Numerical Simulations of Nearly Incompressible Viscoelastic Membranes

TL;DR

This paper introduces a finite element numerical framework for simulating the dynamics of nearly incompressible viscoelastic liquid membranes, focusing on free-boundary flows with Maxwell-type stresses, applied to shear and extensional flows.

Contribution

It develops a novel finite element approach with a penalty method for near incompressibility in viscoelastic membranes, addressing complex free-boundary flow problems.

Findings

Effective simulation of shear flow in viscoelastic membranes

Successful modeling of extensional drawing processes

Demonstrated stability of the penalty method for near incompressibility

Abstract

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.