Abstract
This paper presents a numerical analysis of Joule heating effect of electroosmosis 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, viscosity, 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.
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Communicated by Jian-zhong LIN
Project supported by the National Natural Science Foundation of China (Nos.10872076 and 50805059)
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Chao, K., Wu, Jk. & Chen, B. Joule heating effect of electroosmosis in a finite-length microchannel made of different materials. Appl. Math. Mech.-Engl. Ed. 31, 109–118 (2010). https://doi.org/10.1007/s10483-010-0111-z
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DOI: https://doi.org/10.1007/s10483-010-0111-z