Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2017 / Paper 2 / Section B / 22 / ii

Ignoring access effects and wall charge, the cylindrical conducting liquid hasThe corresponding conductance is approximately $0.982\mathrm{nS}$. A charged surface can contribute mobile counterions and change this estimate. Surface conduction is important when its conductance is comparable with the bulk contribution: for surface conductance $K_s$, their ratio in a cylinder is $2K_s/(\sigma r)$, twice the Dukhin number convention $K_s/(\sigma r)$. Double-layer overlap, when the Debye length is comparable with the pore radius, is another warning that uniform bulk conductivity is inadequate. No surface-charge or ionic-strength data are supplied to quantify those corrections.