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Viscous fingering and deformation of a miscible circular blob in a rectilinear displacement in porous media

Published online by Cambridge University Press:  06 October 2015

Satyajit Pramanik ,
A. De Wit  and
Manoranjan Mishra
Satyajit Pramanik*
Affiliation:
Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140001, India
A. De Wit
Affiliation:
Université libre de Bruxelles (ULB), Nonlinear Physical Chemistry Unit, CP231, 1050 Brussels, Belgium
Manoranjan Mishra
Affiliation:
Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140001, India
*
†Email address for correspondence: satyajit.math16@gmail.com
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Abstract

The deformation of an initially circular miscible blob in a rectilinear displacement is investigated numerically for porous media when the blob is more viscous than the displacing fluid. We find in the parameter space spanned by the Péclet number and log-mobility ratio the existence of a new lump-shaped instability zone between two distinct regimes of comet and viscous fingering (VF) deformations. The more viscous circular blob is destabilized by VF only over a finite window of log-mobility ratio, contrary to the displacement of a more viscous finite slice with planar interfaces. This difference is attributed to the initial curvature of the miscible blob.

JFM classification

Interfacial Flows (free surface): Fingering instability Mixing: Mixing Low-Reynolds-number flows: Porous media
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 782 , 10 November 2015 , R2
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Copyright
© 2015 Cambridge University Press 

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Pramanik supplementary movie

Comet deformation of the blob for R = 3, r = 0.5, Pe = 1000

Download Pramanik supplementary movie(Video)
Video 61 KB

Pramanik supplementary movie

Lump-shaped instability of a circular blob for R = 1.25, r = 0.5, Pe = 900

Download Pramanik supplementary movie(Video)
Video 59 KB

Pramanik supplementary movie

Viscous fingering instability of a circular blob for R = 1.25, r = 0.5, Pe = 1000

Download Pramanik supplementary movie(Video)
Video 66 KB