%0 Report %1 citeulike:7350105 %A Concus, Paul %A Finn, Robert %A McCuan, John %C Leipzig %D 1999 %K 76e17-interfacial-stability 76b45-capillarity 53a10-minimal-surfaces-surfaces-with-prescribed-mean-curvature 49q05-calculus-of-variations-minimal-surfaces %N Preprint no.: 69 %T Liquid Bridges, Edge Blobs, and Scherk-Type Capillary Surfaces %U http://www.iumj.indiana.edu/IUMJ/fulltext.php?artid=1849&\#38;year=2001&\#38;volume=50 %X It is shown that, with the exception of very particular cases, any tubular liquid bridge configuration joining parallel plates in the absence of gravity must change discontinuously with tilting of the plates, thereby proving a conjecture of Concus and Finn Phys. Fluids 10 (1998) 3943. Thus the stability criteria that have appeared previously in the literature, which take no account of such tilting, are to some extent misleading. Conceivable con gurations of the liquid mass following a plate tilting are characterized, and conditions are presented under which stable drops in wedges, with disk-type or tubular free bounding surfaces, can be expected. As a corollary of the study, a new existence theorem for H -graphs over a square with discontinuous data is obtained. The resulting surfaces can be interpreted as generalizations of the Scherk minimal surface in two senses: (a) the requirement of zero mean curvature is weakened to constant mean curvature, and (b) the boundary data of the Scherk surface, which alternate between the constants +1 and ;1 on adjacent sides of a square, are replaced by capillary data alternating between two constant values, restricted by a geometrical criterion.

@techreport{citeulike:7350105, abstract = {It is shown that, with the exception of very particular cases, any tubular liquid bridge configuration joining parallel plates in the absence of gravity must change discontinuously with tilting of the plates, thereby proving a conjecture of Concus and Finn Phys. Fluids 10 (1998) 39{43]. Thus the stability criteria that have appeared previously in the literature, which take no account of such tilting, are to some extent misleading. Conceivable con gurations of the liquid mass following a plate tilting are characterized, and conditions are presented under which stable drops in wedges, with disk-type or tubular free bounding surfaces, can be expected. As a corollary of the study, a new existence theorem for H -graphs over a square with discontinuous data is obtained. The resulting surfaces can be interpreted as generalizations of the Scherk minimal surface in two senses: (a) the requirement of zero mean curvature is weakened to constant mean curvature, and (b) the boundary data of the Scherk surface, which alternate between the constants +1 and ;1 on adjacent sides of a square, are replaced by capillary data alternating between two constant values, restricted by a geometrical criterion.}}, added-at = {2017-06-29T07:13:07.000+0200}, address = {Leipzig}, author = {Concus, Paul and Finn, Robert and McCuan, John}, biburl = {https://www.bibsonomy.org/bibtex/28e9c3b2b66ffcb495aa39bf9ff4f2431/gdmcbain}, citeulike-article-id = {7350105}, citeulike-linkout-0 = {http://www.iumj.indiana.edu/IUMJ/fulltext.php?artid=1849\&\#38;year=2001\&\#38;volume=50}, day = 7, howpublished = {Preprint}, institution = {Max-Planck-Institut fuer Mathematik in den Naturwissenschaften}, interhash = {a00f416b5c224837b9422a07e413bbde}, intrahash = {8e9c3b2b66ffcb495aa39bf9ff4f2431}, keywords = {76e17-interfacial-stability 76b45-capillarity 53a10-minimal-surfaces-surfaces-with-prescribed-mean-curvature 49q05-calculus-of-variations-minimal-surfaces}, month = dec, number = {Preprint no.: 69}, posted-at = {2010-06-23 06:39:14}, priority = {4}, timestamp = {2021-10-14T06:38:49.000+0200}, title = {Liquid Bridges, Edge Blobs, and {S}cherk-Type Capillary Surfaces}, url = {http://www.iumj.indiana.edu/IUMJ/fulltext.php?artid=1849\&\#38;year=2001\&\#38;volume=50}, year = 1999 }