Electrokinetic energy conversion efficiency analysis using nanoscale finite-length surface-charged capillaries

Abstract

Abstract Electrokinetic power generation efficiency using a two-dimensional axisymmetrical model is numerically investigated. A finite-length nanoscale surface-charged cylindrical capillary with reservoirs connected at the capillary ends is considered as the physical domain. The Navier–Stokes, Laplace, Poisson, and Nernst–Planck equations are solved simultaneously to obtain the fluid flow, electrical potential, ion concentration and electrical current in the flow field. The energy conversion efficiency predicted using a one-dimensional model assuming an infinitely long channel, Boltzmann ion distribution and equal ionic electrical mobility is also carried out and compared with the two-dimensional result. The two-dimensional model results show that the electrostatic potential gradient resulting from the concentration changes at the capillary entrance and exit and fluid flow produce a conductive current that reduces the total current in the flow field. The conductive current due to the electrostatic potential gradient increases with the decrease in electrolyte bulk concentration and increase in surface charge density. This results in nonlinear variations in the electric current–voltage curve and maximum conversion efficiency as functions of the surface charge density and dimensionless Debye length when the electrolyte bulk concentration is low. Comparison of the maximum efficiencies predicted from one- and two-dimensional models indicates that the one-dimensional model is valid only when the dimensionless Debye length is large and the surface charge density is small because the electrostatic potential gradient is neglected. The two-dimensional model also predicts that optimum maximum energy conversion efficiency can be obtained when the dimensionless Debye length is equal to 2 and its magnitude increases with the increase in surface charge density.