Analysis of an integro‐differential model for bulk continuous crystallization with account of impurity feeding, dissolution/growth of nuclei and removal of product crystals

Abstract

In this study, the theory of continuous crystallization from a supersaturated solution is developed, taking the concentration‐dependent fines dissolution, product removal, and feed supply rates into account. These rates make it possible to control the operation mode of the crystallizer and obtain the required supersaturation of the solution, the desired crystal‐size distribution in the supersaturated liquid, and the necessary crystal removal rate of the product. The steady‐ and unsteady‐state solutions of model equations are found analytically. It is shown that the non‐stationary crystal‐size distributions approach the stationary distribution with increasing time. The theory developed is the basis for investigating the linear and nonlinear stability of the crystallizer with allowance for the concentration‐dependent fines dissolution, product removal and feed supply rates.

The Boundary Integral Equation for Kinetically Limited Dendrite Growth

“…Here, In the present work, we consider the special case of negligible heat transport to govern the interface motion. This situation is well known in atomistic simulations where the interface motion in melting and crystallization is dictated by the atomistic kinetics at the interface, and the computational domain has (almost) uniform temperature [38][39][40][41]. In this case, the r.h.s.…”

“…the explanations of the sharp transition from thermally controlled to kinetically limited regimes of growth [34][35][36][37]; -the interpretation of the data of molecular dynamics where the interface is governed by interfacial undercooling, i.e., by "kinetic undercooling" [38][39][40][41].…”

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.…”