Access resistance of a circular pore ($R_{\mathrm{access},\mathrm{one}\mathrm{side}}=\rho /(4a)$)

The continuum spreading resistance for current entering a circular aperture of radius $a$ from one uniform semi-infinite reservoir of electrical resistivity $\rho$ is $\rho /(4a)$. Two symmetric reservoirs contribute $\rho /(2a)$ in series with a cylindrical pore resistance $\rho \ell /(\pi a^2)$. Unobstructed access is not the same as zero spreading resistance; molecular-scale pores also require non-continuum transport physics.