Size change for crystalline and amorphous particles

The process of growth of crystalline particles involves several steps, such as diffusion of solute molecules from the bulk of the solution to the crystal surface, adsorption on the crystal surface, diffusion over the surface, attachment to a step, diffusion along a step, and integration into a crystal kink site. The rates of these different processes depend on the type of material and on the operating conditions. The final overall molar flux of solute molecules, which has previously been indicated with /(U, , U, ), will of course be 

An alternative (very popular) approach is based on the very simple idea of calculating the growth rate of particles with the following empirical expression Gp = kg S - 1), where g is derived from experiments, as well as kg, which is in turn very often described with an Arrhenius-type law  

These empirical laws have limited validity and should not be used outside the range of supersaturation values from which they were derived. 

It is important to remind the reader that U is the velocity of the fluid phase seen by the particle, U - U is the slip velocity, dp is the particle diameter, and Vf is the kinematic viscosity of the fluid phase. Note that Eq. (5.33) depends on the particle velocity U and is valid in the zero-Stokes-number limit where U = U so that particles follow the fluid. The correlation in Eq. (5.31) is valid only for RCp 1 and Sc 200. For larger particle Reynolds numbers the following correlations can be used Sh = 2 -i- 0.724Rep Sc, which is valid for 100 RCp 2000, and Sh = 2 -i- 0.425RCp Sc, which is valid for 2000 RCp 10. Among the other correlations available, it is important to cite the one proposed by Ranz Marshall (1952) for macroparticles Sh = 2.0 -i- O.bReJ Sc. These expressions assume that the fluid velocity U is known. For micron-sized (or smaller) particles moving in turbulent fluids for which only the ensemble-mean fluid velocity (Uf) is known, it is instead better to employ the mesoscale model derived by Armenante Kirwan (1989) Sh = 2.0 -i- 0.52(Re ) Sc, where Re = is the modi- 

The inverse process of dissolution, namely solute molecules leaving the lattice of the crystalline particles or the amorphous particles because the particle is in contact with an under-saturated solution (i.e. S 1), is typically controlled by diffusion. Therefore, the mesoscale model reported in Eq. (5.29) can be used to calculate the rate of the size change due to dissolution. 

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