Abstract
By method of the Laplace transform, this article presents semi-analytical solutions for transient electroosmotic and pressure-driven flows (EOF/PDF) of two-layer fluids between microparallel plates. The linearized Poisson-Boltzmann equation and the Cauchy momentum equation have been solved in this article. At the interface, the Maxwell stress is included as the boundary condition. By numerical computations of the inverse Laplace transform, the effects of dielectric constant ratio ɛ, density ratio ρ, pressure ratio p, viscosity ratio µ of layer II to layer I, interface zeta potential difference \(\Delta \bar \psi\), interface charge density jump Q, the ratios of maximum electro-osmotic velocity to pressure velocity α, and the normalized pressure gradient B on transient velocity amplitude are presented. We find the velocity amplitude becomes large with the interface zeta potential difference and becomes small with the increase of the viscosity. The velocity will be large with the increases of dielectric constant ratio; the density ratio almost does not influence the EOF velocity. Larger interface charge density jump leads to a strong jump of velocity at the interface. Additionally, the effects of the thickness of fluid layers (h 1 and h 2) and pressure gradient on the velocity are also investigated.
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The project was supported by the National Natural Science Foundation of China (11062005 and 11202092), Open Fund of State Key Laboratory of Nonlinear Mechanics, the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(NJYT-13-A02), the Natural Science Foundation of Inner Mongolia (2010BS0107 and 2012MS0107), the Research Start Up Fund for Excellent Talents at Inner Mongolia University (Z20080211), the support of Natural Science Key Fund of Inner Mongolia (2009ZD01), the Postgraduate Scientific Research Innovation Project of Inner Mongolia and the Enhancing Comprehensive Strength Project of Inner Mongolia University (14020202).
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Su, J., Jian, YJ., Chang, L. et al. Transient electro-osmotic and pressure driven flows of two-layer fluids through a slit microchannel. Acta Mech Sin 29, 534–542 (2013). https://doi.org/10.1007/s10409-013-0051-0
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DOI: https://doi.org/10.1007/s10409-013-0051-0