Conjugate functional of Gauss curvature and equilibrium forms of liquid drop
UDC
517.5DOI:
https://doi.org/10.31429/vestnik-16-1-6-12Abstract
The conjugate Gauss curvature functional is constructed. It is considered on the class of axisymmetrical surfaces generated by the curves represented by the graphs of functions whose domains are orthogonal to the axis of symmetry. The functional is applied to the variational study of equilibrium forms of liquid drops. It is responsible for the formation of intermediate layer between two phases, that of the liquid and of the gas. In the variational study presented the energies of surface tension, adhesion and of the gravitational forces are included. In contrast with classical approach it is not necessary to consider the adhesion’s angle as known beforehand. It can be calculated if the width of the intermediate layer is given.
Keywords:
axisymmetrical surface, Gauss curvature, mean curvature, equilibrium form, intermediate layer, surface tension, variational problem, conjugate Gauss curvature functionalReferences
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