Begell House Inc.
Journal of Porous Media
JPM
1091-028X
8
6
2005
A Note on the Swimming Problem of a Singly Flagellated Microorganism in a Fluid Flowing through a Porous Medium
551-556
Abdul Majeed
Siddiqui
Department of Mathematics, Pennsylvania State University, York Campus, 1031 Edgecomb Avenue, York, PA 17403, USA
A. R.
Ansari
Department of Mathematics & Statistics, College of Informatics & Electronics, University of Limerick, Limerick, Ireland
The swimming of microscopic organisms employing a single flagellum for propulsion in a fluid flowing through a porous medium is investigated. In a previous study, a simple model of the flow that ignored the inertial terms was adopted. Here, we use a model taking full account of the inertial effects. The flagellum is modeled by an infinite flexible but inextensible transversely waving sheet. Expressions for the velocity of propulsion of the microscopic organism are obtained. We also consider cases involving the viscosity in combination with the effective viscosity of the medium. Finally, we show that as the permeability becomes large, the results reduce to the swimming of such organisms in a viscous fluid (discounting the pores).
Darcy's Law for Immiscible Two-Phase Flow: A Theoretical Development
557-567
Francisco J
Valdes-Parada
Universidad Autonoma,
Metropolitana-Iztapalapa,
Col. Vicentino, Mexico
G.
Espinosa-Paredes
Division de Ciencias Basicas e Ingenieria, Universidad Autonoma, Metropolitana-Iztapalapa, Apartado Postal 55-534, 09340 Mexico D.F., Mexico
The aim of this paper is to show how the method of volume averaging can be used to obtain a closed set of averaged equations for bubbling flow. The Navier-Stokes equations are considered as the starting point for the volume-averaging method. The closure was formulated as an associated problem with the deviations around averaged values of the local variables. When the traditional length-scale restrictions are imposed, the volume-averaged momentum equation can be given by 〈Vk〉k − 〈Vm〉m = Kk · (−∇ 〈pk〉k + ρkgk), which is equivalent to Darcy's law. The tensor Kk is determined by closure problems that must be solved using a spatially periodic model of a two-phase flow medium.
Effect of Magnetic-Field-Dependent Viscosity on a Rotating Ferromagnetic Fluid Heated and Soluted from Below, Saturating a Porous Medium
569-588
Sunil
Department of Mathematics, National Institute of Technology, Hamirpur, (H.P.) 177005, India
Divya
Department of Applied Sciences, National Institute of Technology, Hamirpur, (H.P.)-177 005, India
R. C.
Sharma
Department of Mathematics, Himachal Pradesh University, Summer Hill, Shimla 171 005, India
The paper deals with the linear stability analysis of a rotating ferromagnetic fluid heated and soluted from below, saturating a porous medium in the presence of a uniform vertical magnetic field. The effect of magnetic-field-dependent viscosity is incorporated in the analysis. The exact solution is obtained for a fluid layer contained between two free boundaries that are constrained flat. For the case of stationary convection, rotation, stable solute gradient, and magnetic field-dependent viscosity have a stabilizing effect on the onset of instability, whereas magnetization and medium permeability may have destabilizing or stabilizing effects. The critical wave number and the critical magnetic thermal Rayleigh number for the onset of instability are also determined numerically for sufficiently large values of buoyancy magnetization parameter M1 and the results are depicted graphically. The principle of exchange of stabilities is found to hold true for the ferromagnetic fluid saturating a porous medium heated from below in the absence of stable solute gradient and rotation. The oscillatory modes are introduced due to the presence of the stable solute gradient and rotation, which were nonexistent in their absence. A sufficient condition for the nonexistence of overstability is also obtained.
Sound Absorption Properties of Porous Aluminum
589-597
He
Siyuan
LASMIS University of Technology of Troyes, 12 rue Marie Curie, 10010 Troyes, France; and Department of Materials Science, Southeast University, Nanjing 210096, China
Gong
Xiaolu
Laboratory of Mechanical System and Simultaneous Engineering, P2MN, ICD, University of Technology of Troyes, UMR CNRS STMR 6279,12 Rue Marie Curie, 10010, Troyes, France
Chen
Feng
Department of Materials Science, Southeast University, Nanjing 210096, China
The work presented in this paper concerns an investigation of the sound absorption characteristics of a porous aluminum prepared by the negative-pressure infiltration method. In order to examine the sound absorption mechanism, the curves of the sound absorption coefficient of the material studied were compared to those of a typical sound absorption structure. The effects of different porous structure parameters on the sound absorption properties have been studied. The results show that the porous aluminum has the frequency characteristics of a resonance cavity structure at low frequency, whereas those of a traditional porous sound absorption material are at high frequency. The sound absorption capability of the porous aluminum has been seen increasing with the increase of the material porosity and the decrease of pore diameters.
Numerical Study of Liquid Thermal Pumping in Porous Media
599-612
Mustapha
Najjari
Laboratoire d'Etudes des Systemes Thermiques et Energetiques, Cite Riadh, Zirig 6072 Gabes, Tunisia
Sassi Ben
Nasrallah
Laboratoire d'Études des Systèmes Thermiques et Énergétiques, Ecole Nationale d'Ingénieurs
de Monastir, Monastir 5019 Tunisie
A numerical study of the pumping mechanisms of the liquid phase from a porous medium discretely heated on the bottom face is reported. The governing equations are derived from the two-phase mixture model. Numerical results giving the evolution of the velocity vectors, the temperature, and the pressure fields during the heating and cooling phases are presented. The effects of the porous medium permeability on heat and mass transfer and on the displaced liquid mass are presented and analyzed.
An Extended Pressure Application for Transient Seepage Problems with a Free Surface
613-625
M. Tamer
Ayvaz
Pamukkale University, Faculty of Engineering, Department of Civil Engineering, 20017 Denizli, Turkey
Mustafa
Tuncan
Anadolu University, Faculty of Engineering and Architecture, Department of Civil Engineering, Eskisehir, Turkey
Halil
KARAHAN
Pamukkale University
Ahmet
Tuncan
Anadolu University, Faculty of Engineering and Architecture, Department of Civil Engineering, Eskisehir, Turkey
In this paper, a new finite-difference-solution technique for solving transient seepage problems with an unknown free surface has been proposed. The governing finite-difference equations were derived using flux conservation in the general case of anisotropic and nonuniform permeabilities and variable grid spacing, and these equations were modified by the extended pressure (EP) method. Transient seepage problems may be easily solved by the proposed solution technique, which is based on an iterative spreadsheet calculation. The technique was illustrated by several free-surface seepage problems analyzed previously by several researchers, and good agreement was obtained.
Thermal Development of Forced Convection in a Channel or Duct Partly Occupied by a Porous Medium
627-638
The classical Graetz methodology is applied to semi-analytically investigate the thermal development of forced convection in a parallel-plate channel or a circular tube partly filled by a porous medium. The Beavers-Joseph model for the interface is adopted, together with the Darcy model for the porous medium. For each of the two channel geometries, the cases of a porous core and a porous sheath are studied. For each of these, the variation of Nusselt number with axial coordinate is calculated for various values of the Darcy number and conductivity ratio, for a representative value of the interface position and a representative value of the Beavers-Joseph coefficient.
Indices
639-651