because nanoparticle adsorption to sand (SiO2) and rock (often CaCO3) affects their mobility, we investigated the thermodynamic equilibrium adsorption behavior of citric acid-coated SPIO nanoparticles (CA SPIO NPs) and poly(ethylene glycol)-grafted SPIO nanoparticles (PEG SPIO NPs) on SiO2 (silica) and CaCO3 (calcium carbonate). Adsorption behavior was determined at various pH and salt conditions via chemical analysis and NMR, and the results were compared with molecular theory predictions. Most of the NPs were recovered from silica, whereas far fewer NPs were recovered from calcium carbonate because of differences in the mineral surface properties. NP adsorption increased with increasing salt concentration: this trend was qualitatively explained by molecular theory, as was the role of the PEG grafting in preventing NPs adsorption. Quantitative disagreement between the theoretical predictions and the data was due to NP aggregation, especially at high salt concentration and in the presence of calcium carbonate. Upon aggregation, NP concentrations as determined by NMR T2 were initially overestimated and subsequently corrected using the relaxation rate 1/T2, which is a function of aggregate size and fractal dimension of the aggregate. Our experimental validation of the theoretical predictions of NP adsorption to minerals in the absence of aggregation at various pH and salt conditions demonstrates that molecular theory can be used to determine interactions between NPs and relevant reservoir surfaces. Importantly, this integrated experimental and theoretical approach can be used to gain insight into NP mobility in the reservoir.