Fluid drop shape determination by the Rayleigh--Ritz minimization method

Abstract

The Rayleigh--Ritz (RR) method is well known as a means of minimizing energy functionals. Despite this, the technique most often employed in practice for minimizing a functional is the numerical solution of the Euler--Lagrange (EL) equations derived from the energy functional by variational minimization. In this article we employ the RR method specifically to determine the equilibrium shape of a fluid drop interface deformed by externally applied surface stresses and compare the results with numerical solution of the EL equations. We give examples of conditions where the RR method is superior in terms of simplicity and accuracy to the numerical EL solution, as well as conditions under which the method is less reliable.