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Questions tagged [porous-media]

Porous media are solid materials that contain interconnected pores allowing fluids to pass through.

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Calculating Pore Size from Permeability

I am building an experiment where one has a bed of sand on top of a porous plate. The pores allow air to be blown through the plate from the bottom but the pores must be sufficiently fine to not ...
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Not all anisotropic porous media can be associated with a symmetric permeability tensor $K_{ij}$?

My intuition tells me that permeability $K_{ij}$ of Darcy's Law is symmetric, $K_{ij}=K_{ji}$, and I am looking for an answer to show me why this is not the case. When measuring the permeability of a ...
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Does theory impose a limitation on the size of the sample to be used for measuring permeability?

Theory imposes no limitation on the size of the sample to be used but it is evident that in order to minimize effects due to local inhomogeneities in the material such as concretions, small shale ...
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Time derivative term in Navier Stokes equation for fluid in porous media

I was reading the research paper Homogenization of peristaltic flows in piezoelectric porous media and came across the hydrodynamic equation: $$\mu \nabla^2 v^f -\underline{ \rho_f (\dot{v}^f + w \...
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What is the name and notation given to the inverse of the inertial resistivity $\beta$ (aka non-Darcy factor or Forchhiemer factor)?

The viscous resistivity $\alpha$ is the reciprocal of permeability $k$. That is, $\alpha=1/k$. Considering the 1D isotropic non-Darcy equation, $$\tag{1} -\frac{dp}{dx}=\alpha \mu q+ \beta \rho q^2,$$...
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Diffusion versus dispersion

What is the difference between diffusion and dispersión in porous media? In my model mathematical, Advection-Diffusion-Reaction Equation Or Advection-Dispersion-reaction Equation ? Help please
Fernando Contreras's user avatar
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No slip boundary condition fully developed flow

My question may seem ridiculous but i'm such a mess please help me. Lets assume at the inlet of a (cylindrical) pipe there is a constant water flow with parabolic velocity profile . I know that fully ...
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Kirkendall effect: equilibrium vacancy concentration and pair interaction energy

I am reading the following article on Kirkendall effect leading to the Formation of a Hollow Binary Alloy Nanosphere: A Kinetic Monte Carlo Study. I am unable to understand or find in references the ...
we_are_always_learning's user avatar
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Numerically solving Navier-Stokes-Darcy (Brinkman) equation

I'm trying to learn fluid dynamics in porous media and I need to solve Navier-Stokes-Darcy (Brinkman) equation numerically but I'm not sure how to do that (I was trying to use method of lines for ...
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Permeability determination (estimation) from geometry in undirectional air flow through porous media

So I have to model a porous wind barrier that would stop the majority of dust from entering but also allows air to go in. I have decided to start with a 1D flow assumption with unidirectional porosity....
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The local and average Nusselt number in a square cavity

I am in the process of programming the local & average Nusselt number in a left vertical wall but my Matlab script gives me inappropriate values and it doesn't change with changing of Rayleigh ...
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Ability of some porous solids to tentatively sit on water for a while before sinking

How does a porous solid such as the cereal "Wheatena" manage to tentatively sit on water for a while before sinking? I assume it initially somehow evades capillary action, perhaps through ...
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Leaking water from leaky pots

I have two absolutely identical pots with round bottoms. Each bottom has the same number of absolutely identical holes drilled in it. In the first pot, all the holes are quite far apart, while in the ...
user1615266's user avatar
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Groundwater flow with external forcing

I want to solve the diffusion equation in porous media with some external forcing at the origin. The regular diffusion equation- $$ \frac{\partial h}{\partial t}=D\nabla^2h $$ But I want to solve for ...
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Which kind of paper has highest absorption speed? [closed]

I am experimenting to analyse the liquid wicking(radial) behaviour of various liquids. I have performed initial studies and experiments on household paper towels but they tend to deform and stick to ...
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What does it mean for resistance, as it appears in Ohm's law, to be an integral, evaluated over the body as a whole?

In literature I read: The three linear flux laws mentioned are: As seen, a correspondence exist between the hydraulic conductivity $K$, thermal conductivity $\lambda$, and electrical conductivity $\...
Armadillo's user avatar
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Diffusion in porous media - interface flow

i have been working on a problem lately where i think i m missing some basic understanding: I consider the diffusion of a macromolecule in porous media, which i see as Brownian motion through the ...
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Can Friedlander Equations be used to Model Buried Explosive

To quote from WIKIPEDIA The simplest form of a blast wave has been described and termed the Friedlander waveform.[11] It occurs when a high explosive detonates in a free field, that is, with no ...
majordoctor's user avatar
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Superfluids in areogel and porous media: why?

