Analytical investigations are performed for pressure driven flow of an electrically conducting, incompressible and viscous fluid in a polyelectrolyte-grafted nanotube by using Bessel functions. Nanofluidic tubes whose walls are covered by polyelectrolyte materials, named the fixed charge layer (FCL), are identified as soft nanotubes. The flow relies on an externally imposed pressure gradient and an induced reverse electroosmotic force produced by the streaming potential field which is spontaneously developed due to the ionic charge migration with the fluid flow. Many parametrical ranges are determined to ensure the validity of Debye-Hückel approximation. The analysis is based on the solutions of the linearized Poissson-Boltzmann equation and modified Navier-Stokes equation. To obtain the streaming potential, we use a numerical treatment to solve an integral equation governing the streaming potential. Finally, the electrokinetic energy conversion efficiency is studied. The result shows that both the streaming potential and energy conversion efficiency monotonically increase with the FCL thickness d increasing. However, they present a monotonic decrease trend with the increase of Kλ, which is the ratio of the characteristic scale of the mobile charges to the fixed charge within the FCL. We compare the results in a soft nanotube with those in a rigid one, whose zeta potential is equal to the electrostatic potential at the solid-polyelectrolyte interface of the soft nanotube. We find that the electric potential in a soft nanotube is higher than that in the corresponding rigid nanotube, which results in a larger streaming potential in the soft nanotue. Moreover, for the parameter ranges considered in this work, our results show that the electrokinetic energy conversion efficiency in a soft nanotube is 1.5–3 times higher than that in a rigid nanotube. These findings are important for investigating the streaming potential and electrokinetic energy conversion efficiency in soft nanotubes. They can be used as a kind of new method to enhance the energy conversion efficiency of the electrokinetic transport in nanotube.%柔性纳米通道是在刚性纳米通道壁面处添加一层带某种电荷的聚电解质层或固定电荷层的纳米通道.本文在低Zeta势近似下，通过解析求解电势满足的线性化Poisson-Boltzmann方程和速度满足的Cauchy动量方程，给出了圆柱形柔性纳米通道中电解质溶液的流向势和电动能量转换效率的解析解.在表面Zeta势取值相同，且管径相同(聚电解质层厚度远小于管径前提下)的情形下，将圆柱形柔性纳米通道和刚性纳米通道中电解质溶液的流向势和电动转换效率进行了比较.结果表明，柔性纳米通道中的流向势和转换效率明显高于刚性通道中的流向势和转换效率.在本文选取的参数范围内，柔性纳米通道中的电动转换效率比刚性纳米通道中的转换效率提高1.5—3倍.
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