Electrolytic conduction in periodic arrays of insulators with charges
Electrolytic conduction in periodic arrays of insulators with charges
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带电荷绝缘体周期性阵列中的电解传导
DOI：
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发表时间：
1987
期刊：
影响因子：
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通讯作者：
P. Sen
中科院分区：
文献类型：
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作者：
R. Kan;P. Sen
为了研究含粘土颗粒的饱和盐水多孔介质中的导电问题，我们计算了浸入电解质中的周期性带电圆柱阵列的直流电导率σ。我们扩展的方法，由于主瑞利带电系统，包括扩散电流。代表表面效应的关键无量纲参数ε =Ω+r+/（N 0a）是表面离子密度Ω+乘以双层中的平均扩散系数与外部的平均扩散系数的比率r+除以堆积密度N 0乘以颗粒半径a。我们表明，σ是一个非线性的函数，因此，盐水电导率σw，从而提供了第一个解释，依靠第一性原理，这一众所周知的实验事实。对于给定的几何形状，当Ω+→0，或r+→0或当N 0 <$1时，参数ω →0，得到σ对σw的线性依赖。恒电荷系统的Ω+为常数，但当表面电位ε为常数时，Ω+=2δ N 0 e ε/2随N 0而变化，δ为屏蔽距离。
We compute dc electrical conductivity σ for a periodic array of charged cylinders immersed in an electrolyte in order to elucidate conduction in brine saturated porous medium containing clay particles. We extend a method due to Lord Rayleigh to charged systems and include diffusion currents. The key dimensionless parameter ξ=Ω+r+/(N0a) that represents the surface effects is the surface ion density Ω+ times the ratio r+ of the average diffusion coefficient in the double layer to that outside divided by the bulk density N0 times the particle radius a. We show that σ is a nonlinear function of ξ and hence of brine conductivity σw and thus provide the first explanation, resting on first principles, of this well known experimental fact. With a given geometry, when Ω+→0, or r+→0 or when N0≫1, the parameter ξ→0 and one obtains a linear dependence of σ on σw. The constant charge system have Ω+ constant, but when the surface potential ζ is constant, Ω+=2δN0eζ/2 varies with N0, δ being the screening distance.