Physicochemical Behavior of Particles

There exists an extensive literature on the theory of coagulation (Fuchs, 1964 Zebel, 1966 Hidy and Brock, 1970 Twomey, 1977), and we can treat here only the most salient features. In the absence of external forces, the aerosol particles undergo collisions with each other due to their thermal (Brownian) motion. The mathematical description of thermal coagulation goes back to the classical work of Smoluchowski (1918) on hydrosols. Application to aerosols seems to have been made first by Whitlaw-Gray and Patterson (1932). Let dN, = f(r,) dr, and dN2=f(r2) dr2 describe the number densities of particles in the size intervals r, + dr, and r2+dr2, 

The diffusion coefficients are obtained from the mobilities of the particles, ft, use being made of the Einstein relation D, = kBTb(. For spherical particles the dependence of the mobility on r and A has been derived empirically from careful measurements by Knudsen and Weber (1911) and by Millikan (1923) in the form 

The collision of particles with masses m, and m2 leads to the formation of a new particle with mass m3 = mt + m2. If the new particle is assumed to be spherical, its radius is r3 = (r3 + r3)l/3. To ensure mass conservation, the mathematical description of the coagulation process requires an appropriate weighting of the coagulation function, and the delta function is suitable for this purpose. We define 

There are no simple solutions to this integrodifferential equation, and numerical procedures must be applied in solving it. Note that Eq. (7-9) describes the change with time of the distribution function /(r, t) when sources of particles are absent. If there is a production of new particles, a source term must be added to the right-hand side. 

Walter (1973) has studied the evolution of the particle size spectrum by coagulation for the case where new particles with a radius of 1.2 x 10-3 j.m are continuously generated by nucleation processes. Some of his results are shown in Fig. 7-5. The left-hand side shows the evolution of the size spectrum when other particles are initially absent. A secondary maximum develops 

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The physicochemical properties of particles influence their behavior in transit through the airways of the lungs according to three mechanisms impaction, sedimentation, and diffusion. 

These surface charge effects could also influence other aspects of the physicochemical behavior of the suspension. For example, depending on the solution ionic strength and the pH versus ZPC relationship, particles could aggregate, creating additional pore volume. Furthermore, surface charge and ionic strength must influence the counterion diffusion that is required to maintain electroneutrality. 

The aim of this chapter is to summarize some of the research findings on xylan, a natural polymer extracted from corn cobs, which presents a promising application in the development of colon-specific drug carriers. Physicochemical characterization of the polymer regarding particle size and morphology, composition, rheology, thermal behavior, and crystallinity will be provided. Additionally, research data on its extraction and the development of microparticles based on xylan and prepared by different methods will also be presented and discussed. 

Fine particle powders can be produced by various methods, such as micronization or spray drying. The physicochemical nature of these fine particles largely defines the stability of the bnlk powder, which in turn is critical to the long-term effective performance of the dry powder product. The section Fine Particles and the Solid State in this article is an introduction to understanding better the fundamental properties that underlie the behavior of bulk powders. Commentary on the various means of producing fine powders follows in the section Powder Production Formulation and Processing. ... 

That no indication of the significant influence of particle shape on FFF elution behavior has been published until recently may be attributed to the fact that the majority of the approximately 500 papers so far published have reported on spherical or nearly spherical samples, and that the studies on the non-spherical samples focused only on sample fractionation rather than on a quantitative assessment of physicochemical quantities. This problem can be solved if fractions from FFF are further characterized, for example, by dynamic fight scattering or if an independent detector for diffusion coefficients is available. 

It is clear from the above discussion that the rheological properties of FCOJ will depend on the °Brix, pulp content, size and shape of the pulp particles, and pectin content of FCOJ sample, and the temperature at which the data were obtained. Carter and Buslig (1977) studied particle size distribution in commercial frozen FCOJ samples. Mizrahi and coworkers conducted systematic studies on FCOJ that they described as a physicochemical approach (Mizrahi and Berk, 1970 Mizrahi and Firstenberg, 1975 Mizrahi, 1979). They used a modified Casson equation to describe the flow behavior of FCOJ. 

