The plane Poiseuille flow of viscoelastic fluids with pressure-dependent viscosity is analyzed through a narrow nanochannel, combining with the electrokinetic effect. When the fluid viscosity depends on pressure, the common assumption of unidirectional flow is unsuitable since the secondary flow may exist. In this case, we must solve the continuity equation and two-dimensional (2D) momentum equation simultaneously. It is difficult to obtain the analytical electrokinetic flow characteristics due to the nonlinearity of governing equations. Based on the real applications, we use the regular perturbation expansion method and give the second-order asymptotic solutions of electrokinetic velocity field, streaming potential, pressure field, and electrokinetic energy conversion (EKEC) efficiency. The result reveals a threshold value of Weissenberg number (Wi) exists. The strength of streaming potential increases with the pressure-viscosity coefficient when Wi is smaller than the threshold value. An opposite trend appears when Wi exceeds this threshold value. Besides, the Weissenberg number has no effect on the zero-order flow velocity, but a significant effect on the velocity deviation. A classical parabolic velocity profile transforms into a wavelike velocity profile with the further increase in Wi. Finally, the EKEC efficiency reduces when pressure-dependent viscosity is considered. Present results are helpful to understand the streaming potential and electrokinetic flow in the case of the fluid viscosity depending on pressure.

中文翻译：

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纳米通道中具有压力依赖性粘度的粘弹性流体的流动势

通过狭窄的纳米通道，结合动电效应，分析具有压力依赖性粘度的粘弹性流体的平面泊肃叶流。当流体粘度取决于压力时，单向流的常见假设是不合适的，因为可能存在二次流。在这种情况下，我们必须同时求解连续性方程和二维（2D）动量方程。由于控制方程的非线性，很难获得解析的动电流动特性。基于实际应用，我们采用正则微扰展开法，给出了动电速度场、流电势、压力场和动电能量转换（EKEC）效率的二阶渐近解。结果表明Weissenberg数(Wi)存在一个阈值。当Wi小于阈值时，流动势的强度随着压力粘度系数的增大而增大。当Wi超过该阈值时，出现相反的趋势。此外，Weissenberg数对零级流速没有影响，但对速度偏差有显着影响。随着 Wi 的进一步增加，经典的抛物线速度分布转变为波状速度分布。最后，当考虑压力相关粘度时，EKEC 效率会降低。目前的结果有助于理解流体粘度取决于压力的情况下的流动势和电动流。