Dimensional crossover in the growth of depletion zone in a rectangular capillary: Experiments and Monte Carlo simulations

The diffusion-limited kinetics of the growth of depletion zone around a static point trap in a thin, long stripe geometry was studied using a laser photobleaching experiment of fluorescein dye inside a rectangular capillary. The dynamics of the depletion zone was monitored by the θdistance, defined as the distance from the trap to the point where the reactant concentration has been depleted to the specific fraction of its initial bulk value. A dimensional crossover from two dimensions to one dimension, due to the finite width of the reaction zone, was observed. The crossover seems to occur for all θ values concurrently when the depletion zone touches the boundary for the first time, suggesting that the boundary information spreads faster than diffusion. Monte Carlo simulations were performed to support the experimental results. The crossover time (τ_c) is found to scale with the width (L) of the rectangular reaction zone as τ_c ∼ L², as expected from the Einstein's diffusion law.