Validity of approximated expressions for electro-osmotic flow in nanopores evaluated by continuum electrohydrodynamics and atomistic simulations

Transport in nanofluidic devices is often characterized by complex electrohydrodynamic coupling. Electro-osmotic flow (EOF), i.e. the motion of fluid due to an external electric field, is one of the most common electrohydrodynamic phenomena. However, the classical continuum description of EOF cannot be directly applied at the nanoscale, and no generic experimental techniques exist to measure EOF for nanopores just a few nanometres in size. This led to the development of approximate approaches to express EOF through experimentally accessible quantities. The most popular one, derived by Gu et al. in 2003, employs nanopore selectivity measured via reversal potential experiments and expresses EOF as the sum of water molecules dragged by each ion moving through the pore. Here, combining theoretical arguments, continuum electrohydrodynamic and molecular dynamics simulations, we discuss the limitations of these approximations. Our results indicate that, although some approximate expressions contradict basic fluid dynamics scaling arguments, they still capture the order of magnitude of EOF for very narrow biological nanopores such as MspA, CytK and CsgG. Finally, we highlight some caveats of the method, particularly when dealing with non-cylindrical biological pores and the effects of localized alterations of the pore surface charge, such as point mutations commonly employed in nanopore sensing technology.