以Debye-H¨uckel假设近似下线性化的Possion-Boltzmann方程和黏性不可压缩流体运动的Navier-Stokes方程为基础, 采用漏电介质模型, 分别研究了直流(direct current, DC)稳恒电场和交流(alternating current, AC)周期电场驱动下柱体表面电渗驱动液体薄膜问题, 得到了流场的电位势、速度分布的精确解. 结果表明, 定常解的流速与电位势仅相差一个常数, 而自由面上流速只与自由面电位势和圆柱固壁电位势的比值α有关. 周期电场下的流速振幅、流场中与固壁双电层中的流速相位差, 均与雷诺数有密切的关系: 当雷诺数较小时, 周期电场下流速振幅与定常解相近; 随着雷诺数的增大, 固壁附近流速振幅减小, 相位差增大. 当α较小时, 自由面上流速振幅随着雷诺数的增大而减小; 当α较大时, 流速振幅随着雷诺数的增大而增大.
A thin film flow on a cylinder driven by electro-osmosis in direct current (DC) and alternating current (AC) electric field are analytically investigated respectively. Analytical solutions of electric potential and flow velocity are obtained by solving viscous incompressible hydrodynamic equations coupling with linearized
Possion-Boltzmann equation based on the leaky dielectric model and the Debye-H¨uckel approximation. In a DC electric field, the dimensionless flow velocity just differs from the electric potential by a constant. The flow velocity on free surface only depends on a ratio α between the electric potential on the free surface and the potential on the cylindrical surface. In an AC electric field, the results show the amplitude of flow velocity. The phase difference between flow velocity in flow field and that in the electrical double layer is closely related to the Reynolds number. Amplitude of flow velocity in an AC periodic electric field is similar to that in a DC steady electric field in low Reynolds number. With the increase of the Reynolds number, the amplitude of flow velocity decreases near the solid surface, while the phase difference increases. The amplitude of flow velocity on a free surface decreases/increases as the Reynolds number increases for low/high α.
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