Viscous banding instabilities: non-porous viscous fingering

Kowal, K. N. (2021) Viscous banding instabilities: non-porous viscous fingering. Journal of Fluid Mechanics, 926, A4. (doi: 10.1017/jfm.2021.660)

Abstract

We demonstrate a novel instability found within unconfined viscous bands/rims, or free-surface flows involving a longitudinal viscosity contrast. Such instabilities may be described as viscous banding instabilities, non-porous viscous fingering instabilities or unconfined viscous fingering instabilities of free-surface flows involving the intrusion of a less viscous fluid into a band of more viscous fluid. A consequence of this work is that viscous fingering instabilities, widely known to occur in porous media following the seminal work of Saffman & Taylor (Proc. R. Soc. Lond. A, vol. 245, 1958, pp. 312–329), also occur in non-porous environments. Although the mechanism of the viscous banding instability is characteristically different from that of the Saffman–Taylor instability, there are important similarities between the two. The main similarity is that a viscosity contrast leads to instability. A distinguishing feature is that confinement, such as the rigid walls of a Hele-Shaw cell, is not necessary for viscous banding instabilities to occur. More precisely, Saffman–Taylor instabilities are driven by a jump in dynamic pressure gradient, whereas viscous banding instabilities, or non-porous viscous fingering instabilities, are driven by a jump in hydrostatic pressure gradient, directly related to a slope discontinuity across the intrusion front. We examine the onset of instability within viscous bands down an inclined plane, determine conditions under which viscous banding instabilities occur and map out a range of behaviours in parameter space in terms of two dimensionless parameters: the viscosity ratio and the volume of fluid ahead of the intrusion front.

• Item Type: Articles
• Additional Information: This work was partially funded by L’Oréal-UNESCO UK and Ireland, For Women In Science (FWIS).
• Keywords: Fingering instability, thin films.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Kowal, Dr Katarzyna
• Authors: Kowal, K. N.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Fluid Mechanics
• Publisher: Cambridge University Press
• ISSN: 0022-1120
• ISSN (Online): 1469-7645
• Published Online: 06 September 2021
• Copyright Holders: Copyright © 2021 The Author
• First Published: First published in Journal of Fluid Mechanics 926: A4
• Publisher Policy: Reproduced in accordance with the publisher copyright policy