the solute to fix onto the crystal; Retention time, as an index of the probability of a molecule of solute to come into contact with an existing crystal; Flow pattern, again as an index of the probability of a molecule of solute to come into contact with an existing crystal (higher in laminar flow, lower in turbulent flow, but the reverse applies to the probability of contact). The first value is a consequence of the physical characteristics of the solution, while the others define a difference between a well- and poorly designed crystallizer. Size distribution The appearance and size range of a crystalline product is extremely important in crystallization. If further processing of the crystals is desired, large crystals with uniform size are important for washing, filtering, transportation, and storage, because large crystals are easier to filter out of a solution than small crystals. Also, larger crystals have a smaller surface area to volume ratio, leading to a higher purity. This higher purity is due to less retention of mother liquor which contains impurities, and a smaller loss of yield when the crystals are washed to remove the mother liquor. In special cases, for example during drug manufacturing in the pharmaceutical industry, small crystal sizes are often desired to improve drug dissolution rate and bio-availability. The theoretical crystal size distribution can be estimated as a function of operating conditions with a fairly complicated mathematical process called population balance theory (using population balance equations). Main crystallization processes Some of the important factors influencing solubility are: Concentration Temperature Solvent mixture composition Polarity Ionic strength So one may identify two main families of crystallization processes: Cooling crystallization Evaporative crystallization This division is not really clear-cut, since hybrid systems exist, where cooling is performed through evaporation, thus obtaining at the same time a concentration of the solution. A crystallization process often referred to in chemical engineering is the fractional crystallization. This is not a different process, rather a special application of one (or both) of the above. Cooling crystallization Application Most chemical compounds, dissolved in most solvents, show the so-called direct solubility that is, the solubility threshold increases with temperature. So, whenever the conditions are favorable, crystal formation results from simply cooling the solution. Here cooling is a relative term: austenite crystals in a steel form well above 1000 °C. An example of this crystallization process is the production of Glauber's salt, a crystalline