论文标题
用于充电的泊松式坡度孔的分析解决方案
Analytical solution to the Poisson-Nernst-Planck equations for the charging of a long electrolyte-filled slit pore
论文作者
论文摘要
我们研究了长时间充满电解质缝隙孔的充电动力学，以响应突然应用的电位。特别是，我们通过分析求解了Poisson-Nernst-Planck（PNP）方程式的孔，其中$λ_d\ ll h \ ll l $，带有$λ_d$ debye长度，$ h $ and $ h $和$ l $ the孔的宽度和长度。对于较小的应用电势，我们发现孔隙表面及其中心之间的时间相关电势下降与著名传输线模型的预测完全一致。对于中度到高的应用电位，先前的数值工作表明，充电在晚期下降；我们的分析模型复制并解释了这种Biexporential指控的积累。
We study the charging dynamics of a long electrolyte-filled slit pore in response to a suddenly applied potential. In particular, we analytically solve the Poisson-Nernst-Planck (PNP) equations for a pore for which $λ_D\ll H\ll L$, with $λ_D$ the Debye length and $H$ and $L$ the pore's width and length. For small applied potentials, we find the time-dependent potential drop between the pore's surface and its center to be in complete agreement with a prediction of the celebrated transmission line model. For moderate to high applied potentials, prior numerical work showed that charging slows down at late times; Our analytical model reproduces and explains such biexponential charge buildup.
