Inviscid linear stability analysis of two vertical columns of different densities in a gravitational acceleration field

We study the inviscid linear stability of a vertical interface separating two fluids of different densities and subject to a gravitational acceleration field parallel to the interface. In this arrangement, the two free streams are constantly accelerated, which means that the linear stability analysis is not amenable to Fourier or Laplace solution in time. Instead, we derive the equations analytically by the initial-value problem method and express the solution in terms of the well-known parabolic cylinder function. The results, which can be classified as an accelerating Kelvin–Helmholtz configuration, show that even in the presence of surface tension, the interface is unconditionally unstable at all wavemodes. This is a consequence of the ever increasing momentum of the free streams, as gravity accelerates them indefinitely. The instability can be shown to grow as the exponential of a quadratic function of time.

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Fingering instabilities in vertical miscible displacement flows in porous media

Journal of Fluid Mechanics ◽

10.1017/s0022112095001078 ◽

1995 ◽

Vol 288 ◽

pp. 75-102 ◽

Cited By ~ 89

Author(s):

O. Manickam ◽

G. M. Homsy

Keyword(s):

Porous Media ◽

Stability Analysis ◽

Linear Stability ◽

Critical Velocity ◽

Linear Stability Analysis ◽

Miscible Displacement ◽

Stable Region ◽

Miscible Displacements ◽

Flows In Porous Media ◽

Two Fluids

The fingering instabilities in vertical miscible displacement flows in porous media driven by both viscosity and density contrasts are studied using linear stability analysis and direct numerical simulations. The conditions under which vertical flows are different from horizontal flows are derived. A linear stability analysis of a sharp interface gives an expression for the critical velocity that determines the stability of the flow. It is shown that the critical velocity does not remain constant but changes as the two fluids disperse into each other. In a diffused profile, the flow can develop a potentially stable region followed downstream by a potentially unstable region or vice versa depending on the flow velocity, viscosity and density profiles, leading to the potential for ‘reverse’ fingering. As the flow evolves into the nonlinear regime, the strength and location of the stable region changes, which adds to the complexity and richness of finger propagation. The flow is numerically simulated using a Hartley-transform-based spectral method to study the nonlinear evolution of the instabilities. The simulations are validated by comparing to experiments. Miscible displacements with linear density and exponential viscosity dependencies on concentration are simulated to study the effects of stable zones on finger propagation. The growth rates of the mixing zone are parametrically obtained for various injection velocities and viscosity ratios.

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Linear stability of a two-fluid interface for electrohydrodynamic mixing in a channel

Journal of Fluid Mechanics ◽

10.1017/s0022112007006222 ◽

2007 ◽

Vol 583 ◽

pp. 347-377 ◽

Cited By ~ 61

Author(s):

F. LI ◽

O. OZEN ◽

N. AUBRY ◽

D. T. PAPAGEORGIOU ◽

P. G. PETROPOULOS

Keyword(s):

Stability Analysis ◽

Electric Field ◽

Linear Stability ◽

Linear Stability Analysis ◽

Neutral Stability ◽

Surface Charges ◽

Two Fluids ◽

Long Wave ◽

Normal Electric Field ◽

Two Fluid

We study the electrohydrodynamic stability of the interface between two superposed viscous fluids in a channel subjected to a normal electric field. The two fluids can have different densities, viscosities, permittivities and conductivities. The interface allows surface charges, and there exists an electrical tangential shear stress at the interface owing to the finite conductivities of the two fluids. The long-wave linear stability analysis is performed within the generic Orr–Sommerfeld framework for both perfect and leaky dielectrics. In the framework of the long-wave linear stability analysis, the wave speed is expressed in terms of the ratio of viscosities, densities, permittivities and conductivities of the two fluids. For perfect dielectrics, the electric field always has a destabilizing effect, whereas for leaky dielectrics, the electric field can have either a destabilizing or a stabilizing effect depending on the ratios of permittivities and conductivities of the two fluids. In addition, the linear stability analysis for all wavenumbers is carried out numerically using the Chebyshev spectral method, and the various types of neutral stability curves (NSC) obtained are discussed.

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