Timescales for relaxation to Boltzmann equilibrium in nanopores

In most models for electrokinetic phenomena at charged interfaces, Boltzmann equilibrium is assumed to be established. Here we show that a long nanopore with significant double layer overlap establishes equilibrium quite slowly and that centimeter-long nanopores can take O(105) s to establish Boltzmann equilibrium. The timescale is determined not by diffusion across the double layer, but by diffusion or convective transport along the length of the pore to reservoirs at its ends. An “intermediate equilibrium” state described by Qu and Li (J. Colloid Interface Sci. 224 (2000) 397) may exist for times between the (fast) EDL establishment timescale and (slow) axial transport timescale.