Collision limited reaction rates for arbitrarily shaped particles across the entire diffusive Knudsen number range

Aerosol particle reactions with vapor molecules and molecular clusters are often collision rate limited, hence determination of particle-vapor molecule and particle-molecular cluster collision rates are of fundamental importance. These collisions typically occur in the mass transfer transition regime, wherein the collision kernel (collision rate coefficient) is dependent upon the diffusive Knudsen number, KnD. While this alone prohibits analytical determination of the collision kernel, aerosol particle- vapor molecule collisions are further complicated when particles are non-spherical, as is often the case for particles formed in high temperature processes (combustion). Recently, through a combination of mean first passage time simulations and dimensional analysis, it was shown that the collision kernel for spherical particles and vapor molecules could be expressed as a dimensionless number, H, which is solely a function of KnD. In this work, it is shown through similar mean first passage times and redefinitions of H and KnD that the H(KnD) relationship found for spherical particles applies for particles of arbitrary shape, including commonly encountered agglomerate particles. Specifically, it is shown that to appropriately define H and Kn D, two geometric descriptors for a particle are necessary: its Smoluchowski radius, which defines the collision kernel in the continuum regime (KnD→0) and its orientationally averaged projected area, which defines the collision kernel in the free molecular regime (Kn D→). With these two parameters, as well as the properties of the colliding vapor molecule (mass and diffusion coefficient), the particle-vapor molecule collision kernel in the continuum, transition, and free molecular regimes can be simply calculated using the H(KnD) relationship. © 2011 American Institute of Physics

The collision rate of nonspherical particles and aggregates for all diffusive knudsen numbers

We examine theoretically and numerically collisions of arbitrarily shaped particles in the mass transfer transition regime, where ambiguities remain regarding the collision rate coefficient (collision kernel). Specifically, we show that the dimensionless collision kernel for arbitrarily shaped particles, H, depends solely on a correctly defined diffusive Knudsen number (Kn D, in contrast with the traditional Knudsen number), and to determine the diffusive Knudsen number, it is necessary to calculate two combined size parameters for the colliding particles: the Smoluchowski radius, which defines the collision rate in the continuum (Kn D→0) regime, and the projected area, which defines the collision rate in the free molecular (Kn D) regime. Algorithms are provided to compute these parameters. Using mean first passage time calculations with computationally generated quasifractal (statistically fractal) aggregates, we find that with correct definitions of H and Kn D, the H(Kn D) relationship found valid for sphere-sphere collisions predicts the collision kernel for aggregates extremely well (to within 5%). We also show that it is critical to calculate combined size parameters for colliding particles, that is, a collision size/radius cannot necessarily be defined for a nonspherical particle without foreknowledge of the geometry of its collision partner. Specifically for sequentially produced model aggregates, expressions are developed through regression to evaluate all parameters necessary to predict the transition regime collision kernel directly from fractal descriptors. Copyright 2012 American Association for Aerosol Research © 2012 Taylor and Francis Group, LLC

The unipolar diffusion charging of arbitrary shaped aerosol particles

The unipolar diffusion charging of particles, i.e. the net increase in particle charge through ion-particle collisions, is an important process in a number of aerosol systems. Accurate methods are hence needed to predict the unipolar charging rate, not only for spherical particles, but also particles of arbitrary geometry. In this work, the unipolar charging (described by the particle-ion collision kernel) of conducting, arbitrary shaped particles is studied theoretically. Through a combination of dimensional analysis, Brownian dynamics (BD), and molecular dynamics (MD), the collision kernel is found to be described accurately by a simple-to-use expression across the entire diffusive Knudsen number KnD range (from the continuum regime to the free molecular regime), where KnD is the ratio of the ion mean persistence path to a well-defined particle length scale (proportional to the ratio of orientationally averaged projected area PA to the Smoluchowski radius Rs). In the developed collision kernel expression, the effect of repulsive Coulomb and attractive image potential interactions between the ion and the particle are parameterized by the coulomb potential energy to thermal energy ratio, ψE, and image potential energy to thermal energy ratio, ψI. It is found that the changes in collision rates due to potential interactions in the continuum (KnD→0) and free molecular (KnD→∞) regimes collapse to particle geometry independent functions, expressed in terms of ψE and ψI. In the transition regime, the dimensionless collision kernel H is shown to be geometry independent, and is a function of a suitably defined KnD only. Comparison is made between the predictions of the proposed expression and the flux matching model of Fuchs; for non-spherical particles, theories available in the literature are examined and commented upon. Finally, sample calculations of the mean charge acquired by selected particle geometries are presented and discussed. © 2013 Elsevier Ltd

New possibilities of accurate particle characterisation by applying direct boundary models to analytical centrifugation

