Simulation and experimental study of spray pyrolysis of polydispersed droplets

Abstract

The size distribution and morphology of particles (dense or hollow) produced from polydispersed droplets in spray pyrolysis were studied both experimentally and theoretically. Zirconia, generated from a zirconyl hydroxychloride precursor, was selected as a model material. The simulation method that was previously developed by our group [J. Mater. Res., 15, 733 (2000)], in which droplets were assumed to be uniform, was improved to evaluate the effect of polydispersity in droplets on the size and morphology of the resulting particles. Simultaneous equations for heat and mass transfer of solvent evaporation and solute mass transfer inside droplets were solved numerically for a number of discrete classes of droplet size distribution. The role of the decomposition reaction was also included after the evaporation stage of polydispersed droplets in an attempt to explain the densification of particles. In hollow particle generation, this simulation was used to evaluate the thickness of a particle shell. The experimental results were in good agreement with the simulation data, suggesting that the model provides a more realistic prediction.

Appendix

The activation energy for decomposition reaction can be calculated from the Arrhenius kinetic reaction equation:

((A1))

where θ is the heating rate, T_R is the decomposition temperature, E_a is the activation energy for the decomposition reaction, A is the pre-exponential factor, and R is the gas constant. By using the least-squares statistical method, the activation energy can be obtained. By plotting −ln(θ/T²_R) versus 1/T_R for six selected heating rates it is possible to ascertain the values of E_a and A from the gradient and intercept, respectively, as shown in Fig. A1. The values from this correlation were 159.77 kJ mol⁻¹ and 9.67 × 10¹² min⁻¹, respectively.

FIG. A1

Droplet shrinkage along the furnace length due to evaporation: (a) 150 °C, (b) 300 °C, (c) 500 °C, and (d) 700 °C, C_o = 2 mol l⁻¹ and Q = 2 l min⁻¹.

Three theoretical kinetic equations describing decomposition/crystallization mechanisms were examined. The models correspond to the ordinary kinetics of chemical reactions reflecting different assumptions for nucleation and crystal growth.20, 21 Normal grain growth, Johnson–Mehl–Avrami, and three-dimensional diffusion models tend to be influenced by the reaction order, nucleation controlling reaction, and a diffusion controlling reaction, respectively.

$$\eqalign{ & f\left( {{x_R}} \right) = {\left( {1 - {x_{\text{R}}}} \right)^{n + 1}}\;\;\;{\text{Normal}}\;{\text{grain}}\;{\text{growth}}\left( {{\text{NGG}}} \right) \cr & f\left( {{x_R}} \right) = n\left( {1 - {x_{\text{R}}}} \right){\left[ { - {\text<Subscript></Subscript>}\left( {1 - {x_{\text{R}}}} \right)} \right]^{\left( {n - 1} \right)/n}} \cr & \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\text{Johnson - Mehl - Avrani}}\left( {{\text{JMA}}} \right) \cr & f\left( {{x_R}} \right) = {\left[ {{{\left( {1 - {x_{\text{R}}}} \right)}^{ - 1/3}} - 1} \right]^{ - 1}} \cr & \;\;\;\;\;\;\;\;\;\;\;\;\;\;{\text{Three - dimensional}}\;{\text{diffusion}}\left( {{\text{3D - D}}} \right) \cr} $$

((A2))

The reaction order (n) determined by Kissinger,22 was solved by the nonlinear equation in Eq. (A3) using Microsoft Excel. The value of the reaction order was calculated to be 1.25, not influenced significantly by the decomposition temperature of the selected heating rate.

((A3))

S, α, and β are the analytical parameters derived by Kissinger, which are only a function of the reaction order. ln[k(T)f(x_R)] versus −ln(1 − x_R) for each model was compared with experimental data taken from TG-DTA. Of the three models, the normal grain growth (NGG) showed the best fit, indicating that the NGG reaction mechanism adequately describes the formation of zirconia from the zirconyl hydroxychloride precursor, as shown in Fig. A2.

FIG. A2

Droplet shrinkage along the furnace length due to evaporation: (a) 150 °C, (b) 300 °C, (c) 500 °C, and (d) 700 °C, C_o = 2 mol l⁻¹ and Q = 2 l min⁻¹.