Solution of the system of parametric equations of the sessile drop

Abstract

Several models of parameterization for the problem of free surface of the sessile liquid drop with nonlocal integral condition of prescribed volume are considered. The paper aims to obtain for every model specific algebraic connection among physical and geometrical parameters of the problem and compare them. This connection allows to construct the iterative process for the unknown radius of the drop with more simple boundary conditions. The positiveness of Lagrange multiplier in the problem of constrained minimization as well as uniqueness of positive meaning of the radius of the drop are proven in the paper.

Lašo, gulinčio ant horizontalios plokštumos, laisvo paviršiaus formai nustatyti nagrinejami keli parametrizavimo modeliai. I uždavinio formuluote itraukiama nelokali integraline salyga. Straipsnyje ieškoma algebrines išraiškos, sujungiančios fizikinius ir geometrinius uždavinio parametrus. Ši algebrine išraiška yra ta pati tiek dvieju antros eiles lygčiu sistemos modeliui, tiek triju pirmos eiles lygčiu sistemos modeliui. Taip pat yra irodomas Lagranžo daugiklio teigiamumas bei teigiamos lašo pagrindo spindulio reikšmes vienatinumas.

Key words:

• nonlocal boundary conditions
• free surface problems
• liquid drop