INAUGURAL–DISSERTATION zur Erlangung der Doktorwürde der ...
INAUGURAL–DISSERTATION zur Erlangung der Doktorwürde der ...
INAUGURAL–DISSERTATION zur Erlangung der Doktorwürde der ...
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34 2. Mathematical Modeling<br />
Fig. 2.5: Schematic diagram of stages in single droplet evaporation and drying.<br />
model, achieving fairly good agreement. The droplet generators used in these studies<br />
produce a chain of closely spaced droplets, which leads to droplet–droplet interactions<br />
in processes that are limited by gas phase transport processes.<br />
The aim of the present work is to develop a mathematical model, which can be<br />
applied to predict the evaporation and drying characteristics of droplets of the polymer<br />
PVP dissolved in water and mannitol dissolved in water solution. Prerequisites<br />
of the method are, (1) accounting for the solid layer resistance in mass evaporation<br />
rate and energy calculation, and (2) treatment of the liquid mixture as non-ideal by<br />
computing the activity coefficient of the evaporating component.<br />
The problem un<strong>der</strong> consi<strong>der</strong>ation is the evaporation and drying of an isolated single<br />
spherical droplet consisting of a binary mixture of a liquid and a dissolved solid material<br />
with low or zero vapor pressure.<br />
During the evaporation and drying of the bi-component droplet, the droplet un<strong>der</strong>goes<br />
four stages as explained by Nesic and Vodnik [151], which are depicted in Fig. 2.5.<br />
In the initial stage, the droplet temperature quickly rises to an equilibrium temperature,<br />
which is most often near to the wet bulb temperature for surrounding gas and<br />
humidity, with some solvent evaporation.<br />
In the second stage, the droplet starts to shrink as solvent evaporates causing the<br />
solute mass fraction to increase at the droplet surface; this leads to a slight raise in<br />
the droplet temperature (see Fig. 2.5). The increase in solute mass fraction at the<br />
droplet surface hin<strong>der</strong>s further evaporation as the vapor pressure of the solvent at<br />
the surface drops. The third stage of drying starts when the solute mass fraction at<br />
the surface raises to a threshold value, which most often is equal to the saturation<br />
solubility of the solute in the solvent, whereupon the crust formation starts for salts,<br />
sugar and colloidal material. In the case of polymers, molecular entanglement and