Generalized Electroosmosis transport with a spatially modulated electric permittivity inside a cylindrical micro channel

摘要

After analyzing the behavior of a fluid using an electroosmosis transport system, it was shown that the analysis of a constant electric permittivity could also be extended to a medium in which its electrical properties are space dependent. Using the hydrodynamic analysis with the Navier-Stookes equation in a high symmetric stationary environment and by solving the Maxwell's equations for only electrical charge sources within a micro channel, in the case where the electrical properties of the fluid changed along the space. In this case, it was considered a linear and a quadratic relation of the spatially modulated electric permittivity. For the first case, the solution was obtained in the terms of the Heun functions and in the second case the solution was given in terms of the Legendre polynomials. For both cases, the analytical solutions were obtained using the Maple software. After evaluating these results with the solutions obtained with the Bessel's special functions, it provided a close approximation of the behavior of the fluid under the electroosmosis effect with constant permittivity. With the development of this comparison between these solutions for the non-constant fluid's electric characteristics, the analysis could be brought into the field of non-single-phase fluids, so it might allow a further analysis of the electroosmosis within a more realistic fluid, in which properties changes among the space inside a micro channel.