Numerical simulations of nearly incompressible viscoelastic membranes

This work presents a novel numerical investigation of the dynamics of free-boundary flows of viscoelastic liquid membranes. The governing equation describes the balance of linear momentum, in which the stresses include the viscoelastic response to deformations of Maxwell type. A penalty method is utilized to enforce near incompressibility of the viscoelastic media, in which the penalty constant is proportional to the viscosity of the fluid. A finite element method is used, in which the slender geometry representing the liquid membrane, is discretized by linear three-node triangular elements under plane stress conditions. Two applications of interest are considered for the numerical framework provided: shear flow, and extensional flow in drawing processes.