scispace - formally typeset
Open Access

Linear stability of plane Poiseuille flow of two superposed fluids

S.G. Yiantsios, +1 more
Reads0
Chats0
TLDR
In this paper, the stability of two superposed fluids of different viscosity in plane Poiseuille flow is studied numerically and conditions for the growth of an interfacial wave are identified.
Abstract: 
Stability of two superposed fluids of different viscosity in plane Poiseuille flow is studied numerically. Conditions for the growth of an interfacial wave are identified. The analysis extends Yih’s results [J. Fluid Mech. 27, 337 (1967)] for small wavenumbers to large wavenumbers and accounts for differences in density and thickness ratios, as well as the effects of interfacial tension and gravity. Neutral stability diagrams for the interfacial mode are reported for a wide range of the physical parameters describing the flow. The analysis shows also that the flow is linearly unstable to a shear mode instability. The dependence of the critical Reynolds number for the shear mode on the viscosity ratio is reported. Theoretical predictions of critical Reynolds numbers for both modes of instability are compared with available experimental data.

read more

Citations
More filters
Journal ArticleDOI

Stability of viscosity stratified flows down an incline: Role of miscibility and wall slip

Sukhendu Ghosh, +1 more
- 20 May 2016 - 
TL;DR: In this article, the effects of wall velocity slip on the linear stability of a gravity-driven two-fluid flow down an incline are examined, and the results show that the presence of slip exhibits a promise for stabilizing the miscible flow system by raising the critical Reynolds number at the onset and decreasing the bandwidth of unstable wave numbers beyond the threshold of the dominant instability.

Wall-Bounded Turbulence: Structure and Passive Control

Brian Jeffrey Rosenberg
TL;DR: In terms of coherent structures, a new scaling is proposed that describes the size of the very large-scale motions throughout the flow as discussed by the authors, which suggests that interfacial tension between the two fluids acts to stabilize disturbances, helping to maintain a laminar flow.

Interface capturing in dual-flow microfluidics

Evgeniy Shapiro, +3 more
TL;DR: A computational study of the interface positioning in xylene/water flows used in polymer membrane fabrication in microfluidics finds the high-resolution scheme results in less diusive contact discontinuity and the predicted interface position compares favourably with analytic results.
Journal ArticleDOI

Modelling Bubble Lifetime of Thin Film Surfactants Solution on Fuel Spillage

Shitakha Felistus, +2 more
- 09 Jun 2021 - 
TL;DR: Felistus et al. as mentioned in this paper analyzed the lifetime of the bubble by plotting the rate of mass flow rate change against time, and showed that the stability depends on diffusive viscosity and linearized convection, respectively.
Journal ArticleDOI

Experimental measurements versus linear stability analysis for primary instability of stratified two-phase flows in a square rectangular duct

Yakov Nezihovski, +3 more
- 01 Mar 2022 - 
TL;DR: In this paper , the onset of the primary instability of two-phase stratified flow in a square duct was studied experimentally and a wide range of the two superficial velocities was explored.
References
More filters
Journal ArticleDOI

Instabilities in viscoelastic flows

Ronald G. Larson
- 01 May 1992 - 
TL;DR: In this article, the authors present a review of the latest developments as well as earlier work in this area, organized into the following categories: Taylor-Couette flows, instabilities in cone and plate-and-plate flows, parallel shear flows, extrudate distortions and fracture, Instabilities in shear flow with interfaces, extensional flows, and thermohydrodynamic instabilities.
Journal ArticleDOI

Instability due to viscosity stratification

Chia-Shun Yih
- 02 Feb 1967 - 
TL;DR: In this article, it was shown that the variation of viscosity in a fluid can cause instability, however small the Reynolds number is, and that the unstable modes are in the neighbourhood of a hidden neutral mode for the case of a single fluid, which is entirely ignored in the usual theory of hydrodynamic stability.
Journal ArticleDOI

On the Stability for Three-Dimensional Disturbances of Viscous Fluid Flow between Parallel Walls

Herbert Brian Squire
- 01 Nov 1933 - 
TL;DR: In this article, it was shown that the breakdown of laminar flow depended primarily on the size of the initial disturbance, in agreement with the Reynold's view, and that the reoughness of the walls might not be the determining factor.
Journal ArticleDOI

A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic stability

Michael Gaster
- 01 Oct 1962 - 
TL;DR: In this paper, the frequency and amplification rates for a disturbance growing with respect to time are compared with those of a spatially growing wave having the same wave number, and it is shown that the frequencies are equal to a high order of approximation.
Journal ArticleDOI

Shear-flow instability at the interface between two viscous fluids

A. P. Hooper, +1 more
- 01 Mar 1983 - 
TL;DR: In this paper, the authors considered the linear stability of the cocurrent flow of two fluids of different viscosity in an infinite region and solved the problem using both numerical and asymptotic techniques.