Higuchi model

The Higuchi model captures a simple but counter-intuitive fact about matrix tablets: the drug does not come out at a steady pace — it comes out in proportion to the square root of time. Early on release is brisk, then it slows, because each new molecule must travel a longer route out as the surface region is emptied.

Takeru Higuchi derived this in 1961 for drug diffusing out of a planar matrix in which the drug is dispersed at a concentration well above its solubility. The result is the famous form: cumulative amount released equals a constant times the square root of time. That constant bundles together the drug's diffusion coefficient, its solubility in the matrix, the loading, and the matrix porosity and tortuosity.

It is a workhorse for analysing release data: plot cumulative release against the square root of time, and a straight line signals diffusion-controlled, Higuchi-type behaviour. But the derivation rests on strict assumptions — perfect sink conditions, no swelling or erosion, constant diffusivity, drug loading far above solubility — so real swelling or eroding systems often deviate and need other models such as Korsmeyer-Peppas.