Mathematical Modeling of LDH Nanoparticle Drying: Evaluating Effective Diffusivity and the Role of the Mass Biot Number

Layered Double Hydroxides (LDH) are an important class of inorganic nanomaterials characterized by variable composition, high porosity, significant surface area, and notable ion-exchange capacity. Although coprecipitation is the most widely used synthesis method, the subsequent drying step is often critically overlooked, as it directly affects particle agglomeration and degradation of the porous colloidal structure. This study evaluated the influence of the drying process on MgAl-CO₃/LDH synthesis by determining the effective diffusivity (<i>D</i> _eff) and activation energy (<i>E</i> _a). LDHs were synthesized via coprecipitation (Mg/Al ratio = 2:1). Drying kinetics were investigated at 75, 90, and 105 °C, both without and with forced-air convection (1.0 ± 0.1 m/s). Diffusivity coefficients were determined using Fick's second law. A two-parameter diffusion model, including the mass Biot number (<i>Bi</i> _m), provided a superior fit to the experimental data compared with the one-parameter model, corroborating the strong influence of external drying conditions. <i>D</i> _eff values ranged from a maximum of 4.00 × 10^-7 m²/s (at 105 °C with convection, <i>Bi</i> _m = 0.01) to a minimum of 3.40 × 10^-10 m²/s (at 75 °C without convection). The average activation energy ranged from 12.55 to 26.80 kJ/mol, suggesting that the superficial diffusion of liquid molecules along capillary surfaces is the rate-limiting mass-transfer mechanism. These results establish a quantitative basis for optimizing LDH drying parameters. They can serve as a starting point for other drying systems, such as fluidized-bed, rotary, spray, and freeze-dryers.