  A lattice gas model is proposed for investigating the release of drug
molecules on devices with semi-permeable, porous membranes in two and three
dimensions. The kinetic of this model was obtained through the analytical
solution of the three-dimension diffusion equation for systems without membrane
and with Monte Carlo simulations. Pharmaceutical data from drug release is
usually adjusted to the Weibull function, $\exp [-(t/\tau)^b ]$, also known as
stretched exponential, and the dependence of adjusted parameters $b$ and $\tau$
is usually associated, in the pharmaceutical literature, with physical
mechanisms dominating the drug dynamics inside the capsule. The relation of
parameters $\tau$ and $b$ with porosity $\lambda$ are found to satisfy, a
simple linear relation for between $\tau$ and $\lambda^{-1}$, which can be
explained through simple physically based arguments, and a scaling relation
between $b$ and $\lambda$, with the scaling coefficient proportional to the
system dimension.
