On diffuse interface modeling and simulation of surfactants in two-phase fluid flow

Abstract

An existing phase-field model of two immiscible fluids with a single soluble surfactant present is discussed in detail. We analyze the well-posedness of the model and provide strong evidence that it is mathematically ill-posed for a large set of physically relevant parameters. As a consequence, critical modifications to the model are suggested that substantially increase the domain of validity. Carefully designed numerical simulations offer informative demonstrations as to the sharpness of our theoretical results and the qualities of the physical model. A fully coupled hydrodynamic test-case demonstrates the potential to capture also non-trivial effects on the overall flow.

References in corpus (5)

• A Lattice Boltzmann Model of Ternary Fluid Mixtures
• Numerical Study of the Cahn-Hilliard Equation in One, Two and Three Dimensions
• Kinetics of Surfactant Adsorption: The Free Energy Approach
• Kinetics of Surfactant Adsorption at Fluid-Fluid Interfaces: Surfactant Mixtures
• Kinetics of non-ionic surfactant adsorption at a fluid-fluid interface from a micellar solution

Cited by in corpus (6)

• Coalescence of surfactant-laden drops by Phase Field Method
• Numerical approximation of a phase-field surfactant model with fluid flow
• Effect of surfactant-laden droplets on turbulent flow topology
• On the Stable Numerical Approximation of Two-Phase Flow with Insoluble Surfactant
• Morphology of clean and surfactant-laden droplets in homogeneous isotropic turbulence
• Well-posedness for a Navier-Stokes-Cahn-Hilliard System for Incompressible Two-phase Flows with Surfactant