  In this paper we consider the diffusion of nanoparticles taken up by a
semi-permeable spherical cell placed in the path of a diffusive particle field
generated by an external planar source. The cell interior and exterior are
characterized by different diffusive properties, while the cell is able to
accommodate a different saturation level of particles at steady state than is
present in the external medium. The situation models the practical problem of
biological cells exposed from one direction. The conflict of geometries is
handled by the introduction of an effective boundary condition at a virtual
spherical boundary. A closed-form, large-time asymptotic solution for the local
concentration interior to the cell is developed. We consequently derive an
asymptotic approximation for the rate of nanoparticle accumulation in the cell.
We contrast the resulting time dependence with that of the corresponding
quantity found under strictly spherically symmetric conditions.
