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Viscous fingering of miscible annular ring

Published online by Cambridge University Press:  06 April 2021

Vandita Sharma Open the ORCID record for Vandita Sharma [Opens in a new window] ,
Hamirul Bin Othman ,
Yuichiro Nagatsu Open the ORCID record for Yuichiro Nagatsu [Opens in a new window]  and
Manoranjan Mishra Open the ORCID record for Manoranjan Mishra [Opens in a new window]
Vandita Sharma
Affiliation:
Department of Mathematics, Indian Institute of Technology Ropar, 140001Rupnagar, India
Hamirul Bin Othman
Affiliation:
Department of Chemical Engineering, Tokyo University of Agriculture and Technology, 184-8588Tokyo, Japan
Yuichiro Nagatsu*
Affiliation:
Department of Chemical Engineering, Tokyo University of Agriculture and Technology, 184-8588Tokyo, Japan
Manoranjan Mishra*
Affiliation:
Department of Mathematics, Indian Institute of Technology Ropar, 140001Rupnagar, India
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

Miscible viscous fingering (VF) of the annulus of a more viscous fluid radially displaced by a less viscous fluid is investigated through both numerical computations and experimental study. We aim to understand how VF with finiteness in a radial displacement different from the classical radial VF and the instability of a slice displaced rectilinearly with a uniform velocity. It is observed that the VF of a miscible annular ring is a persistent phenomenon in contrast to the transient nature of VF of a miscible slice. Although new fingers cease to appear after some time but due to the radial spreading of the area available for VF, a finite number of fingers always remain at a later time when diffusion is the ultimate dominating force. A statistical analysis is performed for the numerical data and it is found that the second moment of the averaged profile, variance, is a non-monotonic function of time, contrary to variance in classical radial VF and rectilinear VF with one fluid sandwiched between layers of another. The minimum in the variance indicates the interaction of two fronts which is visible in terms of pressure fingers, but not the concentration fingers indicating a faster growth of pressure than the concentration growth. In addition, for existence of critical parameters for instability in terms of viscosity contrast and amount of sample, the variation of the finger length with flow rate is found to be dependent on the amount of the more viscous fluid confined in the annulus.

JFM classification

Interfacial Flows (free surface): Fingering instability Low-Reynolds-number flows: Hele-Shaw flows Low-Reynolds-number flows: Porous media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 916 , 10 June 2021 , A14
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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