Identification of the compensation effect in the characteristic sintering time model for population balances

•A new characteristic sintering time model is proposed by inverse problem method.•The kinetic compensation effect in the characteristic sintering time is found.•Two dynamic parameters of characteristic sintering time show a linear relationship.•This linear relationship correlates differing sintering model reported before.

The sintering of agglomerates under high temperature determines the diameter and morphology of particles. Accurate sintering model is essential to the process simulation for the particle dynamics. A method of combining population balance modeling and inverse problem methodology was applied in sintering simulation process to investigate relationship between effective kinetic parameters in the characteristic sintering time model, i.e., two dynamic parameters (the pre-exponential factor A and the apparent activation energy E). The polydisperse primary particle (PP) model was introduced to consider the inhomogeneous structure in agglomerates. Two inverse problem methodologies, tabulation method and response surface method, were employed by fitting simulation results to experimental measurements. A contour map about the difference between simulation results and experimental measurements as a function of various parameter sets was obtained. Optimal values were obtained when the difference is small. A linear relationship between the two uncertain kinetic parameters was identified, which is similar to the kinetic compensation effect in the Arrhenius equation for reaction rate. The linear relationship holds true for the sintering of both TiO2 and SiO2 agglomerates at least, which are dominated by the surface diffusion mechanism and the viscous flow transport mechanism, individually.

Graphical abstractA new characteristic sintering time model by identifying two uncertain kinetic parameters (the pre-exponential factor A and the apparent activation energy E) for TiO2 and SiO2 was proposed. The kinetic compensation effect in the characteristic sintering time which is in the Arrhenius form was found. It describes a linear relationship between ln(A) and E. This linear relationship correlated differing sintering model parameters reported before.Download high-res image (133KB)Download full-size image