  Liquid transport through nanopore is central into many applications, from
water purification to biosensing or energy harvesting. Ultimately thin
nanopores are of major interest in these applications to increase driving
potential and reduce as much as possible dissipation sources. We investigate
here the efficiency of the electrical power generation through an ultrathin
nanoporous membrane by means of streaming current (electrical current induced
by ionic flow in the vicinity of the liquid/solid interface) or electroosmosis
(flow rate induced by an electrical potential). Upscaling from one unique pore
to a nanoporous membrane is not straightforward when we consider low aspect
ratio nanopore because of 3D entrance effects, which lead to interactions
between the pores. Whereas these interactions have already been considered for
direct transport (hydrodynamic permeability of the membrane, ionic
conductance), specific effects appear when coupled transports are considered.
We obtain here the expression of the electroosmotic mobility for a nanoporous
membrane including surface conduction, and by a numerical evaluation of our
results, we show that (i) it depends mainly of the distance between the pores
and (ii) it is sublinear with the number of pores. Varying the pore spatial
organization (square, hexagonal, disordered structure) reveals that these
transport properties are only dependent on one parameter, the porosity of the
membrane (if other parameters such as membrane material/thickness are kept
constant). Finally, when considering energy conversion yield, it is shown that
increasing the number of pores is deleterious, and a nonmonotonic behavior with
salt concentration is reported.
