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

## TL;DR

This paper studies how drying affects the structure of LDH nanoparticles and provides a mathematical model to optimize the drying process.

## Contribution

The study introduces a two-parameter diffusion model that includes the mass Biot number for better prediction of LDH drying behavior.

## Key findings

- Effective diffusivity ranged from 4.00 × 10–7 to 3.40 × 10–10 m²/s depending on drying conditions.
- Activation energy values suggest capillary surface diffusion is the rate-limiting step.
- The model can guide optimization of various drying systems for LDH materials.

## Abstract

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 (D
eff) and activation energy (E
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
(Bi
m), provided a superior fit to the
experimental data compared with the one-parameter model, corroborating
the strong influence of external drying conditions. D
eff values ranged from a maximum of 4.00 × 10–7 m2/s (at 105 °C with convection, Bi
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.