Modified Membrane Approximation on a Thin Liquid Sheet

Abstract

Nonlinear evolution equations for a planar liquid sheet in a void are analytically derived through the modified membrane approximation when the finite thickness of the sheet is considered, where modification is made for the evaluation of the pressure term in the momentum equations. It is found that the equations thus derived are coincident with the equations obtained through the power series expansion method with respect to the sheet thickness. It is also found that this modification is effective, in particular, for the dilational mode waves in comparison with our previous results.