On the effusion time of drugs from the open pore of a spherical vesicle

• The effusion time was calculated for a spherical device.
• An analytical solution was derived for the fraction of drug released.
• The effusion time contained geometric characteristics of the device.

Solute permeation through a spherical liposomal vesicle was analyzed using Fick’s second law and a mixed Neumann–Dirichlet boundary condition. The first-principles approach was necessary to help calculate the effusion time of a medication through a pore located on the surface of the device. An infinite series of Bessel functions represented the concentration in the Laplace domain. This method yielded closed-form expressions for the characteristic time and the Laplace-transformed fraction of drug released, which was approximated by the first term of the series. The time constant was inversely proportional to the diffusion coefficient in the system and decreased as the pore size increased. It took 4 times the effusion time to unload nearly ninety-eight percent of the pharmaceutical ingredient.