Noyes-Whitney equation

The Noyes-Whitney equation is the recipe that tells you how fast a solid dissolves. Think of it as a checklist of everything that speeds dissolving up: more exposed surface, a bigger gap between what is dissolved and what could be dissolved, faster stirring — each pushes the rate higher.

In its common form the rate of dissolution dC/dt = (D·A / h)·(Cs − C). Here D is the diffusion coefficient of the drug, A is the surface area of solid in contact with liquid, h is the thickness of the stagnant diffusion layer at the surface, Cs is the saturation solubility, and C is the concentration already in the bulk solution. The term (Cs − C) is the concentration gradient that drives diffusion.

The equation makes the levers obvious. Grinding the drug finer increases A; raising solubility (salt, cosolvent, amorphous form) increases Cs; stirring or reducing viscosity thins h; and keeping C low — the sink condition — keeps the driving force large. Its main idealisation is treating dissolution as purely diffusion-controlled through a uniform layer, which is a good approximation for many but not all drugs.