Viscous fingering in the presence of weak disorder

Eldad Bettelheim¹ ; Oded Agam¹

¹ Racah Institute of Physics, Edmond J. Safra Campus, Hebrew University of Jerusalem, Jerusalem 91904, Israel

Mathematical modelling of natural phenomena, Tome 15 (2020), article no. 2

Résumé

We consider the problem of viscous fingering in the presence of quenched disorder, that is both weak and short-range correlated. The two-point correlation function of the harmonic measure is calculated perturbatively, and is used in order to calculate the correction and the box-counting fractal dimension. We show that the disorder increases the fractal dimension, and that its effect decreases logarithmically with the size of the fractal.

Détail

DOI : 10.1051/mmnp/2018055

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