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

Racah Institute of Physics

The Hebrew University of Jerusalem

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

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	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

Keywords

Disorder
Fractal dimension
Saffman-Taylor problem
Viscous fingereing

All Science Journal Classification (ASJC) codes

Modelling and Simulation
Applied Mathematics

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10.1051/mmnp/2018055

Cite this

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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.",

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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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U2 - 10.1051/mmnp/2018055

DO - 10.1051/mmnp/2018055

M3 - مقالة

SN - 0973-5348

VL - 15

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JO - Mathematical Modelling of Natural Phenomena

JF - Mathematical Modelling of Natural Phenomena

ER -

Viscous fingering in the presence of weak disorder

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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