异粒径颗粒间静态液桥力迟滞的解析分析

Analytical modeling of capillary force hysteresis in liquid bridgebetween two spheres of unequal sizes

两个颗粒间液桥的拉伸和收缩行为会导致接触角发生迟滞,进而使得毛细力出现迟滞,显著影响着颗粒间作用力的合理预测.以往研究多侧重于液桥拉伸时接触线沿着颗粒表面滑移阶段的实验观测和理论分析,因为此时接触角可取一个定值(后退接触角)、液桥型态多为凹形和毛细力随着颗粒间距呈单调下降,极大地简化了问题,但无法探讨接触角和毛细力迟滞.本文针对两个异粒径颗粒,提出了凸形和凹形液桥等六种基本类型及分类判据,采用环形近似法推导了液桥几何参数和毛细力的解析表达式,具有分类表达简洁和模型整体计算量小等优势.与文献实验的对比表明,该模型可快速识别液桥在一个完整的伸缩运动周期内各阶段的液桥型态并合理预测毛细力迟滞.

Stretching and compressing of liquid bridge between two particles could lead to contact angle hysteresis and then capillary force hysteresis,having some significant effects on interparticle force estimation.Most previous experimental and theoretical works focused on the process of contact line sliding on particle surface when the liquid bridge is stretched,due to the facts that a fixed value of contact angle,concave shape of liquid bridge profile,and a decrease of capillary force with respect to particle separation distance could probably occur,which simplifies the problem.The hysteresis of contact angle and capillary force,however,could not be involved.This work proposed six categories of concave and convex liquid bridge profiles according to simple conditions and deduced the closed-form expressions of liquid bridge geometry and capillary force.The comparison between model predictions and measurements in literature shows that the model is able to identify liquid bridge profiles quickly and predict the capillary force hysteresis reasonably well in a complete stretching-compression loop of liquid bridge.