InterPore2021

Averaged Models for Two-Phase Flow in a Pore: The Effect of Hysteretic and Dynamic Contact Angles

1 Jun 2021, 14:55

15m

Oral Presentation (MS6-B) Interfacial phenomena in multiphase systems MS6-B

Speaker

Stephan B. Lunowa (Hasselt University, Computational Mathematics (CMAT))

Description

We consider a model for the flow of two immiscible fluids in a two-dimensional thin strip and in a three-dimensional tube of varying width. This represents an idealization of a pore in a porous medium. The interface separating the fluids forms a freely moving interface in contact with the wall and is driven by the fluid flow and surface tension. The contact line model incorporates Navier-slip boundary conditions and a dynamic and possibly hysteretic contact angle law.
We assume a scale separation between the typical width and the length of the thin strip. Based on asymptotic expansions, we derive effective models for the two-phase flow. These models form a system of differential algebraic equations for the interface position and the total flux. The result is Darcy-type equations for the flow, combined with a capillary pressure - saturation relationship involving dynamic effects.
Finally, we provide some numerical examples to show the effect of a varying wall width, of the viscosity ratio, of the slip boundary condition as well as of having a dynamic contact angle law. Furthermore, we compare the effective model to experimental data for the capillarity rise in tubes.

References

S. B. Lunowa, C. Bringedal, and I. S. Pop, On an averaged model for immiscible two-phase flow with surface tension and dynamic contact angle in a thin strip, Studies in Applied Mathematics, (2021). Accepted. UHasselt preprint available at uhasselt.be/Documents/CMAT/Preprints/2020/UP2006.pdf.