Exact Resistance of an Orifice in a 2D Membrane Blocked by a Cylindrical Obstruction

Abstract

An exact solution is presented for the resistance of an orifice in a 2D membrane separating two infinitely large conductive reservoirs and obstructed by an infinitely long cylinder. The solution is obtained by constructing a curvilinear coordinate system that captures the symmetry of the obstructed system with constant-coordinate surfaces mapping the system boundaries, and by integrating the resistive contributions of infinitesimally thin equipotential slices. As commonly done when assessing the resistance of fluidic channels of finite length, the exact expression of the obstructed 2D orifice can be used as the access region of obstructed cylindrical channels and will thus find use in single molecule sensing applications.