Polydisperse system of particles

For a polydisperse system of particles undergoing both creaming and gravity-induced flocculation, the time evolution of the particle size distribution, and hence the time rate of change of the total particle concentration, can only be determined from the solution of the governing population balance equations (10,11). For the special case of two different sized particles, this system of balance equations reduces to ... 

Dynamic light scattering. Dynamic light scattering measurements provide the electric field correlation function g(q, t), which can be expressed for a polydisperse system of particles as (see [90,91])... 

Using the results of [473] obtained for the flow field in the point force model, one can find the mean Sherwood number for a polydisperse system of particles [74] ... 

Natural soils are polydisperse systems of particles, which are rarely present in the form of loose beds. Nevertheless, if loose particles are available, they will be preferentially mobilized. Other factors that are important are the coverage of the soil surface with roughness elements like pebbles, stubbles, bushes, etc., which partially absorb momentum coherence forces between soil particles due to clay aggregation, organic material, or moisture content and soil texture, that is, the composition of the soil in terms of particle size classes (see Table 7-7). 

Heterodisperse Suspensions. The rate laws given above apply to monodisperse colloids. In polydisperse systems the particle size and the distribution of particle sizes have pronounced effects on the kinetics of agglomeration (O Melia, 1978). For the various transport mechanisms (Brownian diffusion, fluid shear, and differential settling), the rates at which particles come into contact are given in Table 7.2. 

Holland, A. C., and G. Gagne, 1970. The scattering of polarized light by polydisperse systems of irregular particles, Appl. Opt., 9, 1113-1121. 

PEC formation in a concentration range of the component solutions below 1-10-3 g/mL resulted in stable dispersions of PEC particles when non-stoichiometric mixing ratios are used. In general, the scattering functions of the PECs could be well fitted by the model of polydisperse systems of homo-... 

As mentioned above, measurements at finite concentrations lead to a non-vanishing influence of the structure factor S(q). For the overwhelming majority of the latex systems studied by SAS-experiments so far, colloid stability has been achieved by a screened Coulomb interaction [5,62,63]. The structure factor of such a system of particles interacting through a Yukawa-potential has been extensively studied theoretically by Klein and coworkers (see Ref. [63] and further citations given there) who extended the treatment to polydisperse systems. 

Gupta and Seshadri [129] used Ouchiyama and Tanaka s results [130] to calculate the maximum packing parameter of polydisperse systems of spheres given the value for the monodisperse samples and taking into account particle size, size distribution and modality as follows... 

The SANS data were modeled [34, 35] as a system of particles with an inner core radius (/ core) and outer shell radius (/ sheii) assuming that there are no orientational correlations, using the same methodology [26, 27, 34] as that developed for aqueous aggregates. For dilute solutions, interparticle interactions may be neglected [4] and several particle shapes were used. The best fits were given by a spherical core-shell model with a Schultz distribution [35] of particle sizes, with a breadth (polydispersity) parameter (Z) and an aggregation number (i.e. the number of molecules per micelle) A agg- A comparison of independently calibrated... 

For a given structure type we obtain one set of master curves in dependence on the polydispersity. Model calculations were carried out for polydisperse systems of spheres and Gaussian coils, which cover the scattering behavior, observed on PEC particle systems. Figure 1 gives the master representation of the Debye plot for polydisperse spheres, showing significant deviations for different polydispersities. 

As pointed out by Klee et al., such a system can also be modeled using Eq. (6.33). This was accomplished by approximating the dilute phase as a polydisperse system of core-shell particles [37] and assuming a hard sphere structure factor however, the effect of polydispersity on the structure factor was not accounted for [62]. As well, the GIFT analysis has also been used to verify the presence of a core-shell structure [73]. Ultimately, there is more than one single model that can accurately describe the SAXS in terms of the peak intensity, average size, and Porod scattering law. For example, a eore-shell structure can correctly account for the shell of amphiphilic molecules at the surface of the microemulsion, which Eq. (6.36) cannot. 

Particulate systems composed of identical particles are extremely rare. It is therefore usefiil to represent a polydispersion of particles as sets of successive size intervals, containing information on the number of particle, length, surface area, or mass. The entire size range, which can span up to several orders of magnitude, can be covered with a relatively small number of intervals. This data set is usually tabulated and transformed into a graphical representation. 

In order to develop integral equations for the correlation functions, we consider the system composed of N polydisperse spheres. The average density of particles with diameter <7, is given by... 

In order to cadculate a particle size distribution directly from the output chromatogram for a polydisperse system, the integral, dispersion equation for the chromatogram signal, F(V), as a function of elution volume, V, needs to be evaluated (27) ... 

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