Rvi V2 vi V2 o snvinv2

where the size of the nuclei, L0, is zero. Again ordinary differential equations (j = 0-3) have to be solved to attain the lumped properties of the CSD.

To improve the CSD, a controlled cooling or evaporation trajectory can be imposed.

The Crystal Volume-Based Population Balance Equation

When a crystallizing system depends purely on nu-cleation and growth processes, it is favourable to use a PBE with length as the crystal size co-ordinate. For kinetic processes where the volume of particles are combined or split up, like in agglomeration and disruption, a PBE with the particle volume as crystal size coordinate is preferred. This leads to:

The rate constant, ft, commonly called the agglomeration kernel, depends on the particle sizes v1 and v2, the supersaturation 0 and the turbulence level, represented by the power input s. The birth and death terms associated with the agglomeration of two particles, resulting in the birth of a new one and the death of the original two, are:

1 Cv

The factor 2 is needed to avoid double-counting, since the integral takes each interaction twice. The dependency of P on 0 and s has been omitted here for notation simplicity.

There is also disruption of earlier agglomerated particles with a corresponding disruption rate. This disruption process of earlier agglomerated particles

can be described in the PBE by an additional death term for the disrupted particles, and an additional birth term for the newly formed particles:

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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