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💊 Pill Dissolution Kinetics: Noyes-Whitney Lab (2D)

A 2D companion to the 3D glass-of-water scene, built around the real dissolution equations instead of a fixed animation cycle: the Noyes-Whitney equation drives the dissolution rate, the tablet shrinks by the Hixson-Crowell cube-root law, and solubility, stirring, medium volume and temperature all feed live into the numbers on screen.

Medicine & Biophysics2DModerate60 FPS⇄ 3D version

This 2D companion trades the 3D version's fixed fall/settle/dissolve animation timeline for the actual pharmaceutics math behind tablet dissolution. Dissolution rate follows the Noyes-Whitney equation dM/dt = −(D·A/h)(Cₛ − C): the diffusion coefficient D scales with temperature through the Arrhenius equation, the boundary-layer thickness h thins as stirring speeds up, and the tablet's surface area A shrinks with its radius following the Hixson-Crowell cube-root law as mass is lost. A live readout panel tracks elapsed time, remaining mass, instantaneous rate, bulk concentration, percent saturation and the time to 50% dissolved (t₅₀), while a chart traces the dissolved fraction over time so you can see how raising the stirring rate or temperature — or lowering the solubility or medium volume — reshapes the curve.

⚙ Under the hood

2D dissolution-kinetics lab driven by the Noyes-Whitney equation and Hixson-Crowell cube-root shrinkage, with an Arrhenius temperature dependence for the diffusion coefficient and a stirring-dependent boundary layer, plus live mass/rate/concentration/t50 readouts and a dissolved-fraction chart.

dissolution kineticsnoyes-whitney equationhixson-crowell lawpharmaceuticsdiffusionarrhenius equation

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install

Why does the tablet shrink instead of dissolving all at once?

Because dissolution is a surface phenomenon: mass leaves through the tablet's outer area, so as the radius drops, available surface area drops with it (A ∝ r²), which is why the rate slows over the tablet's life even before the medium approaches saturation.

Why does raising the stirring rate speed up dissolution?

Agitation thins the unstirred diffusion boundary layer (h) that clings to the tablet's surface. A thinner layer means a steeper concentration gradient across it for the same bulk concentration, which increases the mass-transfer rate D·A/h even though the drug's own diffusion coefficient hasn't changed.

What happens if the solubility Cₛ is too low for the tablet size and volume?

The bulk concentration C climbs toward Cₛ and the driving force (Cₛ − C) shrinks toward zero, so the dissolution rate falls even though solid tablet remains — the saturation readout and the flattening curve show this "solubility-limited" regime directly.