Relative Damköhler numbers approximate the convection–diffusion–reaction model for diffusion-limited dissolution

Abstract

Diffusion-limited dissolution in reactive media was investigated with the convection-diffusion-reaction (CDR) model using monoprotic weak base and acid dissolution in unbuffered media in the rotating disk setup as an example. It was found that the typical film-based approaches are inaccurate in calculating surface pH and dissolution flux values. However, simple equations that accurately approximate the CDR model can be derived in the form of a relative Damköhler number (RDa) for a reversible reaction. As a result, general equations were developed for dissolution impacted by three different reversible reaction scheme examples. Those equations, actually, represent analytical solutions to the CDR equation for the asymptotic regime of infinitely high reversible reaction rates. The contrast between CDR-based and stagnant film-based models contradicts the commonly held notion of the thermodynamic driving force at the interface during diffusion-limited dissolution being independent of hydrodynamic and geometric factors.