We present a detailed analysis of the electroviscous effect in the squeeze out of thin electrolyte films confined between two charged surfaces. The two charged surfaces consist of a curved surface and a flat surface, which closely simulate the tip–substrate configuration in the force measurement of electrolyte solutions with dynamic atomic force microscopy. In the lubrication limit, we find the analytical solution of the electroviscous-effect-modified squeezing flow field in the thin electrolyte film confined between the tip and substrate by solving the Nernst–Planck–Poisson/Navier–Stokes equation under the justified condition of pseudo-steadiness. We also derive the solution of the tip–substrate interaction, which comprises of a conservative electric double layer (EDL) force and an electroviscous-effect-enhanced dissipative hydrodynamic force. The current work focuses on the dissipative hydrodynamic force since the conservative EDL force has been well described by the well-known Derjaguin–Landau–Verwey–Overbeek theory. We introduce a power-law index ( $n$ ) for the tip surface, which enables an unprecedented quantitative characterization of the tip profile effect on the electroviscous effect. We observe a seemingly counter-intuitive effect that, for a given tip–substrate separation, the electroviscous effect is the strongest at one particular value of the zeta ( $\unicode[STIX]{x1D701}$ ) potential and diminishes as the $\unicode[STIX]{x1D701}$ potential departs from this value. We reveal the counterion conductivity of the EDL to be the governing factor for the electroviscous effect under a given $\unicode[STIX]{x1D701}$ potential. In addition to enhancing the dissipative hydrodynamic interaction force, the electroviscous effect modifies the velocity profiles in the thin electrolyte solution films such that they are much sharper.

中文翻译：

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电粘性对薄电解质溶液薄膜挤压流动的影响

我们详细分析了挤压出限制在两个带电表面之间的薄电解质膜的电粘性效应。两个带电表面由一个曲面和一个平面组成，它们在使用动态原子力显微镜对电解质溶液的力测量中密切模拟尖端 - 基板配置。在润滑极限下，我们通过求解 Nernst-Planck-Poisson/Navier-Stokes 方程，在伪的合理条件下，找到了限制在尖端和基底之间的薄电解质膜中电粘性效应修正的挤压流场的解析解。 - 稳定性。我们还推导出了尖端 - 衬底相互作用的解决方案，其中包括保守的双电层（EDL）力和电粘性效应增强的耗散流体动力。由于保守的 EDL 力已经被著名的 Derjaguin-Landau-Verwey-Overbeek 理论很好地描述，目前的工作集中在耗散流体动力上。我们为尖端表面引入了幂律指数（$n$），这使得尖端轮廓对电粘性效应的影响前所未有的定量表征成为可能。我们观察到一种看似违反直觉的效应，对于给定的尖端 - 基底分离，电粘性效应在 zeta ( $\unicode[STIX]{x1D701}$ ) 电位的一个特定值处最强，并随着 $\ unicode[STIX]{x1D701}$ 潜在偏离此值。我们揭示了 EDL 的反离子电导率是给定 $\unicode[STIX]{x1D701}$ 电位下电粘性效应的控制因素。