GL kg[ a

while for combined volume diffusion and spiral growth surface integration the growth rate becomes:

where Wi(L) = rk/Lfragment and g = 1 for volume diffusion-dominated growth, and 2 for spiral growth. The value of rk is, as mentioned before, a fitting parameter that has to be determined experimentally.

Dissolution of Crystals

Only at very low undersaturations or for extremely insoluble substances such as BaSO4, the dissolution process proceeds by the disappearance of subsequent layers, and a smooth surface is maintained. Normally surface disintegration occurs at the crystal edges and at etch pits, and the surface becomes easily roughened. So the dissolution rate is either given by an expression where only volume diffusion is rate controlling:

With eqn [57] either _Rlin or G can be calculated.

The temperature dependence of kr and kd is given by an Arrhenius-type equation, where the corresponding Arrhenius activation energies are typically of the order of 40-60 kJ mol L_1 for surface integration and 10-20 kJmol-1 for the volume diffusion step.

For easily soluble compounds generally linear growth rates of10~7ms~1 are permissible in order to or by a combined volume diffusion and surface disintegration rate, as given by eqn [65] and, more rarely, by eqn [66], but now with a negative value for the change in mass, and a decreasing A.

Agglomeration

The agglomeration process consists of the transportation and collision of particles, and the attachment of the particles, followed by either disruption or cemen-

Table 2 Predominant agglomeration models for the possible transport mechanism as a function of particle size L and the Kolmogorov length scale ^

Transport mechanism

Particle size L

Collision mechanism

Brownian motion

L< 0.5 |im

Perikinetic

Laminar flow

L < 6 rç

Orthokinetic

Laminar flow

L > 25 rç

Inertial

Turbulent flow

L < 6 rç

Orthokinetic

Turbulent flow

L > 25 rç

Inertial

Relative particle settling

L < 6 rç

Inertial

tation of the attached particles. The cemented particles are agglomerates. If the supersaturation is zero, no cementation occurs and all loosely agglomerated particles fall apart again. Since in practice only the combined result of disruption and cementing can be observed, an effective agglomeration rate is generally defined.

The main transport mechanisms by which particles can collide are Brownian motion, laminar or turbulent flow or relative particle setting. Depending on the particle size and the Kolmogorov length scale of the different flow regimes, different collision mechanisms can be distinguished (Table 2).

In case of orthokinetic collisions the effective agglomeration rate constant or agglomeration kernel can be described as a product of the collision rate constant and an efficiency factor:

ftcoll increases linearly with the shear rate y, that equals ^s/v in a stirred vessel, whereas the efficiency factor ^ decreases strongly with y in this high shear region, and thus ft also decreases after having reached a maximal value at a rather low shear rate value. Although ft should be size-dependent, experimental agglomeration data can often be fitted with a size-independent kernel. Hounslow and co-workers recently introduced a dependence of ftcoll on the mean particle size. The efficiency factor includes the supersaturation dependence that is needed for the cementation of the particles. The supersaturation-dependent cementation explains why, for large cry-stallizers with a sufficiently large circulation time between two subsequent collisions with the impeller blades, abundant agglomeration may occur, while hardly any agglomeration is noticed for small scale crystallizers.

It must also be kept in mind that agglomeration is a kinetic process that depends on collisions, and thus on the local turbulence or power input s. Averaging the power input s for the calculation of ft might therefore lead to a wrong estimation of the degree of agglomeration.

Solar Panel Basics

Solar Panel Basics

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.

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