A Rate-Weighted Framework for Diffusion, Swelling, and Erosion in Monolithic Polymeric Devices: Geometry-Unified...

Mathematical descriptions of bioactive release invoke Fickian diffusion, Case II swelling, and surface erosion, yet each is usually treated in isolation. This work unifies the three within one analytical skeleton for homogeneously loaded monolithic devices of canonical geometry - slabs, cylinders, and spheres - excluding compressed tablets, osmotic systems, and reservoir devices, grounding their coefficients in polymer-solvent thermodynamics.

Eigenfunction series give the diffusion solutions and short-time √t asymptotics; moving-boundary kinematics give polynomial swelling and erosion laws. Coefficients are linked to Hansen-van Krevelen solubility parameters and the Flory-Huggins χ. The mechanisms are coupled as a multiplicative product form and an additive Dirichlet mixture whose weights are fixed a priori by each mechanism's characteristic rate - the leading Laplacian eigenvalue for diffusion, the front-traversal rate for the moving fronts - termed Thermodynamic Rate Decomposition (TRD). Validation comprises an exponent consistency check and fit-free tests against a propranolol-HPMC cylinder, an etofylline-PEO slab, and the published sphere case.

Power-law fitting returns Fickian exponents of 0.50, 0.46, and 0.45 for slab, cylinder, and sphere (consensus 0.50, 0.45, 0.43) and a slab Case II exponent of 1.00. With no parameter fitted to the release curve, predictions reproduce both measured profiles to within about 13% RMSE and assign the dominant mechanism correctly. Weights move by at most 0.03 under an independent moment-based definition.

Geometry enters through one integer index n  $\in$  {1, 2, 3}, giving compact, thermodynamically traceable equations that support a priori mechanism assignment and first-pass quantitative analysis within this device class.