Stable finite element approximations of two-phase flow with soluble surfactant

Abstract

Please cite this article in press as: J.W. Barrett et al., Stable finite element approximations of two-phase flow with soluble surfactant, J. Comput. Phys. (2015), http://dx.doi.org/10. 1016/j.jcp.2015.05.029 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractA parametric finite element approximation of incompressible two-phase flow with soluble surfactants is presented. The Navier-Stokes equations are coupled to bulk and surfaces PDEs for the surfactant concentrations. At the interface adsorption, desorption and stress balances involving curvature effects and Marangoni forces have to be considered. A parametric finite element approximation for the advection of the interface, which maintains good mesh properties, is coupled to the evolving surface finite element method, which is used to discretize the surface PDE for the interface surfactant concentration. The resulting system is solved together with standard finite element approximations of the Navier-Stokes equations and of the bulk parabolic PDE for the surfactant concentration. Semidiscrete and fully discrete approximations are analyzed with respect to stability, conservation and existence/uniqueness issues. The approach is validated for simple test cases and for complex scenarios, including colliding drops in a shear flow, which are computed in two and three space dimensions.

A hybrid finite volume – finite element method for bulk–surface coupled problems

“…We also assume the conservation of solute flux over the edge. Thanks to (4) and (5), this yields the condition:…”

Comparative Simulations of Taylor Flow with Surfactants Based on Sharp- and Diffuse-Interface Methods

“…The solver BGN, realized within the finite element toolbox ALBERTA [51], is based on an implementation of the parametric finite element approximation introduced in [17]. In particular, it is based on an unfitted finite element method for two-phase flow [14,19], where the bulk mesh, on which velocity, pressure and bulk surfactant are approximated, is totally independent of the polygonal interface mesh, on which the curvature and the surface surfactant are approximated.…”

“…Variants of the BGN package have been successfully applied to dendritic growth [12], snow crystal growth [13], two-phase incompressible Navier-Stokes flow [14,19], featuring insoluble [16] and soluble [17] surfactants, as well as to two-phase flow with a Boussinesq-Scriven surface fluid [18] and to the dynamics of fluidic membranes and vesicles [15,20].…”

Phase field modelling of surfactants in multi-phase flow

“…Several approaches to such problems based on the representation of the interfaces by hypersurfaces (here called sharp interface models) are available, among which we mention interface tracking methods [44,47,53,58,59,75], volume-of-fluid methods [5,42,45,61], and ALE methods [10,32,80], see also the books [14,38]. In general, the fluid-fluid interfaces undergo changes of topology, which may manifest as the breakup of droplets, pinching, coalescence, or cusp formation or tip-streaming driven by Marangoni forces.…”