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This article deals with the electroosmotic flow through nanochannel filled with electrolyte solution surrounded by an immiscible oil layer in which the fluid is driven by either DC or AC electric field. The wall of the nanochannel is considered to bear a constant negative surface charge. Additional mobile ions with positive polarity are present in the surface oil layer. The electrostatic potential can be obtained from the nonlinear Poisson-Boltzmann equation. With the known electric potential, we calculate the axial velocity distribution from the unsteady Stokes equation. The effects of intrinsic parameters on the overall electrostatic behavior as well as velocity distribution are discussed in a great detail. We identify several interesting key features of the flow distributions under externally applied DC or AC electric field.
For lower range of Debye-Huckel parameter, the overlapping of adjacent electric double layers significantly impacts the flow profile. In addition for externally applied sinusoidal AC electric field, a finite settling time is required to diffuse the momentum of the fluid in the adjacent region of the channel wall to the bulk fluid. As a result, a phase shift between the applied electric field and the flow may occur. It is also shown that under AC electric field, the oscillatory behaviour of the axial velocity is restricted near the oil layer-electrolyte interface for large values of applied frequency.
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