Modelling mass diffusion for a multi-layer sphere immersed in a semi-infinite medium: application to drug delivery

Area of Science:

• Chemical Engineering
• Physical Chemistry
• Pharmacokinetics

Background:

• Mass diffusion in composite spherical systems is crucial for understanding drug delivery.
• Existing models often require artificial truncation, limiting accuracy.
• Spherical microcapsules are widely used for controlled drug release.

Purpose of the Study:

• To develop a general mechanistic model for mass diffusion in multi-layer composite spheres.
• To derive an analytical, closed-form solution for concentration profiles and drug mass.
• To apply the model to drug kinetics of desorbing and absorbing spherical microcapsules.

Main Methods:

• Formulation of a multi-layer diffusion model with interlayer boundary conditions.
• Derivation of an analytical solution using inverse Laplace transforms.
• Numerical evaluation of concentration profiles and drug mass curves.

Main Results:

• An analytical solution was obtained for mass diffusion in composite spheres without artificial truncation.
• Concentration profiles and drug mass curves were presented for spherical microcapsules.
• The influence of the surface mass transfer coefficient on diffusion was analyzed.

Conclusions:

• The developed model provides an accurate and generalizable method for analyzing mass diffusion in composite spheres.
• The analytical solution is valuable for understanding and optimizing drug kinetics in microcapsule systems.
• This work contributes to the field of drug delivery by offering a robust theoretical framework.