Diffusion: the slow drift down a gradient
Drop dye into still water and, with no stirring at all, the colour spreads. That is diffusion: the net movement of molecules from where they are crowded to where they are sparse, driven only by random thermal motion. Nothing pushes them; statistics alone fills the empty space. In pharmacy this quiet process governs how a drug leaves a patch, crosses a membrane, or seeps out of a gel.
Fick's first law makes this precise: the rate of diffusion through a barrier is proportional to the concentration gradient across it — the difference in concentration divided by the thickness — times a diffusion coefficient and the area available. Steeper gradient, larger area, or thinner barrier all speed flux up; a thicker or more crowded barrier slows it down.
Dissolution: diffusion at the surface of a solid
When a tablet meets fluid, drug at the surface dissolves instantly into a thin, saturated film clinging to the particle. From there it must diffuse out into the bulk liquid — and that diffusion step, not the dissolving itself, usually sets the pace. Dissolution is the whole process of a solid going into solution; the dissolution rate is how fast it happens, and it is often the slowest step before a drug can be absorbed.
The Noyes–Whitney equation is Fick's law dressed for a dissolving particle. The dissolution rate is proportional to surface area, to the diffusion coefficient, and to the gap between the saturation solubility (Cs) and the concentration already in the bulk (C), divided by the film thickness. Grind the powder finer and surface area climbs; the rate climbs with it. That single insight powers the entire field of micronization and nanocrystals.
Noyes-Whitney equation
dC/dt = (D * A / h) * (Cs - C)
D = diffusion coefficient
A = surface area of the dissolving solid
h = thickness of the diffusion (boundary) layer
Cs = saturation solubility of the drug
C = concentration already in the bulk medium
Effect of milling (sink condition, so C ~ 0):
Suppose milling raises surface area A by 5x.
Then dC/dt also rises ~5x, all else equal.
-> A poorly soluble drug can dissolve far faster
simply by reducing particle size.Keeping the gradient alive: sink conditions
Notice that dissolution slows as C climbs toward Cs — the gradient flattens and flux dies. In the body, blood whisks dissolved drug away so C stays near zero and dissolution keeps powering along. We copy this in the lab with a sink condition: enough medium that the dissolved drug never exceeds about one-tenth of its solubility, so the driving force stays strong and the test reflects the formulation, not the volume of the beaker.
To compare two raw drugs fairly — without particle size muddying the result — we measure the intrinsic dissolution rate: dissolution from a compressed disc of fixed surface area. It isolates the molecule's own tendency to dissolve, a clean number that preformulation scientists prize.