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Simulations at T/Tc = 1/4 agree with classical nucleation theory if the droplets are assumed as small cubes instead of spheres.

In this paper, the growth of a gas bubble in a supersaturated liquid is discussed for a constant and variable cases of surface tension effect. The mathematical model is solved analytically by using the method of Plesset and Zwick¹⁸ after modified it. The growth process is affected by: diffusion coefficient D, Jacob number J_a, surface tension σ, adjustment factor b and void fraction ϕ₀. The famous formula of Plesset and Zwick is produced as a special case of the results at some values of the adjustment factors. Moreover, for some values of the adjustment factors, good approximation is obtained when a comparison between our results and the result that produced by Hashemi et al., ⁹ who solved the problem with the method of combining variables.

Crystallization of biological macromolecules is governed by a variety of variables. Since protein crystals are stabilized by rather weak interactions, they are extremely sensitive to subtle variations in solution conditions; consequently, protein crystal growth presents particularly challenging problems. In macromolecular crystallography, the success of a project ultimately resides in the characteristics of the crystals utilized for the study. The growth of suitable protein crystals is therefore the most crucial step in the structure determination of a protein. Physico-chemical parameters such as protein and precipitant concentration, pH, solubility, temperature, ionic strength, pressure and viscosity can play a crucial role in determining the optimal conditions for perfect crystal formation. Biochemical properties such as particle purity and conformational homogeneity and the presence anhd nature of impurities and additives can also influence crystallization. These parameters affect macromolecular solubility and are the major factors behind the complexity of crystallization and therefore make predicting suitable conditions laborious. A phase diagram is a useful tool to design experiments for crystal growth. Applying a phase diagram can provide some guidelines on the various possible conditions that can influence crystallization processes. This can be constructed by setting up many crystallization trials, varying at least two conditions and plotting their outcomes, after a certain period of time, on a two- or many-dimensional parameter grids.

This chapter presents an introduction to crystallization of organic fine chemicals and pharmaceutical compounds, written for newcomers to the field. The coverage includes the fundamental concepts of solubility, supersaturation, nucleation, growth, and polymorphism. We will also discuss the control of crystal size distribution, crystal shape and purity, and specifically address cooling crystallization and reaction crystallization processes.