Stability of liquid bridges between parallel plates

The shape and stability of liquid bridges between parallel plates is investigated. The axisymmetric solutions of the capillary equation under microgravity conditions are nodoids, catenoids, and unduloids. The unduloids fit between parallel plates, if the slope at their inflection point falls short of the contact angle of the liquid with the two plates. Depending on whether the inflection points lie inside or outside the plates, several families of axisymmetric solutions arise. In the case of equal contact angles at both plates, the unduloids become unstable if the slope at the inflection point equals the contact angle. A second stability limit arises from the minimum volume conditions, that is, if two surface shapes enclosing the same liquid volume show up within a family of solutions of the capillary equation. Both kinds of instabilities coincide, if the contact angle equals 31.15 deg. If the contact angles at the two plates differ, the families of unduloids split up accordingly. Their stability is limited by the minimum volume condition. Respective stability diagrams are presented. Another well known asymmetry between the two plates arises from gravity. The stability limits in dependence on Bond number and liquid volume are also given.