Electrokinetic Energy Conversion Efficiency in Rectangular Nanochannels
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摘要: 利用分离变量法,研究了矩形纳米管道内流体的流向势及电动能量转换效率.通过求解电势满足的Poisson-Boltzmann(泊松-玻尔兹曼)方程和速度满足的Navier-Stokes(纳维-斯托克斯)方程,得到了矩形纳米管道内流体的流向势和电动能量转换效率的解析表达式.通过数值计算,分析了电动宽度K(矩形管道的宽度与双电层厚度的比值)、纳米管道高度与宽度的展向比α以及壁面Zeta势ζ等无量纲参数对流向势及电动能量转换效率的影响.结果表明,当其他参数固定时,流向势随K的增加而减小.当K较小时,电动能量转换效率随K的增大而增大;当K较大时,电动能量转换效率随K的增大而减小.此外,流向势随展向比α的增大而变大.对于较小的K,电动能量转换效率随α的增大而变大;当K较大时,电动能量转换效率随α增大而减小.最后,当壁面电势ζ增大,流向势变大,相应的电动能量转换效率有显著的增加.Abstract: The streaming potential and electrokinetic energy conversion efficiency in rigid rectangular nanochannels were studied via the variable separation approach. The analytic expressions for the streaming potential and electrokinetic energy conversion efficiency were obtained through solution of the linearized PoissonBoltzmann equation for the electric potential and the NavierStokes equation for the velocity field. By means of numerical computations, the influences of dimensionless electrokinetic width K,channel width to height ratio α and wall Zeta potential ζ on both the streaming potential and the electrokinetic energy conversion efficiency were discussed. The results show that the streaming potential exhibits monotonic decrease with K, while the electrokinetic energy conversion efficiency first increases with K for small K values, then decreases with K for large K values, when other parameters are given. In addition, the streaming potential increases with α. The electrokinetic energy conversion efficiency first increases with α for small K values, then decreases with α for large K values. Finally, both the streaming potential and the electrokinetic energy conversion efficiency increase significantly with the wall Zeta potential.
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