A Simplistic Preliminary Assessment of Ginstling-Brounstein Model for Solid Spherical Particles in the Context of a Diffusion-Controlled Synthesis

Abstract

Wet precipitation (WP) is a diffusion-controlled synthesis method, which is often used for synthesizing such compounds as hydroxyapatite (HAp). Since the process is limited by diffusion, the choice of a diffusion model becomes a critical aspect. In this simplistic assessment for a preliminary evaluation of the diffusion model applicability, the Ginstling-Brounstein (GB) equation is chosen and analyzed for the case of spherical particles. The nominal kinetic constant K is a parameter in GB model which describes diffusion and is related to the effective molecular diffusivity. When the value of K is known, it becomes possible to predict the required time to achieve desired conversion and design the synthesis accordingly. The GB model is assessed mathematically using simulations, a parametric study and Yates analysis (2n factorial design). Parameters chosen for a preliminary study are in the range of characteristic values for a laboratory-scale WP synthesis of HAp and are thus representative for the application of the model to practice. It should be noted that the analysis is simplistic and is meant to provide only preliminary information for future research, requiring experimental validation.