Analytical centrifugation (AC) is a powerful technique for the characterisation of nanoparticles in colloidal systems. As a direct and absolute technique it requires no calibration or measurements of standards. Moreover, it offers simple experimental design and handling, high sample throughput as well as moderate investment costs. However, the full potential of AC for nanoparticle size analysis requires the development of powerful data analysis techniques. In this study we show how the application of direct boundary models to AC data opens up new possibilities in particle characterisation. An accurate analysis method, successfully applied to sedimentation data obtained by analytical ultracentrifugation (AUC) in the past, was used for the first time in analysing AC data. Unlike traditional data evaluation routines for AC using a designated number of radial positions or scans, direct boundary models consider the complete sedimentation boundary, which results in significantly better statistics. We demonstrate that meniscus fitting, as well as the correction of radius and time invariant noise significantly improves the signal-to-noise ratio and prevents the occurrence of false positives due to optical artefacts. Moreover, hydrodynamic non-ideality can be assessed by the residuals obtained from the analysis. The sedimentation coefficient distributions obtained by AC are in excellent agreement with the results from AUC. Brownian dynamics simulations were used to generate numerical sedimentation data to study the influence of diffusion on the obtained distributions. Our approach is further validated using polystyrene and silica nanoparticles. In particular, we demonstrate the strength of AC for analysing multimodal distributions by means of gold nanoparticles

The effect of mixing on silver particle morphology in flow synthesis

Silver particles, prepared in a T-mixer under different flow rates, were selected to study the influences of mixing on particle shape evolution. Mixing effects on particle growth were visualized by scanning electron microscopy (SEM) and analysed quantitatively by sedimentation coefficient distributions derived from analytical centrifugation (AC). The mixing time under different flow rates was determined by the Villermaux-Dushman method to quantify the mixing quality. Based on the finding of a mixing-induced shape transformation from plates to dendrites, an extended growth mechanism involving mixing effects was proposed. Slow mixing leads to a non-uniform distributed reactant mixture and low effective supersaturation. This causes preferential growth of high-energy facets resulting in plate-like particles with broad, multimodal sedimentation distributions. In contrast, fast mixing, corresponding to uniform reactant mixture and thus high effective supersaturation and nucleation rate, leads to dendritic products, and narrow but bimodal sedimentation distributions. (C) 2018 Elsevier Ltd. All rights reserved.</p

Langevin Simulation of Aggregate Formation in the Transition Regime

<p>We study the aggregation of monomers in an aerosol via non-dimensional Langevin simulations, in which particles remain in point contact upon collision, and report the hydrodynamic radii and projected areas of the formed aggregates with less than 300 primary particles. Unique from prior studies, in examining aggregation we monitor the evolution of the distributions of two Knudsen numbers: the traditional Knudsen number (Kn) and the diffusive Knudsen number (Kn_D), which both shift to smaller mean values as aggregation proceeds. As Kn transitions from large to small values, momentum transfer changes from a free molecular to a continuum process; analogously, as Kn_D decreases, aggregation is altered from occurring ballistically to diffusively in a dilute system. During simulations, the change in drag coefficient with both changing Kn and changing aggregate structure is accounted for. We find that as compared to completely coalescing particles (spheres), non-coalescing aggregates with the same initial Kn and Kn_D have Kn_D values, which decrease more rapidly due to aggregation; hence, aggregates are more likely to collide with one another diffusively when compared with their spherical counterparts of the same Kn distribution. Further, we find that aggregation with evolving Knudsen numbers does not lead to strong scaling between the number of monomers in a formed aggregate and the aggregate radius of gyration for aggregates composed of 300 or fewer primary particles. In spite of this, aggregate hydrodynamic radii and orientationally averaged projected areas are found to scale well with the number of monomers per aggregate.</p> <p>Copyright 2015 American Association for Aerosol Research</p

Enhanced Crystallization of Lysozyme Mediated by the Aggregation of Inorganic Seed Particles

We show that aggregation plays a major role in seeded growth of protein crystals. The seeded batch approach provides the opportunity to set the starting conditions for protein crystallization by adding a defined amount of well-characterized seed particles. The experimental observations for tetragonal hen egg-white lysozyme (LSZ) confirm the concept of the oriented aggregation of larger building blocks to form a protein crystal. It was shown that the aggregation of the seed particles/bioconjugates is advantageous for the product quality in terms of larger and more defined LSZ crystals and in terms of accelerated reaction kinetics. We present a population balance (PB) model for the seeded batch crystallization of LSZ considering the aggregation of growth units to form protein crystals. For the modeling of crystal growth, evolving particle size distributions (PSDs) of agglomerating LSZ molecules were measured by dynamic light scattering (DLS). Moreover, the aggregation of seed particles in LSZ solutions under crystallization conditions was investigated by DLS. In line with our expectations, the number of seeds was found to be important as it strongly affects the collision frequency in the aggregation term of our PB model. Finally, the applied model gives trends of the supersaturation depletion curves and orders of magnitude of the measured CSDs in particle size correctly, ranging from only a few nanometers up to micrometer-sized particles/crystals. Thus, by the combination of PB modeling and experimentally determined crystallization parameters, insights into the crystal formation mechanism were obtained. To the best of our knowledge, this is the first attempt to model growth within a crystal population by an aggregation mechanism induced by seeding with foreign particles