Viscous fingering in the presence of weak disorder

Eldad Bettelheim; Oded Agam

doi:10.1051/mmnp/2018055

Viscous fingering in the presence of weak disorder

Eldad Bettelheim, Oded Agam^*

^*Corresponding author for this work

Racah Institute of Physics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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.

Original language	American English
Pages (from-to)	1-11
Number of pages	11
Journal	Mathematical Modelling of Natural Phenomena
Volume	15
DOIs	https://doi.org/10.1051/mmnp/2018055
State	Published - 2020

Bibliographical note

Funding Information:
This research was supported by the Israel Science Foundation (ISF) Grants Nos. 302/14 (O.A.) and

Publisher Copyright:
© EDP Sciences, 2020.

Keywords

Disorder
Fractal dimension
Saffman-Taylor problem
Viscous fingereing

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10.1051/mmnp/2018055

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abstract = "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.",

keywords = "Disorder, Fractal dimension, Saffman-Taylor problem, Viscous fingereing",

author = "Eldad Bettelheim and Oded Agam",

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N2 - 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.

AB - 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.

KW - Disorder

KW - Fractal dimension

KW - Saffman-Taylor problem

KW - Viscous fingereing

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DO - 10.1051/mmnp/2018055

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ER -

Viscous fingering in the presence of weak disorder

Abstract

Bibliographical note

Keywords

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