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PreprintCC BY 4.0arXiv

Newtonian fluid invasion into a Yield-Stress Fluid-Saturated Medium

  • Nathan Abitbol
  • Alex Hansen
  • Alberto Rosso
  • Federico Lanza
  • Laurent Talon
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Abstract

We investigate pressure imposed two-phase flows in porous media where a Newtonian fluid displaces an immiscible Bingham yield-stress fluid. Using a pore-network model, we identify invasion patterns governed by three dimensionless parameters: the pressure-based capillary number CaP, the viscosity ratio M , and a number Rτ, the ratio of yield stress to capillary forces. Beyond the classical Lenormand regimes (viscous fingering, capillary fingering, stable displacement), we discover two new regimes: a tree-like pattern at low viscosity ratios and a progressively widening column-like pattern at high viscosity ratios. We characterize all regime transitions and establish a breakthrough condition for the invading fluid.

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Cite

BibTeXRIS
BibTeX
@misc{abitbol2026newtonian,
  title = {{Newtonian fluid invasion into a Yield-Stress Fluid-Saturated Medium}},
  author = {Nathan Abitbol and Alex Hansen and Alberto Rosso and Federico Lanza and Laurent Talon},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12824},
  eprint = {2609.12824},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12824},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Newtonian fluid invasion into a Yield-Stress Fluid-Saturated Medium
AU  - Nathan Abitbol
AU  - Alex Hansen
AU  - Alberto Rosso
AU  - Federico Lanza
AU  - Laurent Talon
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.12824
UR  - https://arxiv.org/abs/2609.12824
AB  - We investigate pressure imposed two-phase flows in porous media where a Newtonian fluid displaces an immiscible Bingham yield-stress fluid. Using a pore-network model, we identify invasion patterns governed by three dimensionless parameters: the pressure-based capillary number Ca_P, the viscosity ratio M , and a number R_τ, the ratio of yield stress to capillary forces. Beyond the classical Lenormand regimes (viscous fingering, capillary fingering, stable displacement), we discover two new regimes: a tree-like pattern at low viscosity ratios and a progressively widening column-like pattern at high viscosity ratios. We characterize all regime transitions and establish a breakthrough condition for the invading fluid.
ER  -