Configurational forces and shape of a sessile droplet on a rotating solid substrate

Abstract

The shape of a uniformly rotating liquid droplet deposited on a solid substrate is determined by an iterative numerical integration of the governing nonlinear differential equation. The differential equation and the boundary conditions are derived by means of the variational analysis which delivers the expressions for the specific configurational force per unit area of the liquid/vapor interface, and the configurational force along the liquid/solid/vapor contact circle. An analytical proof for the orthogonality of the specific configurational force to the surface of the droplet is constructed. The effect of rotation on the droplet?s gyrostatic shape is discussed.Ravnotezni oblik rotirajuce kapljice na ravnoj podlozi u polju gravitacije je odredjen numerickim resenjem nelinearne diferencijalne jednacine, uz koriscenje odgovarajuce iterativne procedure. Nelinearna diferencijalna jednacina i njeni granicni uslovi su izvedeni varijacionom analizom, koja daje analiticke izraze za konfiguracione sile na povrsini kapljice i uzduz linije kontakta izmedju kapljice, cvrste podloge i gasnog okruzenja. Dokazano je da je specificna konfiguraciona sila u pravcu normale na povrs kapljice. Kvalitativni i kvantitativni uticaj ugaone brzine na ravnotezni oblik kapljice je diskutovan.