Is there a known relation between the diffusion of a molecule and the diffusion of the reactants?
More a set of queries and comments than an answer.

I don't understand why you make A and B vary with time irrespective of your reaction scheme.

You should really analyse using Fick's diffusion equations with the reaction scheme added and do so for each species. This will have to be a numerical calculation in space and time. (There are well established methods to do this. e.g. Crank-Nicholson). By the symmetry of your experiment you may be able to reduce this to one dimension and time. 

You should be able to 'guestimate' the diffusion coefficient from kinetic theory at least their ratio which should be quite accurate.

Your second equation ('new formula') is that for a reaction $\ce{A + B -&gt;[k_1] AB -&gt;[k_1] }$ where both rate constants are the same. In your case there seems to be no reason why the two rate constants are the same, only you know enough about your experiment to explain this :)