Toward droplet dynamics simulation in polymer electrolyte membrane fuel cells: Three-dimensional numerical modeling of confined water droplets with dynamic contact angle and hysteresis

Abstract

This work focuses on three-dimensional simulation of the dynamics of droplets with contact-angle hysteresis. In order to consistently model the dynamics of the contact line, a combination of the linear molecular kinetic theory and the hydrodynamic theory is implemented in the present numerical method. Without presetting the contact line and/or the contact angle, such simulations are generally prone to irregularities at the contact line, which are mainly due to the imposition of the pinning and unpinning mechanisms associated with the hysteresis phenomenon. An effective treatment for this issue is proposed based on a simple procedure for calculating the nodal contact angle within the framework of enriched finite element/level set method. The resulting method also benefits from a manipulated momentum conservation equation that incorporates the effect of the liquid mass conservation correction, which is essentially important for simulations with a rather long (physical) run-time. In this paper, the proposed numerical model is validated against the previously published experimental data addressing the configuration of a water droplet on a tilted rough hydrophobic surface. In this test, the effect of the contact-line pinning as the underlying mechanism for droplet hysteresis phenomenon is also studied. The model is further employed to simulate a liquid droplet confined in a channel in the presence of air flow.

An enriched finite element/level-set model for two-phase electrohydrodynamic simulations

“…Several classes of numerical schemes have been reported in the literature for treating such discontinuities. Based on how the interface is treated, the most common classes of methods are levelset, [8][9][10][11][12] volume-of-fluid, [13][14][15] and phase-field. 16,17 Other methods include the lattice-Boltzmann, 18,19 smoothed-particle-hydrodynamics, 20,21 Immerse Interface Method (IIM), 9,22 embedded Eulerian-Lagrangian, 23,24 and Particle Finite Element Method (PFEM), 25,26 to name just a few.…”