# Dissolution rate in the NanoFASE Model

The importance of dissolution for specific nanoparticles depends upon their chemical composition. For example, metals and metal oxides such as $$Ag, ZnO, CuO$$ and $$Fe_{2}O_{3}$$ may all be considered soluble to some extent, but the intrinsic degree of solubility is highly variable across metals. Metallic ENPs such as $$Ag, Fe$$ and $$Cu$$ dissolve via an oxidation process (e.g. $$2Ag^{0}+0.5O_{2}+2H^{+}\rightarrow 2Ag^{+}+H_{2}O$$), while dissolution of metal oxide ENPs such as $$ZnO$$ and $$CuO$$ does not require prior oxidation (e.g. $$CuO+2H^{+}\rightarrow Cu^{2+}+H_{2}O$$).

The NanoFASE modelling approach was developed alongside the experimental method. Basic dissolution modelling approaches are frequently based on the Noyes–Whitney equation:

### $${d[M_{z+}]}{dt} = k_{diss}([M_{z+}]_{eq}-[M_{z+}]_{t})d[M_{z+}]dt=kdiss([M_{z+}]eq-[M_{z+}]t)$$

Where $$[M_{z+}]_{t}$$ and $$[M_{z}]_{eq}$$ are the dissolving metal ion concentrations at time $$t$$ and at equilibrium, respectively and $$k_{diss}$$ is a dissolution rate constant which encompasses the diffusion coefficient of the dissolved species, surface area and thickness of the boundary layer, and is usually expressed in $$ug$$  $$kg^{-1} s^{-1}$$ or $$ug$$ $$m^{-2} s^{-1}$$.

## Execution

A number of approaches for modelling nanoparticle dissolution have been adopted, such as empirical formulae that express the dissolution rates as a function of natural organic matter (NOM) concentration, pH, T, dissolved oxygen and other variables that are dependent on the aggregate number, initial concentration and diameter.

## Used in

 Majedi, S. M., Kelly, B. C. & Lee, H. K. Combined effects of water temperature and chemistry on the environmental fate and behavior of nanosized zinc oxide. Sci. Total Environ. 496 (2014) 585-593.