Stabilized finite element formulations for liquid membranes and their application to droplet contact

Abstract

A liquid membrane formulation is presented that is suitable to analyze liquid films and their contact behavior. The governing strong form and weak form equations are presented in the general framework of the curvilinear coordinate system that is used for the surface description of the membrane. Particular emphasis is placed on the stabilization of the in-plane equilibrium equations, which is essential for the quasi-static description of liquid membranes. Two new stabilization schemes are proposed that affect only the in-plane membrane behavior while leaving the out-of-plane membrane behavior unaffected. Further emphasis is placed on the description of line contact needed to impose nontrivial contact angles. The proposed formulation is discretized within the finite element method considering both standard Lagrange-based and isogeometric NURBS-based finite elements. Computational contact algorithms are formulated both for surface and line contact. The complete linearization of the discretize formulation is given. A large range of numerical examples is presented to illustrate the different physical aspects that are captured by the proposed formulation. The examples are further used to analyze the performance of the new stabilization schemes. © 2014 John Wiley & Sons, Ltd.