In a microfluidic system, the flow slip velocity on a solid wall can be the same order of magnitude as the average velocity in the microchannel. The flow-electricity interaction in a complex microfluidic system subjected to a joint action of wall slip and electro-viscosity is an important topic. An analytical solution for the periodical pressure-driven flow in a two-dimensional uniform microchannel, with consideration of wall slip and electro-viscous effect is obtained based on the Poisson-Boltzmann equation for the Electric Double Layer （EDL） and the Navier-Stokes equations for the liquid flow. The analytic solutions agree well with the numerical solutions. The analytical results indicate that the periodical flow velocity and the Flow-Induced Electric Field （FIEF） strongly depend on the frequency Reynolds number （Re = （wh2/v ）, that is a function of the frequency, the channel size and the kinetic viscosity of fluids. For Re 〈 1, the flow velocity and the FIEF behave similarly to those in a steady flow, whereas they decrease rapidly with Re as Re 〉 1. In addition, the electro-viscous effect greatly influences the periodical flow velocity and the FIEF, particularly, when the electrokinetic radius kH is small. Furthermore, the wall slip velocity amplifies the FIEF and enhances the electro-viscous effect on the flow.
This paper presents a numerical analysis of Joule heating effect of electroosmo- sis in a finite-length microchannel made of the glass and polydimethylsiloxane （PDMS） polymer. The Poisson-Boltzmann equation of electric double layer, the Navier-Stokes equation of liquid flow, and the liquid-solid coupled heat transfer equation are solved to investigate temperature behaviors of electroosmosis in a two-dimensional microchannel. The feedback effect of temperature variation on liquid properties （dielectric constant, vis- cosity, and thermal and electric conductivities） is taken into account. Numerical results indicate that there exists a heat developing length near the channel inlet where the flow velocity, temperature, pressure, and electric field rapidly vary and then approach to a steady state after the heat developing length, which may occupy a considerable portion of the microchannel in cases of thick chip and high electric field. The liquid temperature of steady state increases with the increase of the applied electric field, channel width, and chip thickness. The temperature on a PDMS wall is higher than that on a glass wall due to the difference of heat conductivities of materials. Temperature variations are found in the both longitudinal and transverse directions of the microchannel. The increase of the temperature on the wall decreases the charge density of the electric double layer. The longitudinal temperature variation induces a pressure gradient and changes the behavior of the electric field in the microchannel. The inflow liquid temperature does not change the liquid temperature of steady state and the heat developing length.
