Abstract
This study deals with trapping of particles diffusing on a flat surface by a circle whose boundary contains identical, evenly spaced absorbing arcs separated by reflecting arcs. This means that the particle concentration on the circle satisfies heterogeneous boundary conditions which make the trapping problem rather complicated for analytical treatment. Boundary homogenization discussed in this note allows to bypass this difficulty by the approximate replacement of heterogeneous boundary conditions on the circle by an effective homogeneous one with a properly chosen effective trapping rate. We obtain a formula which gives this rate in terms of the circle radius, number of absorbing arcs, the fraction of the circle boundary occupied by the arcs, and the particle diffusivity.
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