The diffusion-limited kinetics of the growth of a depletion zone around a static point trap in a thin, long channel geometry was studied using a laser photobleaching experiment of fluorescein dye inside a flat rectangular capillary. The dynamics of the depletion zone was monitored by the θ distance, defined as the distance from the trap to the point where the reactant concentration has been locally depleted to the specified survival fraction (θ) 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. We define a "parallel" and a "perpendicular" θ distance, along the slab long and short dimensions, respectively, and study their time development as a means to study the asymmetrical nature of the slab geometry. For all θ values, the crossover occurs concurrently for both θ distances when the depletion zone touches the boundary for the first time. We derive theoretical expressions for this geometry and compare them with the experimental data. We also obtain important insight from the ratio of the reactant concentration profiles in the parallel and perpendicular directions. Exact enumeration and Monte Carlo simulations support the anomalous depletion scaling results. Nevertheless, the crossover time (τ C) is still found to scale with the width (W) of the rectangular reaction zone as τ C∼W 2, as expected from the basic Einstein diffusion law.