Sedimentation, aggregate size determination

Before beginning a size determination, it is customary to look at the material, preferably under a microscope. This examination reveals the approx size range and distribution of the particles, and especially the shapes of the particles and the degree of aggregation. If microscopic examination reveals that the ratios between max and min diameters of individual particles do not exceed 4, and indirect technique for particle size distribution based on sedimentation or elutria-tion may be used. Sedimentation techniques for particle size determination were first used by Hall (Ref 2) in 1904, He showed that the rate of fall of individual particles in a fluid was directly related to the particle size by the hydrodynamic... 

The interaction in a two-body collision in a dilute suspension has been expanded to provide a useful and quantitative understanding of the aggregation and sedimentation of particulate matter in a lake. In this view, Brownian diffusion, fluid shear, and differential sedimentation provide contact opportunities that can change sedimentation processes in a lake, particularly when solution conditions are such that the particles attach readily as they do in Lake Zurich [high cc(i,j)exp]. Coagulation provides a conceptual framework that connects model predictions with field observations of particle concentrations and size distributions in lake waters and sediment traps, laboratory determinations of attachment probabilities, and measurements of the composition and fluxes of sedimenting materials (Weilenmann et al., 1989). 

A useful method for determining relative aggregate sizes and distributions is by centrifugal sedimentation. For a sphere, the diameter can be derived from the sedimentation rates in the gravitational field according to Stokes equation. For the nonspherical particles such as carbon black aggregates, an equvalent Stokes... 

Once nanoparticles have been formed, whether in an early state of growth or in a more or less final size, their fate depends on the forces between the individual particles and between particles and solid surfaces in the solution. While particles initially approach each other by transport in solution due to Brownian motion, convection, or sedimentation, when close enough, interparticle forces will determine their final state. If the dominant forces are repulsive, the particles will remain separate in colloidal form. If attractive, they will aggregate and eventually precipitate. In addition, they may adsorb onto a solid surface (the substrate or the walls of the vessel in which the reaction is carried out). For CD, both attractive particle-sur-... 

The size of the droplets in an emulsion has a strong influence on many of its physicochemical and sensory properties, e.g., shelf life, appearance, texture, and flavor (1,2, 4). For example, the stability of an emulsion to gravitational separation or droplet aggregation can be greatly improved by decreasing the droplet size. This is because the velocity of sedimentation is proportional to the square of the droplet size. The size of the droplets in an emulsion is largely determined by the emulsifier type and concentration, the physicochemical properties of the component phases, and the homogenization conditions (4). A food manufacturer normally specifies a preestablished desirable droplet size distribution for a particular product. If the product does not meet this specification, it typically must be reprocessed or even discarded. 

For example, an alumina coating with a median pore size of typically 100 nm can be prepared from a suspension (in water) of commercially available submicron alumina powder with a mass based median diameter of 500 nm. In such a suspension colloidal interactions determine to a large extent the properties of the suspension. The particle packing properties are disturbed by the presence of a fraction of aggregates which always exist in such commercial powders. This fraction can be removed from a colloidally stable suspension by means of sedimentation fractionation (see Ref. [5] for an example). 

One ways of characterization the morphology and aggregation of materials is to determine their sizes. The lignin particles sizes have been studied previously with a variety of methods such as viscometry, sedimentation, and diffusion measurements in the solution state [163], the box counting method applied on a lignin surface [164], and simulations of the ceU wall structure have brought up the idea about fractal lignin [165]. 

For completeness we note that two other FFF subtechniques can be applied to certain polymeric materials, although applications are so far limited. Sedimentation FFF is the most notable example. For this system the driving force (centrifugally induced sedimentation) is directly proportional to molecular mass in a form that is calculable from first principles (see eqn 8.7). Accordingly, molecular mass distributions can in theory be obtained by calculation without empirical calibration. This principle has been successfully applied to the determination of the molecular mass and particle size distribution of numerous colloidal particles including viruses, latices, emulsions, liposomes, protein aggregates, and water-borne colloids [5,7,9]. However, as noted earlier, sedimentation FFF is not applicable to many polymers of interest because sedimentation forces (even in a powerful centrifuge) are not adequate to drive the components to the accumulation wall of the FFF channel. Thus molecular masses of less than 10 cannot be well... 

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