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Numerical simulation of incompressible two‐phase flows with a Boussinesq–Scriven interface stress tensor
Author(s) -
Reusken Arnold,
Zhang Yuanjun
Publication year - 2013
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.3835
Subject(s) - hagen–poiseuille equation , solver , compressibility , cauchy stress tensor , mechanics , viscous stress tensor , viscosity , flow (mathematics) , tensor (intrinsic definition) , physics , computer simulation , boussinesq approximation (buoyancy) , phase (matter) , classical mechanics , mathematics , mathematical analysis , geometry , convection , mathematical optimization , natural convection , thermodynamics , quantum mechanics , rayleigh number
SUMMARY We consider the numerical simulation of a three‐dimensional two‐phase incompressible flow with a viscous interface. The simulation is based on a sharp interface Navier–Stokes model and the Boussinesq–Scriven constitutive law for the interface viscous stress tensor. In the recent paper [Soft Matter 7, 7797–7804, 2011], a model problem with a spherical droplet in a Stokes Poiseuille flow with a Boussinesq–Scriven law for the surface viscosity has been analyzed. In that paper, relations for the droplet migration velocity are derived. We relate the results obtained with our numerical solver for the two‐phase Navier–Stokes model to these theoretical relations. Copyright © 2013 John Wiley & Sons, Ltd.