I'm trying to determine the neutralization time (tn) of strong acid and strong base. Strong acid, A, is initially in a slab of thickness -2δ and strong base, B, is initially in a slab of thicknss 2δ. Slabs alternate with a slab of A next to one of B next to one of A next to one of B and so on. Because of symmetry, only the half slab thicknesses of each slab of reactant needs to be considered. The slabs only have diffusion of the reactants and when the reactants meet they react instantaneously in a stoichiometry of 1 to 1. So at the reaction plane, the concentration of each reactant is zero. The problem is a moving boundary problem and is illustrated in the attachment.
The boundary conditions at -δ and +δ are no flux conditions. The other boundary is the reaction plane which moves with time. At this plane the concentration of either A or B is zero.
Fick's 2nd law applies. Because the reaction is instantaneous and irreversible, the effect of the reaction is to keep the concentration of each reactant at zero at the reaction plane. Therefore, no reaction term is need nor a convection term; it is just Fick's 2nd law involving only diffusion. I have not been able to come up with an analytical solution so I want to try a numerical method. Could I use MatLab to solve this problem or is the moving boundary aspect of the problem beyond its capabilities?