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Effect of thermodynamic instability on viscous fingering of binary mixtures in a Hele-Shaw cell

Published online by Cambridge University Press:  02 October 2023

Min Chan Kim Open the ORCID record for Min Chan Kim [Opens in a new window] ,
Lopamudra Palodhi Open the ORCID record for Lopamudra Palodhi [Opens in a new window] ,
Joung Sook Hong Open the ORCID record for Joung Sook Hong [Opens in a new window]  and
Manoranjan Mishra Open the ORCID record for Manoranjan Mishra [Opens in a new window]
Min Chan Kim
Affiliation:
Department of Chemical Engineering, Jeju National University, Jeju 63243, Republic of Korea
Lopamudra Palodhi
Affiliation:
Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140001, India
Joung Sook Hong
Affiliation:
School of Chemical and Biological Engineering, Institute of Chemical Processes, Seoul National University, Seoul 08826, Republic of Korea
Manoranjan Mishra*
Affiliation:
Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140001, India
*
†Email address for correspondence: manoranjan@iitrpr.ac.in
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Abstract

The coupled effects of thermodynamic and hydrodynamic instabilities are studied during viscous fingering (VF). We introduced a modified Cahn–Hilliard phase-field model in conjunction with the Korteweg force in the classical VF model and derived consistent governing equations. The free energy of the partially miscible system is described using a modified Flory–Huggins model, which allows us to investigate the temporal evolution of spatial inhomogeneities. The mass flux in the Cahn–Hilliard equations is modified according to modern diffusion theory. The governing equations have been solved through an in-house model implementation using the COMSOL multiphysics software. We successfully demonstrated the transition from the finger-like structures to the droplet formation during spinodal decomposition as demonstrated experimentally in the literature. Our results are also in agreement with earlier numerical results obtained using a classical Landau type mixing energy. We further systematically studied the effects of the Margules parameter (interaction parameter) and the gradient parameter, which is associated to the thermodynamic length scale and capillary number on the VF. Aysmmetric features of the binary mixture are also investigated showing a stronger thermodynamic effect on the system with increasing phase separation and, hence, droplet formation.

JFM classification

Interfacial Flows (free surface): Fingering instability Low-Reynolds-number flows: Hele-Shaw flows Multiphase and Particle-laden Flows: Multiphase flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 972 , 10 October 2023 , A23
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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