The drug payload sits dissolved in the capsule core at high concentration and diffuses outward across the shell toward the low-concentration exterior. Fick's first law gives the flux across the shell as proportional to the concentration gradient and inversely proportional to shell thickness, which collapses to first-order release kinetics for a thin shell:
J = -D·(Ccore − Cext)/L
dQ/dt = k·(Q∞ − Q), k = D·swell/L²
D(T) = D₀·exp[−Ea/R·(1/T − 1/Tref)]
- Shell thickness (L) — the polymer or lipid wall the drug must cross; a thicker shell divides the release-rate constant k by L², slowing release sharply.
- Temperature — diffusion coefficient D follows an Arrhenius law, so warming the capsule (e.g. body vs. room temperature) speeds release exponentially.
- Environment (pH) — switching to acidic tumor/endosomal pH mimics a pH-responsive shell swelling or partially degrading, multiplying effective permeability and triggering a release burst — the "stimulus-responsive trigger" strategy used for tumor-targeted delivery.
- Drug loading (EE%) — encapsulation efficiency sets how much active ingredient is available to release; it does not change the rate, only the total ceiling.
Real-world relevance: this first-order shell-diffusion model is the basis for designing sustained-release and stimulus-triggered nanocapsules — from PLGA drug depots to pH-sensitive liposomal doxorubicin used in oncology.