Begell House
Journal of Porous Media
Journal of Porous Media
1091-028X
11
4
2008
Numerical Investigation of Impact and Penetration of a Droplet onto a Porous Substrate
A numerical study of droplet penetration and spreading in a porous substrate is presented. The porous substrate is modeled using a staggered arrangement of fiber-like obstacles. It is shown that the droplet penetration is sensitive to the initial impact condition. The impact of a droplet on a porous substrate results in mainly radial spreading of the drop on the surface of the substrate, with only a small fraction of the liquid penetrating into the substrate. Effect of contact angle, β, between the liquid and the substrate on the penetration of a droplet is presented. The results are described based on two parameters: (1) penetration factor, ε, which describes penetrated depth of the droplet and (2) remaining droplet mass ratio, α, which is the ratio of the mass of the droplet remaining on the top of the substrate to the initial droplet mass.
A.
Golpaygan
Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, Canada M5S-3G8
N.
Hsu
Analytic Energy Systems, Woburn, MA 01801, USA
Nasser
Ashgriz
University of Toronto
323-341
Large Particle Transport in Porous Media: Effect of Pore Plugging on the Macroscopic Transport Properties
Large particle transport in porous media plays an important role in chemical and mechanical engineering but also in the medical field, especially in cancer treatment. The major difficulty in large particle transport results from the fact that the particles themselves influence the effective transport properties by pore plugging due to particle entrapment. In this study, we used a random walk model describing the particle transport inside the pores. The effective macroscopic transport properties are determined using the results of the random walk model. It is shown that the permeability tensor strongly depends on the particle size and the injection point location, whereas the dispersion coefficients remain independent. We also determined the maximal particle radius for which particle transport can be described by the convection-diffusion equation. Another important point in the chemical and medical field is the final particle distribution, and particularly the distribution of the quantity of liquid transported by the particles. Our results show that large particles do not lead to a homogeneous liquid distribution. Hence when a large quantity of liquid should be homogeneously distributed in the porous medium, the use of smaller particles is recommended.
D.
Bauer
Universite Pierre et Marie Curie-Paris 6, Universite Paris-Sud, CNRS, F-91405, Lab FAST, Orsay F-91405, France
Benoit
Goyeau
CentraleSupélec
Dominique
Gobin
Laboratoire FAST-URA CNRS 871 (Universites Paris VI et Paris XI) Campus Universitaire − Batiment 502 91405 Orsay Cedex, France
343-360
Effect of Temperature Modulation on the onset of Darcy Convection in a Rotating Porous Medium
In this article, we study the effect of temperature modulation on the onset of thermal instability in a horizontal layer of a fluid-saturated porous medium heated from below and subjected to constant rotation. An extended Darcy model, which includes the time derivative term, has been considered, and a time-dependent periodic temperature field is applied to modulate the surfaces' temperature. A perturbation procedure based on the small amplitude of imposed temperature modulation is used to study the combined effect of rotation, permeability, and temperature modulation on the stability of flow through a porous medium. The correction in the critical Darcy Rayleigh number is calculated as a function of amplitude and frequency of modulation, the Darcy Taylor number, and the Vadasz number. It is found that both rotation and permeability suppress the onset of thermal instability. Furthermore, we find that temperature modulation can advance or delay the onset of convection.
Beer S
Bhadauria
Department of Applied Mathematics, School for Physical Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, India; Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, India
361-375
Effects of Combined Horizontal and Vertical Heterogeneity on the Onset of Transient Convection in a Porous Medium
The effects of both horizontal and vertical hydrodynamic and thermal heterogeneity on the onset of convection in a horizontal layer of a saturated porous medium, uniformly heated from below but with a nonuniform basic temperature gradient resulting from transient heating or otherwise, are studied analytically using linear stability theory for the case of weak heterogeneity. It is found that the effect of such heterogeneity on the critical value of the Rayleigh number Ra based on mean properties is of second order if the properties vary in a piecewise constant or linear fashion. The effects of horizontal heterogeneity and vertical heterogeneity are then comparable once the aspect ratio is taken into account and, to a first approximation, are independent.
Donald A.
Nield
Department of Engineering Science, University of Auckland, Auckland 1142, New Zealand
377-387
Some MHD Flows of a Second Grade Fluid through the Porous Medium
In this article, we investigate the effects of magnetic field and porous medium on some unidirectional flows of a second grade fluid. These magnetohydrodynamic (MHD) flows are produced by the application of periodic pressure gradient or by the impulsive motion of one or two boundaries or by an oscillating plate. Modified Darcy's law has been used for the flow modeling. Seven illustrative examples have been taken into account and exact analytic solutions for velocity are obtained. Besides that analytic expressions for frictional forces have been established. The corresponding results of velocity and frictional forces in the absence of a porous medium and applied magnetic field Rajagopal, 1982; Hayat et al., 2000, can be obtained from the present analysis by taking M → 0 and K → 0. The similar results for a Newtonian fluid can also be gotten as a limiting case.
I.
Khan
Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan
R.
Ellahi
Department of Mathematics and Statistics, FBAS, IIUI, Islamabad, Pakistan; Department of Mathematics, Faculty of Science, Taibah University, Al-Madeenah, Saudi Arabia
Constantin
Fetecau
Academy of Romanian Scientists, Bucharest 050094, Romania; Department of Mathematics, Technical University of Iasi 700050, Romania
389-400
Flow and Solute Transport in Saturated Porous Media: 1. The Continuum Hypothesis
The continuum hypothesis provides one alternative to dealing with transport phenomena in porous media. If adapted correctly, the continuum approach may be easier than dealing with the system at the microscopic level. However, to adopt the continuum approach to phenomena occurring in porous media, certain conditions and length scale constraints need to be satisfied. Failing to satisfy these conditions may restrict the use of this approach, and other sophisticated methods need to be devised. This article provides an overview of the conditions and length scale constraints needed to be able to adopt the continuum hypothesis. Two types of length scale constraints may be identified. The first type arises when establishing the conditions and requirements for proper upscaling; they are thus essential and hence have to be completely satisfied. They have been collected in four constraints. The second type represents those derived during mathematical manipulations and order of magnitude analysis to neglect higher-order terms. It will be shown that most of the second type of length scale constraints are automatically satisfied once the essential constraints are satisfied.
Amgad
Salama
King Abdullah University of Science and Technology (KAUST), Kingdom of Saudi Arabia; Nuclear Research Center, AEA, Abu Zabal, Egypt
Paul J.
Van Geel
Civil and Environmental Engineering Department, Carleton University, Ottawa K1S 5B6, Canada
403-413
Exact Solutions for Mixed Convection Flow Near a Stagnation Point on a Vertical Surface in a Porous Medium
We analyze some of the equations regarding the unsteady mixed convection boundary layer flow using the symmetry properties underlying in the equations. These symmetries, in particular, approximate symmetries, provide a useful tool in the reduction of the equations, which, in this case, leads to exact, invariant solutions. We present three-dimensional graphical representations of the results for some cases of the constants and the mixed convection parameter.
Saleem
Ashgar
Department of Mathematical Sciences, COMSATS Institute of Information Technology, Islamabad, Pakistan
Muhammad
Mushtaq
Department of Mathematics, COMSATS Institute of Information Technology, H-8 Islamabad, Pakistan
A. H.
Kara
School of Mathematics and Centre for Differential Equations, Continuum Mechanics and Applications, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa
415-419