Volume fraction, general dynamic

A linear relationship exists between the ESA or CVP amplitude and the volume fraction of the suspended particles. At relatively high-volume fractions, hydrodynamic and electric double-layer interactions lead to a non-linear dependence of these two effects on volume fraction. Generally, non-linear behavior can be expected when the electric double-layer thickness is comparable to the interparticle spacing. In most aqueous systems, where the electric double layer is thin relative to the particle radius, the electro-acoustic signal will remain linear with respect to volume fraction up to 10% by volume. At volume-fractions that are even higher, particle-particle interactions lead to a reduction in the dynamic mobility. 

In order to integrate the differential equations (2)-(5) the additional relation is need because number density of the dimmers is determined from number density of monomers in case of steady state only. In general case, the time dependence of the number densities of all clusters can be found as solving of master equation of cluster dynamics. Now we have interest to the short description and we are looking for the additional approximation relation. The fluence dependence of the volume fraction of CEC is estimated by saturation tank) form " that is roughly equivalent to a Johnson Mehl-type function ... 

Dukhin et al. [83-85] have performed the direct calculation of the CVI in the situation of concentrated systems. In fact, it must be mentioned here that one of the most promising potential applicabilities of these methods is their usefiilness with concentrated systems (high volume fractions of solids, 4>) because the effect to be measured is also in this case a collective one. The first generalizations of the dynamic mobility theory to concentrated suspensions made use of the Levine and Neale cell model [86,87] to account for particle-particle interactions. An alternative method estimated the first-order volume fraction corrections to the mobility by detailed consideration of pair interactions between particles at all possible different orientations [88-90]. A comparison between these approaches and calculations based on the cell model of Zharkikh and Shilov [91] has been carried out in Refs. [92,93],... 

The flow properties of a colloidal system are very much dependent on its microstructure, as determined by the molecular arrangement and interaction of its components. ME systems show flow typical of a Newtonian liquids, for which the shear stress is directly proportional to the shear rate. Since viscosity measurements are dynamic experiments, they will give information on dynamic properties of the ME. These will depend on the miCTOStructure, type of aggregates, or interactions within the ME, which in turn are determined by the concentration of the various components and the temperature. The dispersion of one component in another, e.g., water in oil, will generally increase the bulk viscosity in comparison to the individual components (oil and water) [58]. For at true colloidal dispersion, viscosity will increase with increasing volume fraction of dispersed phase according to the formula generated by Einstein ... 

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