Griffiths Stewart K, Nilson Robert H
Sandia National Laboratories, Livermore, CA 94551-0969, USA.
Electrophoresis. 2005 Jan;26(2):351-61. doi: 10.1002/elps.200406169.
Numerical methods are employed to examine the work, electric power input, and efficiency of electrokinetic pumps at a condition corresponding to maximum pump work. These analyses employ the full Poisson-Boltzmann equations and account for both convective and conductive electric currents, including surface conductance. We find that efficiencies at this condition of maximum work depend on three dimensionless parameters, the normalized zeta potential, normalized Debye layer thickness, and a fluid property termed the Levine number indicating the nominal ratio of convective to conductive electric currents. Efficiencies at maximum work exhibit a maximum for an optimum Debye layer thickness when the zeta potential and Levine number are fixed. This maximum efficiency increases with the square of the zeta potential when the zeta potential is small, but reaches a plateau as the zeta potential becomes large. The maximum efficiency in this latter regime is thus independent of the zeta potential and depends only on the Levine number. Simple analytical expressions describing this maximum efficiency in terms of the Levine number are provided. Geometries of a circular tube and planar channel are examined.
采用数值方法研究电动泵在对应最大泵功条件下的功、输入电功率和效率。这些分析采用完整的泊松 - 玻尔兹曼方程，并考虑对流电流和传导电流，包括表面电导。我们发现，在这个最大功条件下的效率取决于三个无量纲参数，即归一化的zeta电位、归一化的德拜层厚度以及一个称为莱文数的流体属性，该属性表示对流电流与传导电流的标称比率。当zeta电位和莱文数固定时，最大功时的效率在最佳德拜层厚度处呈现最大值。当zeta电位较小时，这个最大效率随zeta电位的平方增加，但当zeta电位变大时达到平稳状态。因此，在后一种情况下，最大效率与zeta电位无关，仅取决于莱文数。提供了用莱文数描述这个最大效率的简单解析表达式。研究了圆形管道和平面通道的几何形状。
