Polydisperse mixture

Several colloidal systems, that are of practical importance, contain spherically symmetric particles the size of which changes continuously. Polydisperse fluid mixtures can be described by a continuous probability density of one or more particle attributes, such as particle size. Thus, they may be viewed as containing an infinite number of components. It has been several decades since the introduction of polydispersity as a model for molecular mixtures [73], but only recently has it received widespread attention [74-82]. Initially, work was concentrated on nearly monodisperse mixtures and the polydispersity was accounted for by the construction of perturbation expansions with a pure, monodispersive, component as the reference fluid [77,80]. Subsequently, Kofke and Glandt [79] have obtained the equation of state using a theory based on the distinction of particular species in a polydispersive mixture, not by their intermolecular potentials but by a specific form of the distribution of their chemical potentials. Quite recently, Lado [81,82] has generalized the usual OZ equation to the case of a polydispersive mixture. Recently, the latter theory has been also extended to the case of polydisperse quenched-annealed mixtures [83,84]. As this approach has not been reviewed previously, we shall consider it in some detail. 

In another effort, by Nickolay Smirnov s group at the M. V. Lomonosov Moscow State University, Moscow, a model for theoretical investigation of turbulent mixing and combustion of polydispersed mixtures in confined volumes was developed (Chapter 14). The numerical model and the software created make it possible to determine the combustion and ignition characteristics of polydispersed mixtures. The model has been validated with experiments. 

The problems of polydispersed mixtures ignition and combustion modeling are very acute for the description of processes taking place in motor chambers and burners of different types as well as for making forecasts of accidental explosions. 

The results were obtained for the polydispersed mixtures possessing the following characteristic properties of particle size distribution function (Figs. 14.1-14.2) ... 

The second set of numerical simulations was performed for the polydispersed mixture characterized by the presence of larger particles ... 

The initial conditions for all the experiments were nearly the same but for the initial turbulence and initial density of the particulate phase. It was shown that for the larger RMS values the combustion zone was wider and the flame propagated faster. Thus the increase of the initial level of the flow turbulization promotes the flame propagation in polydispersed mixtures due to the increase of the turbulent transport processes. 

Physical and numerical models are created describing the d3mamics of turbulent combustion in heterogeneous mixtures of gas with polydispersed particles. The models take into account the thermal destruction of particles, chemistry in the gas phase, and heterogeneous oxidation on the surface influenced by both diffusive and kinetic factors. The models are validated against independent experiments and enable the determination of peculiarities of turbulent combustion of polydispersed mixtures. 

The preliminary results obtained show that the initiation limits for polydispersed mixtures and stability of flame propagation strongly depend on inhomogeneity of particles (droplets) concentration distribution typical for the majority of practical cases wherein the ignition and combustion of polydispersed mixtures take place. Thus to ensure stable ignition and combustion characteristics... 

In tile application of surfactants, physical and use properties, precisely specified, are of primary concern. Chemical homogeneity is of little significance in practice. In fact, surfactants are generally polydisperse mixtures, such as the natural fats as precursors of fatty acid-derived surfactant structures e.g., coconut oil contains glycerol esters of Cc-Qa fatly acids. Nonionic surfactants of die alcohol edioxylate type are polydisperse not only with respect to the hydrophobe but also in the number of edivlene oxide units attached. 

The dependence of the cmc on the length of the insoluble block and its poly-dispersity was calculated, and reasonable agreement with experimental results for the PS-PI/hexadecane (Price etal. 1987) and PS-poly(sodium acrylate)/water systems (Astafieva et al. 1993) were obtained.The cmc was found to decrease as the polydispersity increased, in agreement with the calculations of Linse discussed above.The fraction of dispersed chains and molecular weight distributions of the dispersed chain and the micelles were found to be influenced by the dependence of the cmc of each component in the polydisperse mixture on the insoluble block length (Gao and Eisenberg 1993). 

Though plants are the predominant source of most of this material, microbial inputs are important as well (Cheshire, 1977). Carbohydrate extracts from soils and sediments probably contain only a small fraction of the total carbohydrate concentration since much of the carbohydrate content appears to be polysaccharides bound to the humic components (Lowe, 1978), and probably to clay minerals as well. Its presence is recognized by the release of simpler sugars upon hydrolysis of the sample (Greenland and Oades, 1975 Lowe, 1978). Isolated polysaccharide fractions are generally polydisperse mixtures. 

The product of hydrolytic cocondensation is a polydisperse mixture of oligomethylsiloxanes of the following composition (%) ... 

The polyalumophenylsiloxane obtained is a polydisperse mixture of polymer homologues consisting of the abovementioned ladder macromolecules and branched macromolecules of the following common formula [C6H5Si(OH)2.xO0.5x(O)]3AI n... 

If particles of size dpi represent a weight fraction a of the entire polydisperse mixture, then the following set of difference equations can be set up ... 

Polymers exist as polydisperse mixtures with different molecular weights. The resulting physical pro( rties such as, e.g., a redox potential cannot be ascribed to a specific length of the extended r-chain [53]. This and the large size of the molecules create an element of uncertainty in the physical description. 

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