On Two-Phase Flows with Soluble Surfactant

TL;DR

This paper develops a mathematical model for two-phase flows with soluble surfactants, extending Navier-Stokes equations, and proves local well-posedness using advanced Lp-regularity techniques.

Contribution

It introduces a generalized two-phase flow model with soluble surfactants and establishes local well-posedness through maximal Lp-regularity analysis.

Findings

Model generalizes two-phase Navier-Stokes equations with surfactants

Proves local well-posedness of the model

Utilizes recent Lp-theory results for two-phase flows

Abstract

The presence of surfactants has a pronounced effect on the surface tension and, hence, on the stress balance at the phase separating interface of two-phase flows. The transport of momentum induced by the local variations of the capillary forces are known as Marangoni effects. Here we study a model, which assumes the surfactant to be soluble in one of the adjacent bulk phases and which represents a generalization of the two-phase Navier-Stokes equations. Based on maximal Lp-regularity results for suitable linearizations we obtain local well-posedness of this model. We employ recent results from the Lp-theory of two-phase flows without surfactant.