Aerogels are materials that are like ~90% or more air. As I understand, the topology of the material (i.e. of that part of the aerogel that is not air) is not such that air is contained into bubbles. ...
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Definition of (fully) saturated porous medium

Let us consider a porous medium and let $\psi$ be a hydraulic head. If $\psi \geq 0$ we say that porous medium is fully saturated, otherwise is unsaturated. How can I imagine saturated porous medium? ...
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Porous media flow equation in terms of fluid compressibility and determination of coefficients?

I'm having trouble understanding an equation and solution method given in literature. The 1D flow equation for "high rate" linear gas flow through a porous medium is given as: $$\tag{1} p_1-...
Armadillo's user avatar
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Fluid dynamics for the sepiolite

I would like to know some about the physics of an interesting material, the sepiolite. I mean the material from the Wikipedia article Sepiolite where are explained the general and identification ...
user250478's user avatar
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Origin of terms in the Nernst-Planck equation

We know the Nernst Planck equation is $$ \frac{\partial c}{\partial t} = - \nabla \cdot J \quad | \quad J = -\left[ D \nabla c - u c + \frac{Dze}{k_\mathrm{B} T}c\left(\nabla \phi+\frac{\partial \...
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"Directional" conductivity in linear flux-potential laws?

Question: Has the notion of "directional conductivity" been defined and used in the study of heat flow and electric current flow? Context: The table below gives three laws that describe linear flux-...
Armadillo's user avatar
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Reynolds limits on laminar flow between irregular plates (fracture)

I'm trying to understand the limits of laminar flow in a system comprised of two plates of varying width. The idea is to model a naturally fractured system and understand up to when flow and pressure ...
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Dimension reducing of heat equation 2D problem

I have two metal objects of different thickness and conductivity: 1) thicker, but poorly conductive. It's properties: $k_1, H$ 2) thin and much better conductive. It's properties: $k_2, h$ ...
EugenS's user avatar
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What are the assumptions for porous media to be considered as continuum?

The poroelastic models like - Biot theory- are built on the continuum approach. But I am not able to understand, how this heterogeneous media can be considered as a continuum. However, If the porous ...
Suman Kumari's user avatar
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2 answers
446 views

What is the meaning of effective density in porous media? Is the density of air inside the pore space not same as density of free air?

I am trying to understand the physical meaning of using effective density in porous media. Is it a fictitious value? Can't I use the density of solid and fluid as it is while modeling porous media?
Suman Kumari's user avatar
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Onsager reciprocal relations and Darcy's permeability tensor for anisotropic porous media

The Wikipedia entry on soil tensor permeability states that The tensor is symmetric by the Onsager reciprocal relations. Bear & Cheng (2010, p122) state that: The hydraulic conductivity tensor, ...
Armadillo's user avatar
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Acoustics: Construction of the pressure field with transmitted and reflected plane waves

So I have been reading one of the papers about wave manipulation, which takes advantage of the phase shifted reflection by tailoring the design of the system. The design has two domains: air and foam (...
Zhang Ze's user avatar
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Computing the porosity of a core sample from a set of digital images

Are there any references of books and/or papers about methods to compute the porosity of a given core sample (from an oil and gas reservoir) if this core is given as a set of digital images (for ...
Rodolfo Conde's user avatar
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Can the principal values and directions (axes) of a rock's permeability anisotropy be determined on a single cylindrical core sample?

If a rock core (a right-cylinder of rock), as shown at the left of the image below, has bedding planes oriented arbitrarily with respect to the long axis of the core, how does one go about determining ...
Armadillo's user avatar
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Percolation theory: What is the critical amplitude for the "backbone" of a 2-D network?

Disclaimer: I am just learning about percolation theory for the first time, so I am not too familiar with some of the terminology. Suppose you have a 2-D square lattice with bonds connecting sites. ...
Darcy's user avatar
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Percolation theory: Is there a clear relationship between "probability of connection" and "effective porosity"?

Disclaimer: I am a geophysicist, not a physicist. Sometimes we speak a slightly different language and use different terms. Suppose you have an $N$ x $N$, 2-D rectangular lattice with bonds which ...
Darcy's user avatar
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Can the coefficient of inertial resistivity ($\beta$-factor) be a 2nd rank tensor?

