Liquid bridges, edge blobs, and Scherk-type capillary surfaces

It is shown that, with the exception of very particular cases, any tubular liquid bridge configuration joining parallel plates in the absence of gravi ty must change discontinuously with tilting of the plates, thereby proving a conjecture of Concus and Finn [Phys. Fluids 10 (1998) 39-43]. Thus the st ability criteria that have appeared previously in the literature, which tak e no account of such tilting, are to some extent misleading. Conceivable co nfigurations of the liquid mass following a plate tilting are characterized , and conditions are presented under which stable drops in wedges, with dis k-type or tubular free bounding surfaces, can be expected. As a corollary o f the study, a new existence theorem for H-graphs over a square with discon tinuous data is obtained. The resulting surfaces can be interpreted as gene ralizations of the Scherk minimal surface in two senses: (a) the requiremen t of zero mean curvature is weakened to constant mean curvature, and (b) th e boundary data of the Scherk surface, which alternate between the constant s +infinity and -infinity on adjacent sides of a square, are replaced by ca pillary data alternating between two constant values, restricted by a geome trical criterion.