Interfacial instability in non-Newtonian fluid layers

2003 ◽  
Vol 15 (11) ◽  
pp. 3370-3384 ◽  
Author(s):  
N. J. Balmforth ◽  
R. V. Craster ◽  
C. Toniolo
Keyword(s):  
Newtonian Fluid ◽  
Interfacial Instability ◽  
Fluid Layers

scholarly journals Interfacial instability of two inviscid fluid layers under quasi-periodic oscillations

2019 ◽  
Vol 286 ◽  
pp. 07011
Author(s):  
A. Eljaouahiry ◽  
A. Arfaoui ◽  
M. Assoul ◽  
S. Aniss
Keyword(s):  
Numerical Study ◽  
Mathieu Equation ◽  
Immiscible Fluids ◽  
Interfacial Instability ◽  
Periodic Case ◽  
Inviscid Fluid ◽  
Helmholtz Instability ◽  
Periodic Oscillations ◽  
Fluid Layers ◽  
The Stability

We investigate the effect of horizontal quasi-periodic oscillations on the stability of two immiscible fluids of different densities. The two fluid layers are confined in a cavity of infinite extension in the horizontal directions. We show in the inviscid theory that the linear stability analysis leads to the quasi-periodic Mathieu equation, with damping, which describes the evolution of the interfacial amplitude. Thus, we examine the effect of horizontal quasi-periodic vibration, with two incommensurate frequencies, on the stability of the interface. The numerical study shows the existence of two types of instability: the Kelvin-Helmholtz instability and the quasi-periodic resonances. The numerical results show also that an increase of the frequency ratio has a distabilizing effect on the Kelvin-Helmholtz instability and curves converge towards those of the periodic case.

scholarly journals Poiseuille flow in a fluid overlying a porous medium

2008 ◽  
Vol 603 ◽  
pp. 137-149 ◽  
Author(s):  
ANTONY A. HILL ◽  
BRIAN STRAUGHAN
Keyword(s):  
Porous Medium ◽  
Porous Material ◽  
Newtonian Fluid ◽  
Poiseuille Flow ◽  
Transition Layer ◽  
Layer Depth ◽  
Porous Layers ◽  
Depth Ratio ◽  
Fluid Layers ◽  
The Stability

This paper numerically investigates the instability of Poiseuille flow in a fluid overlying a porous medium saturated with the same fluid. A three-layer configuration is adopted. Namely, a Newtonian fluid overlying a Brinkman porous transition layer, which in turn overlies a layer of Darcy-type porous material. It is shown that there are two modes of instability corresponding to the fluid and porous layers, respectively. The key parameters which affect the stability characteristics of the system are the depth ratio between the porous and fluid layers and the transition layer depth.

Interfacial instability due to MHD mode coupling in aluminium reduction cells

1994 ◽  
Vol 263 ◽  
pp. 343-360 ◽  
Author(s):  
A. D. Sneyd ◽  
A. Wang
Keyword(s):  
Cell Model ◽  
Threshold Current ◽  
Interfacial Instability ◽  
Interaction Matrix ◽  
Cell Parameters ◽  
Reduction Cell ◽  
Fluid Layers ◽  
Perturbation Force ◽  
Low Threshold ◽  
Aluminium Reduction

This paper analyses instabilities on the cryolite/aluminium interface in an aluminium reduction cell. The simplified cell model is a finite rectangular tank containing the two fluid layers, and carrying a uniform normal current. The magnetic field is assumed to be a linear function of position. Several previous studies have considered waves consisting of a single Fourier component but here we consider perturbations which are a general combination of the normal gravity-wave modes. We derive a system of coupled ordinary differential equations for the time-development of the mode amplitudes, and show that instability can occur via mode interactions, the electromagnetic perturbation force due to one mode feeding energy into the other. Growth rates are determined by computing the eigenvalues of an interaction matrix, and an approximate method using only the three leading diagonals is developed. If two modes have similar frequencies they may resonate and become unstable at a very low threshold current. We consider the influence of various cell parameters and draw some general conclusions about cell design.

Effect of Periodic Oscillation on the Interfacial Instability of Two Superposed Fluid Layers in a Fully Saturated Porous Media

2021 ◽  
Author(s):  
J. Bouchgl ◽  
S. Aniss
Keyword(s):  
Porous Media ◽  
Parametric Instability ◽  
Practical Interest ◽  
Periodic Oscillation ◽  
Interfacial Instability ◽  
Physical Parameters ◽  
Saturated Porous Media ◽  
Fluid Layers ◽  
Oil Reservoir Engineering ◽  
Horizontal Oscillation

We investigate the effect of horizontal periodic oscillation on the interfacial instability of two immiscible and viscous fluids of different densities in a fully saturated porous media. A linear stability analysis of the viscous and time-dependent basic flow leads to a periodic oscillator describing the evolution of the interfacial perturbation amplitude. The horizontal oscillation leads to the occurrence of two types of instability, the Kelvin–Helmholtz’s instability and the parametric resonance. These instabilities appear at the frontier between water and petroleum and have a practical interest in oil reservoir engineering. The results show that, an increase of the oscillation frequency destabilizes the Kelvin–Helmholtz instability and displaces the parametric instability regions toward the short wavelength perturbation. Also, we examine mainly how the other physical parameters of the system affect the instabilities for various permeability and porosity values of the porous medium as well as for relative heights of the two fluid layers.

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