  Diffusion-mediated surface phenomena are crucial for human life and industry,
with examples ranging from oxygen capture by lung alveolar surface to
heterogeneous catalysis, gene regulation, membrane permeation and filtration
processes. Their current description via diffusion equations with mixed
boundary conditions is limited to simple surface reactions with infinite or
constant reactivity. In this letter, we propose a probabilistic approach based
on the concept of boundary local time to investigate the intricate dynamics of
diffusing particles near a reactive surface. Reformulating surface-particle
interactions in terms of stopping conditions, we obtain in a unified way major
diffusion-reaction characteristics such as the propagator, the survival
probability, the first-passage time distribution, and the reaction rate. This
general formalism allows us to describe new surface reaction mechanisms such as
for instance surface reactivity depending on the number of encounters with the
diffusing particle that can model the effects of catalyst fooling or membrane
degradation. The disentanglement of the geometric structure of the medium from
surface reactivity opens far-reaching perspectives for modeling, optimization
and control of diffusion-mediated surface phenomena.
