Abstract We consider a model for the flow of two immiscible fluids in a two-dimensional thin strip 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.
%0 Journal Article
%1 https://doi.org/10.1111/sapm.12376
%A Lunowa, Stephan B.
%A Bringedal, Carina
%A Pop, Iuliu Sorin
%D 2021
%J Studies in Applied Mathematics
%K pa-a pa-c rp-a5 rp-c2 sfb1313
%N n/a
%R https://doi.org/10.1111/sapm.12376
%T On an averaged model for immiscible two-phase flow with surface tension and dynamic contact angle in a thin strip
%U https://onlinelibrary.wiley.com/doi/abs/10.1111/sapm.12376
%V n/a
%X Abstract We consider a model for the flow of two immiscible fluids in a two-dimensional thin strip 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.
@article{https://doi.org/10.1111/sapm.12376,
abstract = {Abstract We consider a model for the flow of two immiscible fluids in a two-dimensional thin strip 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.},
added-at = {2021-04-15T12:30:15.000+0200},
author = {Lunowa, Stephan B. and Bringedal, Carina and Pop, Iuliu Sorin},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/26ad2ceef6bdbea52ffe1b10e6f817037/sfb1313-puma},
doi = {https://doi.org/10.1111/sapm.12376},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1111/sapm.12376},
interhash = {15aa7fb16aa78fa290dc173a3aaacb9c},
intrahash = {6ad2ceef6bdbea52ffe1b10e6f817037},
journal = {Studies in Applied Mathematics},
keywords = {pa-a pa-c rp-a5 rp-c2 sfb1313},
number = {n/a},
timestamp = {2021-04-15T10:30:15.000+0200},
title = {On an averaged model for immiscible two-phase flow with surface tension and dynamic contact angle in a thin strip},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/sapm.12376},
volume = {n/a},
year = 2021
}
