Precipitation processes aggregation

Thus under ideal circumstances the modes of aggregation can be discriminated by such plots. Deviations below the expected slopes are usually attributed to collision inefficiency leading to imperfect aggregation. In a crystallization or precipitation process, of course, deviations may also occur due to growth and nucleation unless properly accounted for. 

The significance of this novel attempt lies in the inclusion of both the additional particle co-ordinate and in a mechanism of particle disruption by primary particle attrition in the population balance. This formulation permits prediction of secondary particle characteristics, e.g. specific surface area expressed as surface area per unit volume or mass of crystal solid (i.e. m /m or m /kg). It can also account for the formation of bimodal particle size distributions, as are observed in many precipitation processes, for which special forms of size-dependent aggregation kernels have been proposed previously. 

FA can interact with clay minerals and are known to form stable complexes with metal ions and hydrous oxides [59,61]. The operational technique for isolation of HA involves a pH-induced precipitation and it is likely that accessory minerals may be associated with the precipitation process. Complexes of HA and clay minerals are also formed, the increased ash content of HA suggesting that amorphous silica, iron hydroxides, and clay may aggregate with the HA fraction [58,60,61]. 

Order-disorder, or rod-to-coil , transitions in dilute solution have been reported for polydiacetylenes (2, 5-11), polysilylenes (12-15), and alkyl-substituted polythiophenes (16). The interpretation of the experimental observations has been the subject of considerable controversy with respect to whether the observations represent a single-polymer-molecule phenomenon or a many-chain aggregation or precipitation process (3-16). Our own experimental evidence (12, 13) and that of others (5-8, 10, 16) weigh heavily in favor of the single-chain interpretation. In our theoretical interpretation, we will assume that the order-disorder transitions observed in dilute pol-ysilylene solutions represent equilibrium, single-chain phenomena. 

This misconception is particularly common in crystallization. The hypothesis of a perfectly mixed system is, for crystallization and precipitation processes, labeled as mixed-suspension, mixed-product removal (MSMPR). With diis model the crystalUzer is modeled with a spatially homogeneous NDF, generally called the crystal-size distribution (CSD). However, the fact that the CSD is constant through the vessel does not mean that the rates of crystal nucleation, molecular growth, aggregation, and breakage are constant. 

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