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

TL;DR

This paper derives an exact mathematical solution for calculating the electrical resistance of a 2D membrane orifice obstructed by a cylindrical object, useful for fluidic and sensing applications.

Contribution

It introduces a novel curvilinear coordinate system approach to obtain an exact resistance expression for an obstructed 2D orifice, advancing precise modeling in related fields.

Findings

Provides an exact resistance formula for an obstructed 2D orifice

The solution employs a specialized curvilinear coordinate system

Applicable to single molecule sensing and fluidic channel analysis

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.