Three-dimensional linear instability in pressure-driven two-layer channel flow of a Newtonian and a Herschel-Bulkley fluid

Sahu, Kirti Chandra and Matar, O K (2010) Three-dimensional linear instability in pressure-driven two-layer channel flow of a Newtonian and a Herschel-Bulkley fluid. Physics of Fluids, 22 (11). pp. 1-14. ISSN 1070-6631

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Abstract

The three-dimensional linear stability characteristics of pressure-driven two-layer channel flow are considered, wherein a Newtonian fluid layer overlies a layer of a Herschel-Bulkley fluid. We focus on the parameter ranges for which Squire's theorem for the two-layer Newtonian problem does not exist. The modified Orr-Sommerfeld and Squire equations in each layer are derived and solved using an efficient spectral collocation method. Our results demonstrate the presence of three-dimensional instabilities for situations where the square root of the viscosity ratio is larger than the thickness ratio of the two layers; these "interfacial" mode instabilities are also present when density stratification is destabilizing. These results may be of particular interest to researchers studying the transient growth and nonlinear stability of two-fluid non-Newtonian flows. We also show that the "shear" modes, which are present at sufficiently large Reynolds numbers, are most unstable to two-dimensional disturbances.

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IITH Creators:
IITH CreatorsORCiD
Sahu, Kirti Chandrahttp://orcid.org/0000-0002-7357-1141
Item Type: Article
Uncontrolled Keywords: Density stratification; Dimensional instability; Herschel-Bulkley fluids; Linear instabilities; Linear Stability; Newtonian fluids; Newtonians; Non-linear stabilities; Parameter range; Pressure-driven; Spectral collocation method; Square roots; Thickness ratio; Transient growth; Two layers; Two-fluid; Viscosity ratios
Subjects: Chemical Engineering > Biochemical Engineering
Divisions: Department of Chemical Engineering
Depositing User: Mr. Siva Shankar K
Date Deposited: 13 Oct 2014 04:51
Last Modified: 21 Jun 2018 11:25
URI: http://raiith.iith.ac.in/id/eprint/201
Publisher URL: https://doi.org/10.1063/1.3502023
OA policy: http://www.sherpa.ac.uk/romeo/issn/1070-6631/
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