Cell to cell ratio meaning, growth rate in the mesh. Are you using CHEMKIN mechanism (encrypted or non-encrypted)? And as you are using DES which is transient, try using lower Under-relaxation factors initially until the residuals are stable and afterwards you may increase the URFs.
Try to converge the steady state first in the reaction and then using the converged solution, proceed with the DES. Use suitable time step and the number of iterations in each time step. Maintain the Courant number.