Force and shapes of liquid bridges between circular pads

An analytical model is presented relating the shape of an axisymmetric liqu id bridge in terms of volume, v, height, h, bounding radius, r, and contact angle, theta, to the residual force, f, resulting from the surface tension at the liquid-vapor interface. The model is based on the assumption that g ravity is negligible and the surface of the liquid bridge possesses constan t mean curvature. Measurements are made of the height, bounding radius, con tact angle and force for known volumes of individual, axisymmetric liquid b ridges between parallel plates. Force and height comparisons are made for m ercury 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 bri dges spanning a contact angle range between 138 deg and 150 deg. Finally, t he shapes of liquid bridges are compared to analytical predictions. The res ults suggest that the constant mean curvature model, even when gravity is n eglected, is an appropriate design tool that can be useful for specifying s older volumes and standoff heights for solder grid array packages.