SFB 1313 Publication "Upscaling a Navier-Stokes-Cahn-Hilliard model for two-phase porous-media flow with solute-dependent surface tension effects"

New SFB 1313 Publication (Hasselt University / University of Stuttgart), published in the scientific journal Applicable Analysis. The work has been developed within the SFB 1313 research projects A05 and C02.

"Upscaling a Navier-Stokes-Cahn-Hilliard model for two-phase porous-media flow with solute-dependent surface tension effects"

Authors

• Sohely Sharmin (Hasselt University)
• Manuela Bastidas (Hasselt University)
• Carina Bringedal (University of Stuttgart, SFB 1313 research project A05)
• Iuliu Sorin Pop (Hasselt University, SFB 1313 co-investigator of research project C02 and Mercator Fellow)

Abstract

We consider a model for the flow of two immiscible and incompressible fluid phases in a porous medium. A surfactant is dissolved in one of the fluid phases, and its concentration at the interface separating the two fluids can change the surface tension. At the scale of pores, we assume that the flow is governed by the Navier-Stokes equations, while for the phase separation, a Cahn-Hilliard phase-field model is adopted. Using formal homogenization, we derive a two-scale model describing the averaged behaviour of the system at the larger Darcy scale, where effective quantities are found through local (cell) problems at the smaller pore scale. For this two-scale model, we formulate a numerical scheme and present numerical results highlighting the influence of the solute-dependent surface tension.