Division of Mechanics, Research Center for Applied Sciences, Academia Sinica, Taipei, Taiwan, ROC.
Electrophoresis. 2011 Nov;32(23):3341-7. doi: 10.1002/elps.201100181. Epub 2011 Nov 10.
The present study is concerned with unsteady electroosmotic flow (EOF) in a microchannel with the electric charge distribution described by the Poisson-Boltzmann (PB) equation. The nonlinear PB equation is solved by a systematic perturbation with respect to the parameter λ which measures the strength of the wall zeta potential relative to the thermal potential. In the small λ limits (λ<<1), we recover the linearized PB equation - the Debye-Hückel approximation. The solutions obtained by using only three terms in the perturbation series are shown to be accurate with errors <1% for λ up to 2. The accurate solution to the PB equation is then used to solve the electrokinetic fluid transport equation for two types of unsteady flow: transient flow driven by a suddenly applied voltage and oscillatory flow driven by a time-harmonic voltage. The solution for the transient flow has important implications on EOF as an effective means for transporting electrolytes in microchannels with various electrokinetic widths. On the other hand, the solution for the oscillatory flow is shown to have important physical implications on EOF in mixing electrolytes in terms of the amplitude and phase of the resulting time-harmonic EOF rate, which depends on the applied frequency and the electrokinetic width of the microchannel as well as on the parameter λ.
本研究关注于具有泊松-玻尔兹曼（PB）方程描述的电荷分布的微通道中非稳态电渗流（EOF）。通过相对于参数 λ 的系统摄动来求解非线性 PB 方程，该参数 λ 衡量壁 ζ 电位相对于热势的强度。在小 λ 极限（λ<<1）下，我们恢复了线性化的 PB 方程 - 德拜-休克尔近似。通过在摄动级数中仅使用三项得到的解被证明是准确的，对于 λ 高达 2 的情况，误差<1%。然后，使用准确的 PB 方程解来求解两种类型的非稳态流的动电流体输运方程：由突然施加的电压驱动的瞬态流和由时谐电压驱动的振荡流。瞬态流的解对于 EOF 作为在具有各种动电宽度的微通道中输送电解质的有效手段具有重要意义。另一方面，振荡流的解对于混合电解质的 EOF 具有重要的物理意义，这体现在所得时谐 EOF 速率的幅度和相位上，这取决于所施加的频率和微通道的动电宽度以及参数 λ。