We have studied the effea of preparation procedure, crystallite shape and size, and oxidation conditions on the oxidation behavior of silicon micro- and nanopowders. The oxidation process is shown to occur in two steps, with a transition at a certain thickness of the oxidized layer, which depends on the oxidation time, particle shape, and particle size. The composition and physicochemical properties of the oxide films have been detennined in relation to the shape and size of the silicon particles. The results indicate that the silicon micro- and nanopowdeis differ in oxidation mechanism from singlecrystal silicon. 

The present data on the effect of the preparation procedure and particle size on the oxidation rate of silicon micro- and nanopowders and the physicochemical properties of the silicon oxide films produced fi-om the powders shed light on the origin of the irreproducibility of the published data. Comparison of the oxidation behavior of silicon powders with that of single-crystal Si indicates that these materials are sensitive to the oxidation conditions. Silicon nanopowders have the... 

The combined information obtained by the different characterization methods applied allows the conclusion that deposits of ruthenium oxide at BDD, ranging from approximately one hundredth of a monolayer, maintain the physicochemical properties of RUO2, which proves the very limited degree of chemical interaction with the support. The deposits are most probably organized in nanoparticles growing around nucleation sites. When particles and clusters of particles reach a size of 50-60 nm, their charge-storage and catalytic behavior closely resembles that of thick oxide films. 

The environmental behavior of plutonium is highly dependent on physicochemical properties of both the Pu compounds and the environmental media. As a rule, plutonium adsorbed on soil or sediment particles migrates very slowly, although the rate can be accelerated depending on Pu oxidation state and soil characteristics (mineral makeup, pH, presence of ligands). Uptake and concentration in edible plants is relatively low (concentration ratio on the order of 10 " in vegetative parts). 

Speciation studies have been carried out for methylated species of As, Sb, Ge, and Sn and on different redox states of these elements—As(III-V), Sb(III-V), or Cr(III-VI)— (Andreae and Froehlich, 1984), as shown in Fig. 13.2. In oxic Baltic waters the pentavalent species of As and Sb predominate, while in the anoxic basins the distribution shifts to the trivalent species and possibly also to polysulfide complexes. The methylated species of As, Sb, and Ge are detectable throughout the water column. Since the mid-1980s, an improvement in the understanding of the behavior of trace elements in the Baltic Sea has been achieved. First investigations into the speciation of mercury have been realized by Brugmann (1979) and Brugmann et al. (1991). A special emphasis has been made on the different physicochemical forms, such as dissolved Hg, weakly associated Hg with particles, and total Hg. 

The minerals in coal are converted to ash during combustion. The portion of the fly ash impacting on heat transfer surfaces, which is retained as deposits, depends on the particle size, its chemistry and its physicochemical behavior during combustion in the steam generator furnace, as well as subsequent cooling in the convective heat... 

The enhanced physical properties for supercritically produced salme-terol (e.g., high crystallinity, polymorphic purity, powder uniformity) correlate well with the enhanced dispersion and flow behavior of this powder. However, as shown in some other investigations (12,28), particle size and shape, surface energy, and crystallinity may have to be optimized separately, using all process parameters available, perhaps including a coformulation step. For some compounds with low solubility in water, a compromise must be found between improved bioavailability and physicochemical stability. 

It has been reported several times that the type of deposition strongly affects the physicochemical characteristics and thus the catalytic behavior of the final catalysts [1,2]. In most of the cases, interfacial deposition results to catalysts with very small supported particles. This is because their size is controlled by the physicochemical characteristics and the size of the interface. Therefore, interfacial deposition results to supported catalysts with very high dispersion of the supported phase [2]. This is frequently reflected to the relatively high activity of the final catalysts [2]. 

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