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Stability analysis of a particle band on the fluid–fluid interface

Published online by Cambridge University Press:  25 April 2019

Alireza Hooshanginejad ,
Benjamin C. Druecke  and
Sungyon Lee Open the ORCID record for Sungyon Lee [Opens in a new window]
Alireza Hooshanginejad
Affiliation:
Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA
Benjamin C. Druecke
Affiliation:
Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA
Sungyon Lee*
Affiliation:
Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA
*
†Email address for correspondence: [email protected]
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Abstract

We present experiments and theory for viscous fingering of a suspension of non-colloidal particles undergoing radial flow in a Hele-Shaw cell. As the suspension displaces air, shear-induced migration causes particles to move faster than the average suspension velocity and to accumulate on the suspension–air interface. The resultant particle accumulation generates a pattern in which low-concentration, low-viscosity suspension displaces high-concentration, high-viscosity suspension and is unstable due to the classic Saffman–Taylor instability mechanism. While the destabilising mechanism is well-understood, what remains unknown is the stabilising mechanism that suppresses fine fingers characteristic of miscible fingering. In this work, we demonstrate how the stable suspension–air interface interacts with the unstable miscible interface to set the critical wavelength. We present a linear stability analysis for the time-dependent radial flow and show that the wavenumber predicted by the analysis is in good agreement with parametric experiments investigating the effect of suspension concentration and gap thickness of the Hele-Shaw cell.

JFM classification

Interfacial Flows (free surface): Fingering instability Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 869 , 25 June 2019 , R2
Copyright
© 2019 Cambridge University Press 

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References

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Hooshanginejad et al. supplementary movie

The movie shows the injection of the particle suspension (30% volume fraction) into a Hele-Shaw cell at the flow rate of 100 mL/min. The gap thickness of the cell is set to 1.1 mm, while the particle diameter is given by 0.33 mm. The movie clearly demonstrates the emergence and then break-up of the particle band (with the wavenumber of 17). Following the initial break-up, a secondary break-up of the particle band is observed on the fluid-fluid interface.

Download Hooshanginejad et al. supplementary movie(Video)
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Supplementary material: PDF

Hooshanginejad et al. supplementary material

Supplementary data

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