This paper presents an adaptive finite-volume numerical scheme for simulating diffusion in spherical condensates with semipermeable interfaces, focusing on interfacial permeability, reflectivity, and preferential internal mixing. The method uses non-uniform mesh refinement near the interface for accuracy and efficiency, demonstrating first-order accuracy and validating against analytical solutions.
Key findings
Adaptive finite-volume scheme accurately captures concentration gradients in spherical condensates.
First-order accuracy achieved with mass conservation errors below 10^-6.
Adaptive grid reduces numerical errors by 30-40% compared to uniform grids.
Application to FRAP experiments reveals control of recovery kinetics by reflective bias and interfacial resistance.
Limitations & open questions
Analytical solutions available only for simplified geometries and special cases.
Further exploration needed for more complex interfacial properties.