TU Darmstadt / ULB / TUbiblio

On the Two-Phase Navier-Stokes Equations with Boussinesq-Scriven Surface

Bothe, D. and Prüss, J. (2010):
On the Two-Phase Navier-Stokes Equations with Boussinesq-Scriven Surface.
12, In: Fluid J. Math. Fluid Mech., (1), pp. 133-150, [Article]

Abstract

Abstract. Two-phase ows with interface modeled as a Boussinesq- Scriven surface uid are analysed concerning their fundamental mathematical properties. This extended form of the common sharp-interface model for two-phase ows includes both surface tension and surface viscosity. For this system of partial differential equations with free interface it is shown that the energy serves as a strict Ljapunov functional, where the equilibria of the model without boundary contact consist of zero velocity and spheres for the dispersed phase. The linearizations of the problem are derived formally, showing that equilibria are linearly stable, but nonzero velocities may lead to problems which linearly are not wellposed. This phenomenon does not occur in absence of surface viscosity. The present paper aims at initiating a rigorous mathematical study of two-phase ows with surface viscosity.

Item Type: Article
Erschienen: 2010
Creators: Bothe, D. and Prüss, J.
Title: On the Two-Phase Navier-Stokes Equations with Boussinesq-Scriven Surface
Language: English
Abstract:

Abstract. Two-phase ows with interface modeled as a Boussinesq- Scriven surface uid are analysed concerning their fundamental mathematical properties. This extended form of the common sharp-interface model for two-phase ows includes both surface tension and surface viscosity. For this system of partial differential equations with free interface it is shown that the energy serves as a strict Ljapunov functional, where the equilibria of the model without boundary contact consist of zero velocity and spheres for the dispersed phase. The linearizations of the problem are derived formally, showing that equilibria are linearly stable, but nonzero velocities may lead to problems which linearly are not wellposed. This phenomenon does not occur in absence of surface viscosity. The present paper aims at initiating a rigorous mathematical study of two-phase ows with surface viscosity.

Journal or Publication Title: Fluid J. Math. Fluid Mech.
Volume: 12
Number: 1
Uncontrolled Keywords: Navier-Stokes equations, surface tension, surface viscosity, equilibria, asymptotic behaviour, Ljapunov functionals, well-posedness, linearization.
Divisions: Exzellenzinitiative > Clusters of Excellence > Center of Smart Interfaces (CSI)
04 Department of Mathematics > Mathematical Modelling and Analysis
UNSPECIFIED
Zentrale Einrichtungen
04 Department of Mathematics
Exzellenzinitiative
Exzellenzinitiative > Clusters of Excellence
Date Deposited: 05 Apr 2011 12:29
Identification Number: doi:10.1007/s00021-008-0278-x
Export:
Suche nach Titel in: TUfind oder in Google
Send an inquiry Send an inquiry

Options (only for editors)

View Item View Item