Numerical Simulation of Variable Water Diffusivity during Drying of Peeled and Unpeeled Tomato

Drying Process of HPMC-Based Hard Capsules: Visual Experiment and Mathematical Modeling

Using plant-based polysaccharide gels to produce hard capsules is a novel application of this technology in the medicinal field, which has garnered significant attention. However, the current manufacturing technology, particularly the drying process, limits its industrialization. The work herein employed an advanced measuring technique and a modified mathematical model to get more insight into the drying process of the capsule. Low field magnetic resonance imaging (LF-MRI) technique is adopted to reveal the distribution of moisture content in the capsule during drying. Furthermore, a modified mathematical model is developed by considering the dynamic variation of the effective moisture diffusivity (D_eff) according to Fick's second law, which enables accurate prediction of the moisture content of the capsule with a prediction accuracy of ±15%. The predicted D_eff ranges from 3 × 10^-10 to 7 × 10^-10 m²·s^-1, which has an irregular variation with a time extension. Moreover, as temperature increases or relative humidity decreases, there is an increased acceleration of moisture diffusion. The work provides a fundamental understanding of the drying process of the plant-based polysaccharide gel, which is crucial for enhancing the industrial preparation of the HPMC-based hard capsules.

Analysis of Finite Difference Discretization Schemes for Diffusion in Spheres with Variable Diffusivity

Two finite difference discretization schemes for approximating the spatial derivatives in the diffusion equation in spherical coordinates with variable diffusivity are presented and analyzed. The numerical solutions obtained by the discretization schemes are compared for five cases of the functional form for the variable diffusivity: (I) constant diffusivity, (II) temporally-dependent diffusivity, (III) spatially-dependent diffusivity, (IV) concentration-dependent diffusivity, and (V) implicitly-defined, temporally- and spatially-dependent diffusivity. Although the schemes have similar agreement to known analytical or semi-analytical solutions in the first four cases, in the fifth case for the variable diffusivity, one scheme produces a stable, physically reasonable solution, while the other diverges. We recommend the adoption of the more accurate and stable of these finite difference discretization schemes to numerically approximate the spatial derivatives of the diffusion equation in spherical coordinates for any functional form of variable diffusivity, especially cases where the diffusivity is a function of position.