A finite membrane element formulation for surfactants

TL;DR

This paper introduces a finite membrane element formulation for liquids with dynamic, concentration-dependent surface tension, enabling accurate modeling of pulmonary surfactants and related phenomena in biomechanical applications.

Contribution

It presents a novel NURBS-based finite element framework for simulating liquids with variable surface tension, including contact line modeling and line tension effects.

Findings

Successfully modeled liquid films and drops with experimental validation

Demonstrated the framework's capability in simulating pulmonary surfactant behavior

Enabled analysis of complex liquid structures like bridges and sessile drops

Abstract

Surfactants play an important role in various physiological and biomechanical applications. An example is the respiratory system, where pulmonary surfactants facilitate the breathing and reduce the possibility of airway blocking by lowering the surface tension when the lung volume decreases during exhalation. This function is due to the dynamic surface tension of pulmonary surfactants, which depends on the concentration of surfactants spread on the liquid layer lining the interior surface of the airways and alveoli. Here, a finite membrane element formulation for liquids is introduced that allows for the dynamics of concentration-dependent surface tension, as is the particular case for pulmonary surfactants. A straightforward approach is suggested to model the contact line between liquid drops/menisci and planar solid substrates, which allows the presented framework to be easily used for drop shape analysis. It is further shown how line tension can be taken into account. Following an isogeometric approach, NURBS-based finite elements are used for the discretization of the membrane surface. The capabilities of the presented computational model is demonstrated by different numerical examples - such as the simulation of liquid films, constrained and unconstrained sessile drops, pendant drops and liquid bridges - and the results are compared with experimental data.