The initial validation of the random walk simulation is presented in Figure , which shows the steady-state concentration profiles of all four ECL compounds across the nanochannel. These profiles were obtained by averaging over a central segment (in the x-direction) of the channel. Proare shown in Figures and and are compared to profiles from a previous finite element calculation under identical conditions in Figures and. For both the stochastic and COMSOL simulations, diffusion coefficients D = 10 -9 m 2 /s were chosen for all compounds. The time step t was set to 0.001 µs µs to ensure that the Brownian step length 1.4 nm is small compared to the 100 nm channel diameter. In the stochastic simulation, computational limits restrict the number of particles and concentration. Here, the simulation was scaled to over 100,000 particles (~0.1 mM), approximately two orders of magnitude lower than in experiments and finite element sities allowed reaction (3) to occur in the channel center and prevented electrochemically generated particles from reaching the opposite electrode. When comparing results between stochastic and finite element methods for decay rates = 10 5 s -1 (Figures and) and 10 6 s -1 (Figures and), both approaches produced fully plementation of the physic chemistry and Python script, without errors or "hallucinations."