Mean first-passage time of surface-mediated diffusion in spherical domains

Abstract We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain, for a molecule alternating phases of surface diffu-sion on the domain boundary and phases of bulk diffusion. The presented approach is based on an integral equation which can be solved analytically. Numerically validated approxi-mation schemes, which provide more tractable expressions of the mean first-passage time are also proposed. In the framework of this minimal model of surface-mediated reactions, we show analytically that the mean reaction time can be minimized as a function of the desorption rate from the surface