Shrinking aggregate model

A new micromixing (shrinking aggregate)model has been proposed, which describes the first stages of mixing in stirred tanks. 

Modified shrinking core model that accounts for globule aggregation and emulsion break-up. 

Fig. 6 Formation of an aggregate and the dependence of its average hydrodynamic radius ((Rh ) on temperature. The polymer is PNIPAM-g-PEO-51, c= 1.0gI.. Top model describing the steps for the formation of an aggregate and its shrinking upon slow heating from a 20 °C to b 45 °C and to c 60 °C. (Adapted from Refs. [165,170])...

This approach gives a reasonable description of the density distribution in heavy atoms. In fact, it can be shown to be exact for atoms, molecules and solids in the limit as the atomic number Z - oo However, one should not be surprised that it has serious flaws. In the present context, it is noteworthy that molecular bonding is impossible, i.e. the lowest energy of an aggregate of atoms is always reached when the nuclei are infinitely far apart. Furthermore, the atoms do not show the shell structure familiar from the periodic table and, in fact, shrink with increasing Z (as Z The electron density is infinite at the nucleus, so that the description of the kinetic energy is seriously in error. Nevertheless, the approach continues to be of interest as a simple, well defined model, and its mathematical properties have been subject to considerable scrutiny. The focus on the charge density is also shared by the density functional formalism, as we discuss below. 

There are number of publications in the technical literature which utilize the spherical grain theory to model the sulfation reaction of CaO with SO2. In these models it is assumed that the solid reactant pellet is an aggregation of spherical grains and each grain is modelled by the shrinking core with a sharp reacting interface (Figure 3). In these models, R, can be expressed as... 

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