NernstBrunner

The Nernst-Brunner equation is a foundational expression in dissolution kinetics that describes the rate at which a solid dissolves into a solvent. It links the dissolution rate to the surface area of the dissolving solid, the diffusion coefficient, and the driving force for dissolution, which is the difference between the solubility of the solute (Cs) and the bulk concentration (C). The equation is commonly written as dM/dt = k A (Cs − C), where M is the amount dissolved, A is the surface area, and k is a mass-transfer coefficient.

The mass-transfer coefficient k is often expressed as D/δ, with D the diffusion coefficient of the solute in the solvent and δ the thickness of the stagnant diffusion boundary layer around the particle. The model assumes steady-state diffusion through this boundary layer and that the surface remains in equilibrium with the solution, justifying the use of Cs. It is frequently applied to poorly or moderately soluble solids in dilute suspensions and is widely used in pharmaceutical dissolution testing because it reduces complex transport phenomena to a simple, parameterizable rate law.

Limitations of the Nernst-Brunner model include its assumption of a constant surface area, neglect of changes in particle size during dissolution, and the exclusion of erosion-controlled or surface-reaction kinetics. It also presumes constant D and δ, which may vary with temperature, agitation, and concentration. Nevertheless, the equation remains a central reference for understanding diffusion-controlled dissolution and is described in many pharmaceutical and chemical engineering texts.