Force and shapes of liquid bridges between circular pads

An analytical model is presented relating the shape of an axisymmetric liquid bridge in terms of volume,v, height,h, bounding radius,r, and contact angle, , to the residual force,f, resulting from the surface tension at the liquid-vapor interface. The model is based on the assumption that gravity is negligible and the surface of the liquid bridge possesses constant mean curvature. Measurements are made of the height, bounding radius, contact angle and force for known volumes of individual, axisymmetric liquid bridges between parallel plates. Force and height comparisons are made for mercury on aluminum plates, mercury on polysiloxane-coated plates and water on polysiloxane-coated plates in air for dimensionless volumes (v/r ³) of 10 and 18. Comparisons with model predictions are also made for mercury bridges spanning a contact angle range between 138 deg and 150 deg. Finally, the shapes of liquid bridges are compared to analytical predictions. The results suggest that the constant mean curvature model, even when gravity is neglected, is an appropriate design tool that can be useful for specifying solder volumes and standoff heights for solder grid array packages.