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Motivated by the interest that microelectrolytic systems are gaining in the development of the so-called lab-on-a-chip systems, i.e., miniature microfluidic devices for biochemical analysis, we present an analytical study of Ohmic conduction in rectangular charged microchannels filled with electrolytic solution. The study complements a previous one [M. Campisi et al., J. Chem. Phys. 123, 204724 (2005)], concerning ac electro-osmosis. The problem is framed within the theory of nonequilibrium thermodynamics and is based on the solution of the incompressible Navier-Stokes equation with an electrical body force due to the interaction of the applied electric field with the charged electric double layer (EDL) which forms at the solid-liquid interface. We analyze in detail the dependence of the system complex conductance on the ratio linear dimensions over Debye length with an eye on finite EDL effects, and compare its scaling properties with those of electrokinetic and hydraulic complex conductances.

Motivated by the growing interest in ac electroosmosis as a reliable no moving parts strategy to control fluid motion in microfluidic devices for biomedical applications, such as lab-on-a-chip, we study transient and steady-state electrokinetic phenomena (electroosmosis and streaming currents) in infinitely extended rectangular charged microchannels. With the aid of Fourier series and Laplace transforms we provide a general formal solution of the problem, which is used to study the time-dependent response to sudden ac applied voltage differences in case of finite electric double layer. The Debye-Huckel approximation has been adopted to allow for an algebraic solution of the Poisson-Boltzmann problem in Fourier space. We obtain the expressions of flow velocity profiles, flow rates, streaming currents, as well as expressions of the complex hydraulic and electrokinetic conductances. We analyze in detail the dependence of the electrokinetic conductance on the extension of linear dimensions relative to the Debye length, with an eye on finite electric double layer effects.