The stability of a viscous liquid in a vertical tube containing porous material

1959 ◽  
Vol 252 (1268) ◽  
pp. 120-134 ◽  
Keyword(s):  
Porous Medium ◽  
Porous Material ◽  
Density Gradient ◽  
Capillary Tube ◽  
Saturated Porous Medium ◽  
Vertical Tube ◽  
Neutral Stability ◽  
Molecular Diffusivity ◽  
Dimensionless Ratio ◽  
The Stability

If a long vertical tube filled with porous material contains a viscous solution, the density of which increases with height as a result of the presence of the dissolved substance, the equilibrium of the liquid is stable provided that the density gradient does not anywhere exceed the value d ρ /d Z = 3·390 μκ / gkb 2 Here κ , the diffusivity of the solute through the saturated porous medium, is defined to be the quantity of solute diffusing across unit area within the porous medium per unit time under unit density gradient. The above expression for the density gradient at neutral stability has been compared experimentally with Taylor’s value for the corresponding density gradient in a vertical capillary tube. For a porous medium consisting of randomly packed glass spheres of mean diameter about 0·2 mm and porosity ϵ = 0·365, it has been found that the two results are consistent provided that the ratio κ / Dϵ = 0·633, where D is the molecular diffusivity of the solute when the porous medium is absent. As this dimensionless ratio is a property of the porous material alone, it can be determined directly by diffusion measurements. An alternative method of measuring κ / Dϵ , based upon an electrical analogue, has led to a value of 0·641 for the same porous material, which is in good numerical agreement.

scholarly journals Stability and nonlinear regimes of flow over a saturated porous medium

2013 ◽  
Vol 20 (4) ◽  
pp. 543-547 ◽  
Author(s):  
T. P. Lyubimova ◽  
D. T. Baydina ◽  
D. V. Lyubimov
Keyword(s):  
Porous Medium ◽  
Saturated Porous Medium ◽  
Base Flow ◽  
Nonlinear Flow ◽  
Wave Number ◽  
Neutral Stability ◽  
Steady Plane ◽  
Stability Of Water ◽  
Parameter Values ◽  
Nonlinear Regimes

Abstract. The paper deals with the investigation of stability and nonlinear regimes of flow over the saturated porous medium applied to the problem of stability of water flow over the bottom covered with vegetation. It is shown that the velocity profile of steady plane-parallel flow has two inflection points, which results in instability of this flow. The neutral stability curves, the dependencies of critical Reynolds number and the wave number of most dangerous perturbations on the ratio of porous layer thickness to the total thickness are obtained. The nonlinear flow regimes are investigated numerically by finite difference method. It is found that at supercritical parameter values waves travelling in the direction of the base flow take place.

Effect of Local Thermal Non-Equilibrium On the Stability of the Flow in a Vertical Channel Filled with Nanofluid Saturated Porous Medium

2021 ◽  
Author(s):  
D Srinivasacharya ◽  
Dipak Barman
Keyword(s):  
Porous Medium ◽  
Saturated Porous Medium ◽  
Normal Mode Analysis ◽  
Critical Rayleigh Number ◽  
Vertical Channel ◽  
Fluid Particle ◽  
Mode Analysis ◽  
Solid Matrix ◽  
The Stability ◽  
Non Equilibrium

Abstract The stability of nanofluid flow in a vertical channel packed with a porous medium is examined for the local thermal non-equilibrium state of the fluid, particle and solid-matrix phases. The effects of Brownian motion along with thermophoresis are incorporated in the nanofluid model. The Darcy-Brinkman model for the flow in a porous medium and three-field model, each representing the fluid, particle and solid-matrix phases separately, for temperature is used. A normal mode analysis is used to obtain the eigenvalue problem for the perturbed state, which is then solved using the Chebyshev spectral collocation technique. The critical Rayleigh number and corresponding wavenumber are presented graphically for the effect of different local thermal non-equilibrium parameters. It is noticed that the influence of LTNE parameters on the convective instability is significant.

Stability of two-dimensional convection in a fluid-saturated porous medium

1995 ◽  
Vol 292 ◽  
pp. 305-323 ◽  
Author(s):  
M. De La Torre Juárez ◽  
F. H. Busse
Keyword(s):  
Porous Medium ◽  
Temporal Dynamics ◽  
Saturated Porous Medium ◽  
Two Dimensional ◽  
Viscous Effects ◽  
Oscillatory Solutions ◽  
Oscillatory State ◽  
Spatially Periodic ◽  
Fluid Saturated Porous Medium ◽  
The Stability

The range of existence and the stability of spatially periodic solutions has been studied for steady and oscillatory two-dimensional convection in a fluid-saturated porous medium. We have analysed the limit where viscous effects are dominant and Darcy's law can be applied. A Galerkin method has been used to obtain the steady and the centrosymmetric oscillatory solutions that appear in nonlinear convection at Rayleigh numbers up to 20 times the critical value. Their stability boundaries to arbitrary infinitesimal perturbations have been obtained. Above a given Rayleigh number stable oscillatory solutions are possible at wavenumbers close to the critical values. The stability of this oscillatory state with respect to infinitesimal perturbations of any wavenumber has also been studied. The resulting temporal dynamics in the different unstable regimes is briefly discussed. We show the existence of 3:1 spatial resonances of the steady roll solutions and the existence of stable centrosymmetric and non-centrosymmetric oscillatory solutions.

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.

Linear Stability Analysis of Bioconvection in Porous Media: The Effect of Fouling

2003 ◽  
Author(s):  
A. V. Kuznetsov ◽  
A. A. Avramenko
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Stability Analysis ◽  
Saturated Porous Medium ◽  
Porous Matrix ◽  
Critical Porosity ◽  
Gyrotactic Microorganisms ◽  
Porosity And Permeability ◽  
Fluid Saturated Porous Medium ◽  
The Stability

In this paper, the effect of fouling on the stability of a uniform suspension of gyrotactic motile microorganisms in a fluid saturated porous medium is investigated. Fouling may occur because of the deposition of microorganisms on a porous matrix. This deposition decreases porosity and permeability of the porous medium. Stability analysis carried out in this paper reveals that there is a critical porosity of the porous medium. If the porous medium utilized for this process has a smaller porosity than critical, the uniform suspension of gyrotactic microorganisms is stable and bioconvection does not develop. If the porous medium has lager porosity than critical, the uniform suspension is unstable and bioconvection develops.

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