# The capillary problem for an infinite trough

- Authors
- Publication Date
- Jan 01, 1993
- Source
- OpenGrey Repository
- Keywords
- Language
- English
- License
- Unknown

## Abstract

Consider an infinite trough (or wedge) with dihedral angle 2#alpha#, 0 < #alpha# < #pi# and a quantity of fluid inside contacting the edge. In equilibrium the free interface of the fluid will be a surface of constant mean curvature meeting the planar walls at a constant angle #gamma# determined from physical considerations. One obvious configuration is for the free surface to be a section of a round circular cylinder parallel to the axis of the wedge whose position is determined by the angles #alpha# and #gamma#. For #alpha# + #gamma# > #pi#/2 the cylinder configuration is unstable and bifurcation occurs. We exhibit the full family of bifurcating solutions starting with the round cylinder solution and proceeding through a ''beading up'' process into a series of spherical sections suitably positioned. Furthermore, if the edge of the wedge is a re-entrant corner (#alpha# > #pi#/2) then there are further bifurcating families. One is a secondary bifurcation from the family initially constructed while the other is a primary bifurcation from the cylinder which are less symmetric than the initial families. (orig.) / Available from TIB Hannover: RO 5389(316) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische Informationsbibliothek / SIGLE / DE / Germany