Two-phase flow with surfactants: Diffuse interface models and their analysis

TL;DR

This paper introduces new diffuse and sharp interface models for surfactants, analyzing their relationships and proving an existence result for a specific diffuse interface model.

Contribution

It presents novel models for soluble and insoluble surfactants that satisfy energy inequalities and provides an asymptotic analysis and an existence proof.

Findings

Models satisfy energy inequalities

Asymptotic analysis relates diffuse and sharp interface models

Existence result established for a specific diffuse interface model

Abstract

New diffuse interface and sharp interface models for soluble and insoluble surfactants fulfilling energy inequalities are introduced. We discuss their relation with the help of asymptotic analysis and present an existence result for a particular diffuse interface model.