Vertical excitation of axisymmetric liquid bridges

This study presents an analytical model of the dynamics of an axisymmetric liquid bridge confined between two circular pads and subjected to small vertical periodic perturbations. Such system finds important applications in microassembly and microjoint design, where force and damping need to be precisely controlled. The liquid bridge is modelled by an equivalent spring/dashpot/mass system characterised by the spring constant k, the damping coefficient b and the equivalent mass m, respectively. An abacus for k as well as analytical approximations for k, b and m based on simplifications of the Navier-Stokes equation are provided. The study is validated by experiments and numerical simulations of the system. We describe the experimental setup we designed to investigate vertical forces arising on the bottom pad from small periodic perturbations of the top pad confining the liquid meniscus. The setup allowed the accurate control of all physical and geometrical parameters relevant for the experiments. The parameters we investigated are both physical (viscosity and surface tension of the fluid) and geometrical (the edge angle between the meniscus and the pad, the height of the meniscus). The good agreement between model predictions and results let us conclude that k, b and m involve only one physical property of the liquid, namely the surface tension, the viscosity and the density, respectively.