arXiv subjects

Nathan Abitbol

Publications and source records attributed to Nathan Abitbol.

2 recordsLinked to original sources

arXiv2026

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

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.

physics.flu-dyn↗

arXiv2026

Flow of yield stress fluid in a percolating network

We study the flow of a Bingham yield-stress fluid in a pore network model where the throats have radii drawn from a uniform distribution. We consider the case in which a fraction of the largest radii is blocked. The fluid can flow only through the percolating cluster that exists when the fraction is above the percolation threshold. Two distinct flow regimes are identified: above the percolation threshold the flow curve can be characterized by deterministic values of the critical pressure drop, permeability, and other observables, with subleading fluctuations that we quantify. At the percolation threshold these quantities become non-self-averaging, and their scaling is governed exclusively by the critical percolation backbone, independent of the specific realization of the radii.

physics.flu-dyn↗