Electrohydrodynamic linear stability of two immiscible fluids in channel flow

2006 ◽  
Vol 51 (25) ◽  
pp. 5316-5323 ◽  
Author(s):  
O. Ozen ◽  
N. Aubry ◽  
D.T. Papageorgiou ◽  
P.G. Petropoulos
Keyword(s):  
Linear Stability ◽  
Channel Flow ◽  
Immiscible Fluids

On the linear stability of channel flow over riblets

1996 ◽  
Vol 8 (11) ◽  
pp. 3194-3196 ◽  
Author(s):  
Uwe Ehrenstein
Keyword(s):  
Linear Stability ◽  
Channel Flow

The linear stability of a core–annular flow in an asymptotically corrugated tube

2002 ◽  
Vol 466 ◽  
pp. 113-147 ◽  
Author(s):  
HSIEN-HUNG WEI ◽  
DAVID S. RUMSCHITZKI
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Linear Stability ◽  
Annular Flow ◽  
Immiscible Fluids ◽  
Base Flow ◽  
Leading Order ◽  
Partial Differential ◽  
The Mean ◽  
Liquid Displacement

This paper examines the core–annular flow of two immiscible fluids in a straight circular tube with a small corrugation, in the limit where the ratio ε of the mean undisturbed annulus thickness to the mean core radius and the corrugation (characterized by the parameter σ) are both asymptotically small and where the surface tension is small. It is motivated by the problems of liquid–liquid displacement in irregular rock pores such as occur in secondary oil recovery and in the evolution of the liquid film lining the bronchii in the lungs whose diameters vary over different generations of branching. We investigate the asymptotic base flow in this limit and consider the linear stability of its leading order (in the corrugation parameter) solution. For the chosen scalings of the non-dimensional parameters the core's base flow slaves that of the annulus. The equation governing the leading-order interfacial position for a given wall corrugation function shows a competition between shear and capillarity. The former tends to align the interface shape with that of the wall and the latter tends to introduce a phase shift, which can be of either sign depending on whether the circumferential or the longitudinal component of capillarity dominates. The asymptotic linear stability of this leading-order base flow reduces to a single partial differential equation with non-constant coefficients deriving from the non-uniform base flow for the time evolution of an interfacial disturbance. Examination of a single mode k wall function allows the use of Floquet theory to analyse this equation. Direct numerical solutions of the above partial differential equation agree with the predictions of the Floquet analysis. The resulting spectrum is periodic in α- space, α being the disturbance wavenumber space. The presence of a small corrugation not only modifies (at order σ2) the primary eigenvalue of the system. In addition, short-wave order-one disturbances that would be stabilized flowing to capillarity in the absence of corrugation can, in the presence of corrugation and over time scales of order ln(1/σ), excite higher wall harmonics (α±nk) leading to the growth of unstable long waves. Similar results obtain for more complicated wall shape functions. The main result is that a small corrugation makes a core–annular flow unstable to far more disturbances than would destabilize the same uncorrugated flow system. A companion paper examines that competition between this added destabilization due to pore corrugation with the wave steepening and stabilization in the weakly nonlinear regime.

Curvature- and rotation-induced instabilities in channel flow

1990 ◽  
Vol 210 ◽  
pp. 537-563 ◽  
Author(s):  
O. John E. Matsson ◽  
P. Henrik Alfredsson
Keyword(s):  
Reynolds Number ◽  
Linear Stability ◽  
Channel Flow ◽  
Stability Theory ◽  
Critical Reynolds Number ◽  
Secondary Instability ◽  
Linear Stability Theory ◽  
Curved Channel ◽  
Dean Vortices ◽  
Coriolis Effects

In a curved channel streamwise vortices, often called Dean vortices, may develop above a critical Reynolds number owing to centrifugal effects. Similar vortices can occur in a rotating plane channel due to Coriolis effects if the axis of rotation is normal to the mean flow velocity and parallel to the walls. In this paper the flow in a curved rotating channel is considered. It is shown from linear stability theory that there is a region for which centrifugal effects and Coriolis effects almost cancel each other, which increases the critical Reynolds number substantially. The flow visualization experiments carried out show that a complete cancellation of Dean vortices can be obtained for low Reynolds number. The rotation rate for which this occurs is in close agreement with predictions from linear stability theory. For curved channel flow a secondary instability of travelling wave type is found at a Reynolds number about three times higher than the critical one for the primary instability. It is shown that rotation can completely cancel the secondary instability.

scholarly journals Linear stability analysis and numerical simulation of miscible two-layer channel flow

2009 ◽  
Vol 21 (4) ◽  
pp. 042104 ◽  
Author(s):  
K. C. Sahu ◽  
H. Ding ◽  
P. Valluri ◽  
O. K. Matar
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Linear Stability ◽  
Channel Flow ◽  
Linear Stability Analysis

scholarly journals Spatio-temporal linear stability of double-diffusive two-fluid channel flow

2012 ◽  
Vol 24 (5) ◽  
pp. 054103 ◽  
Author(s):  
Kirti Chandra Sahu ◽  
Rama Govindarajan
Keyword(s):  
Linear Stability ◽  
Channel Flow ◽  
Fluid Channel ◽  
Spatio Temporal ◽  
Two Fluid ◽  
Double Diffusive

Linear stability analysis of pressure-driven flows in channels with porous walls

2008 ◽  
Vol 604 ◽  
pp. 411-445 ◽  
Author(s):  
NILS TILTON ◽  
LUCA CORTELEZZI
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Channel Flow ◽  
Porous Wall ◽  
Inertial Effects ◽  
Porous Layers ◽  
Wall Permeability ◽  
Porous Walls ◽  
The Stability ◽  
Pressure Driven

We present the three-dimensional linear stability analysis of a pressure-driven, incompressible, fully developed, laminar flow in a channel delimited by rigid, homogeneous, isotropic, porous layers. We consider porous materials of small permeability in which the maximum fluid velocity is small compared to the mean velocity in the channel region and for which inertial effects may be neglected. We analyse the linear stability of symmetric laminar velocity profiles in channels with two identical porous walls as well as skewed laminar velocity profiles in channels with only one porous wall. We solve the fully coupled linear stability problem, arising from the adjacent channel and porous flows, using a spectral collocation technique. We validate our results by recovering the linear stability results of a flow in a channel with impermeable walls as the permeabilities of the porous layers tend to zero. We also verify that our results are consistent with the assumption of negligible inertial effects in the porous regions. We characterize the stability of pressure-driven flows by performing a parametric study in which we vary the permeability, porosity, and height of the porous layers as well as an interface coefficient, τ, associated with the momentum transfer process at the interfaces between the channel and porous regions. We find that very small amounts of wall permeability significantly affect the Orr–Sommerfeld spectrum and can dramatically decrease the stability of the channel flow. Within our assumptions, in channels with two porous walls, permeability destabilizes up to two Orr–Sommerfeld wall modes and introduces two new damped wall modes on the left branch of the spectrum. In channels with only one porous wall, permeability destabilizes up to one wall mode and introduces one new damped wall mode on the left branch of the spectrum. In both cases, permeability also introduces a new class of damped modes associated with the porous regions. The size of the unstable region delimited by the neutral curve grows substantially, and the critical Reynolds number can decrease to only 10% of the corresponding value for a channel flow with impermeable walls. We conclude our study by considering two real materials: foametal and aloxite. We fit the porosity and interface coefficient τ to published data so that the porous materials we model behave like foametal and aloxite, and we compare our results with previously published numerical and experimental results.

Sign in / Sign up

Export Citation Format

Share Document