[rdemyan]

I am modeling an acid-base reaction that includes a fluorescence indicator. My simple model is a slab of acid next to a slab of base and so on. These slabs are very thin, typically less than 10 microns and are assumed to be laminar such that diffusion is the only method of mass transport. At the interface of acid and base the reaction occurs and the pH is 10^-7 (which is shown as zero on the attached figure).

The attached figure shows an example of the concentration gradients of acid and base at some time t. Because of symmetry only a half slab of acid is shown next to a half slab of base. I want to calculate the total fluorescence emitted from both half slabs together. I have an equation which gives me the fluorescence as a function of pH.

So the way I have been calculating the fluorescence is to get the pH for each slice shown in the figure and assume that the pH is constant for that slice (of course as the slice thickness is decreased this becomes a better assumption). Then the fluorescence is calculated for each slice based on the known pH and the equation.

Now comes my question: If I want to calculate the total fluorescence for both slabs, can I just simply add up the fluorescence from each slice in the acid slab and base slab? Is this the correct methodology?