Question: Can the Forchheimer $\beta$-factor be a 2nd rank tensor (like permeability, $k$)? In most cases in literature, the quadratic Forchheimer equation is applied only to one-dimensional flow. ...
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Integrating the quadratic Forchheimer equation

Starting with the commonly cited Forchheimer equation: $$\tag{1} -\frac{dp}{ds}=\frac{\mu q}{kA}+\frac{\beta \rho q^2}{A^2}$$ multiplying through by density $$\tag{2} -\rho \frac{dp}{ds}=\frac{\mu \...
Armadillo's user avatar
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Darcy's law using Hubbert potential vs pseudo-pressure for a gas

How does one show the equivalence (or difference) of Darcy's law written using Hubbert's potential of a real gas to that of Darcy's law written using the concept of pseudo-pressure (aka pseudo-...
Armadillo's user avatar
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When does a finite size random graph percolate?

Assume we are simulating percolation on a 2d lattice. While the system is of finite size, we say that the critical state appears when a cluster connects two opposing ends of the lattice. The bigger ...
Dionysios Georgiadis's user avatar
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How to implement Hubbert's potential to calculate permeability using Darcy's law?

Question: How does one implement Hubbert's potential to calculate permeability without making assumptions to neglect any aspects of the potential defined by Hubbert? Question's supplemental material: ...
Armadillo's user avatar
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Permeability anisotropy of porous media

Imagine if one were to cut a cylindrical plug out of a perfectly homogeneous rock exactly along one of the principal axis of permeability anisotropy, specifically Kmax. Then, imagine inserting only ...
Armadillo's user avatar
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Biot coefficient as function of porosity

Can the Biot poroelasticity coefficient $\alpha$ be approximated as a function solely of porosity $\phi$, and if so then how (and under what conditions)? I've read (e.g. 2.02-3 here) that it can, ...
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Does groundwater flow depend on the geometry of the aquifer?

I consider two cases of a confined aquifer and want to calculate the pressure / hydraulic head in a quasi 1d case. These two cases are shown in my drawing. I assume homogenious, isotropic darcy flow, ...
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Non-Darcy Flow : Forchheimer plotting method

Recalling Darcy's equation for gas flow, assuming ($z\mu_g$) = Constant $$\tag{1} q_{g,sc}=\frac{kA}{L}\left(\frac{T_{sc}}{Tp_{sc}}\right)\left(\frac{1}{2z\mu_g}\right)(p_1^2-p_2^2)$$ For ...
Armadillo's user avatar
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Darcy Flow in porous material - consider porosity in cross-section area?

According to Darcy's Law, the volumetric flow rate Q of a fluid occuring due to a pressure difference $\Delta p$ over a distance L and through a cross-sectional area A of a porous medium (volume V) ...
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Can Smoothed-Particle Hydrodynamics (SPH) be used to simulate porous media flow and deformation?

I am trying to use Smoothed-Particle Hydrodynamics (SPH) to study fluid flow in and around porous media. The aim is to observe how it causes erosion and failure. For this, from my understanding, there ...
vkumar's user avatar
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Are there solid materials with controllable porosity?

In analogy to piezoelectric materials, where the application of an electrical field creates mechanical deformation in the material, I have the following question. Are there solid materials whose ...
seb's user avatar
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Can facial surgical mask effectively filter particles of smoke pollution?

Singapore is having an episode of its regular hazy season because of smoke from forest fires. Some people have been using surgical masks like the the one shown at the bottom of this post, presumably ...
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Darcy law yields extreme speed for gas flow through packed spheres

The Darcy law is as follows: $$u=-\frac{k}{\mu}\nabla p.$$ Assume we have a gas, then $\mu$ is about $10^{-5}$. For packed spheres a few $\rm mm$ in diameter, $k$ is of order $10^{-8}\ {\rm m^2}$. Say ...
tiam's user avatar
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How do I simulate a constant velocity flow in porous media

I am modelling gas combustion in porous media. Most contemporary models assume that the pressure drop from the porous media is small enough to disregard, but I want to include that in my investigation....
tiam's user avatar
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How can one build a multi-scale physics model of fluid flow phenomena?

I am working on a problem in Computational Fluid Dynamics, modeling multi-phase fluid flow through porous media. Though there are continuum equations to describe macroscopic flow (darcy's law, ...
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