Diffusion and finite kinetics Reaction in a Hele-Shaw cell

Making use of an original chemical reaction between two transparent reactants (fluorescin and potassium ferricyanide) producing a fluorescent product in water (fluorescein) which allows for the quantitative measurement of the product formation, we investigate the interplay between molecular diffusion and reaction kinetics in a variety of situations. When a drop of fluorescin is injected in a Hele-Shaw cell filled with potassium ferricyanide, we distinguish two limits depending on the value of the Damkhöler number Da = τ_Diff/τ_Reac, with τ_Diff and τ_Reac the characteristic times of diffusion, and reaction. In the diffusion limited regime(Da > 1), the total quantity of product increases as √t with a maximum concentration C_F constant in time t. In the chemical limited regime (Da < 1), C_F relaxes exponentially toward a final concentration which depends on the radial position r in the cell within a characteristic time also a function of r. We will underline the potential interest of this method to fundamental concerns in mixing, and other fields of application.