Desupersaturation dynamics in solutions with applications to bovine and porcine insulin crystallization

Abstract

Evolution of crystal ensembles in supersaturated solutions is studied at the initial and intermediate stages of bulk crystallization. An integro-differential model includes fluctuations in crystal growth rates, initial crystal-size distribution and arbitrary nucleation and growth kinetics of crystals. Two methods based on variables separation and saddle-point technique for constructing a complete analytical solution to this model are considered. Exact parametric solutions based on these methods are derived. Desupersaturation dynamics is in good agreement with the experimental data for bovine and porcine insulin. The method based on variables separation has a strong physical limitation on exponentially decaying initial distribution and leads to the distribution function increasing with time. The method based on saddle-point technique leads to a dome-shaped crystal-size distribution function decreasing with time and has no strong physical limitations. The latter circumstance makes this method more reasonable for describing the kinetics of bulk crystallization in solutions and melts.

The Boundary Integral Equation for Kinetically Limited Dendrite Growth

“…From a mathematical point of view, such processes are described by the hyperbolic equation of impurity diffusion changing the concentration part of the BIE. In addition, the presence of a constant translational velocity V tr (the growth velocity of the dendritic tip in any reference frame moving with the steady-state velocity V ss with respect to the laboratory reference frame) should be taken into account when considering the evolution of various patterns and solid/liquid interfaces [37,[47][48][49][50][51][52][53][54]. moves along the z axis and is characterized by the function z intrerface = ζ(x, t), where t is the process time.…”

The Solid–Liquid Phase Interface Dynamics in an Undercooled Melt with a Solid Wall

“…The BIE describing the morphology of solid phase protrusions in the two-phase region can also be used to determine the solid phase fraction in this region and, consequently, how the heat and mass transfer coefficient depends on the solid phase fraction. Therefore, it is reasonable to combine the present approach with the two-phase region theory [44][45][46][47][48][49][50] for more accurate modeling of the directional solidification process. The influence of these effects is important for studying the dynamics of a curved crystallization front in the presence of a solid wall.…”