Dynamics of the depletion zone at a finite-sized imperfect trap in two dimensions: Photobleaching experiments and simulations

The kinetics of the growth of depletion zones around a static trap in an effective two-dimensional geometry were studied experimentally with photobleaching of fluorescein dye by a focused laser beam. The phototrap served as an imperfect trap with a finite size. The growth of the depletion zone was monitored by the θ distance, defined as the distance from the trap to the point where the concentration of the reactants reaches a given arbitrary fraction θ [Formula presented] of its initial value, which could be directly measured experimentally. At the asymptotic limit, the results confirm the theoretical nonuniversal [Formula presented] scaling behavior for the θ distance. We also find an effect of fast expansion at an early time of the depletion zone inside an imperfect trap. Both the imperfect trapping strength and the finite trap size are found to control the early-time behavior, while the trap shape does not much affect the dynamics of the θ distance. A dimensional crossover was found for a perfect trap with a finite radius, when the θ distance was measured from the trap surface. The actual trapping efficiency was determined for different laser powers of the phototrap. Results are supported by analytical equations, exact enumerations, and Monte Carlo simulations.