On the stability of plane parallel flows of an inhomogeneous fluid

1960 ◽  
Vol 24 (2) ◽  
pp. 357-369 ◽  
Author(s):  
L.A. Dikii
Keyword(s):  
Inhomogeneous Fluid ◽  
Plane Parallel ◽  
Parallel Flows ◽  
The Stability

Stability of Two-Immiscible-Fluid Systems: A Review of Canonical Plane Parallel Flows

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
Alireza Mohammadi ◽  
Alexander J. Smits
Keyword(s):  
Fluid Layer ◽  
Future Research ◽  
Immiscible Fluid ◽  
Weakly Nonlinear ◽  
Plane Parallel ◽  
Fluid Systems ◽  
Parallel Flows ◽  
Lower Fluid ◽  
And Performance ◽  
The Stability

A brief review is given on the stability of two-fluid systems. Our interest is primarily driven by drag reduction using superhydrophobic surfaces (SHS) or liquid-infused surfaces (LIS) where the longevity and performance strongly depends on the flow stability. Although the review is limited to immiscible, incompressible, Newtonian fluids with constant properties, the subject is rich in complexity. We focus on three canonical plane parallel flows as part of the general problem: pressure-driven flow, shear-driven flow, and flow down an inclined plane. Based on the linear stability, the flow may become unstable to three modes of instabilities: a Tollmein–Schlichting wave in either the upper fluid layer or the lower fluid layer, and an interfacial mode. These instabilities may be further categorized according to the physical mechanisms that drive them. Particular aspects of weakly nonlinear analyses are also discussed, and some directions for future research are suggested.

Stability of plane parallel flows of electrically conducting fluids

1953 ◽  
Vol 49 (1) ◽  
pp. 166-168 ◽  
Author(s):  
D. H. Michael
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Electrically Conducting ◽  
Plane Parallel ◽  
Parallel Flows ◽  
Lower Reynolds Number ◽  
The Stability ◽  
Conducting Fluids

The ordinary theory of stability of plane parallel flows is considerably simplified by a result due to Squire (2) which says that if a velocity profile becomes unstable to a small three-dimensional disturbance at a given Reynolds number, then it will become unstable to a small two-dimensional disturbance at a lower Reynolds number. This result enables us to restrict investigation of the stability to the cases of two-dimensional disturbances.

On the stability of homogeneous orientation in the plane-parallel cell of a liquid crystal doped with nanoparticles

2014 ◽  
Vol 49 (5) ◽  
pp. 196-201 ◽  
Author(s):  
M. R. Hakobyan ◽  
A. A. Ghandevosyan ◽  
R. S. Hakobyan ◽  
Yu. S. Chilingaryan
Keyword(s):  
Liquid Crystal ◽  
Plane Parallel ◽  
The Stability
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