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Approximate analytical formula and numerical evaluation of static liquid bridge force between two wet balls of different radii

DOI：10.7511/jslx20210820003

 作者 单位 李艳洁 北京林业大学 工学院, 北京 100083 邱洋平 北京林业大学 工学院, 北京 100083 徐泳 中国农业大学 理学院, 北京 100083 黄文彬 中国农业大学 理学院, 北京 100083

针对异径球形湿颗粒间液桥力，以Young-Laplace公式为基础，结合环形近似法并引入等效半径，在宽松设定的条件下推导出了简化的近似解析公式。此公式形式简洁，且当两球半径相等时，可回归到Pitois等提出的径球液桥力公式。本文对此近似解析公式进行参数敏感度分析，发现随着颗粒间距的增大，液桥力对颗粒半径的敏感度降低。此外，本文近似解析公式与其他实验和理论结果进行对比发现，该近似解析公式与上述实验和数值结果相当吻合，表明该近似解析公式可以较准确地计算接触角较小时的异径球颗粒间的液桥力，因而适于湿颗粒系统的数值模拟。

For the liquid bridge force between spherical wet particles of different radii, based on Young-Laplace formula, combined with toroidal approximation method and introducing harmonic radius, a simplified approximate analytical formula is derived under loose setting conditions.This formula is simple in form, and when the radii of the two balls are equal, it can be regressed to the Pitois liquid bridge force formula between balls of equal radii balls.It is found that the sensitivity of liquid bridge force to particle radius decreases with the increase of distance between the two particles.In addition, by comparing the approximate analytical formula with the experimental and theoretical results of others, it is found that the approximate analytical formula is in quite good agreement with the above experimental and numerical results, which shows that the approximate analytical formula can accurately calculate the liquid bridge force between spherical particles of different radii with small contact angles, so it is applicable for the numerical simulation of a wet particle system.