146,795 research outputs found

### Asymptotic analysis of pollution filtration through thin random fissures between two porous media

We describe the asymptotic behaviour of a filtration problem from a
contaminated porous medium to a non-contaminated porous medium through thin
vertical fissures of fixed height h>0, of random thinness of order {\epsilon}
and which are $\epsilon$-periodically distributed. We compute the limit
velocity of the flow and the limit flux of pollutant at the interfaces between
the two porous media and the intermediate one

### Correlation effects during liquid infiltration into hydrophobic nanoporous mediums

Correlation effects arising during liquid infiltration into hydrophobic
porous medium are considered. On the basis of these effects a mechanism of
energy absorption at filling porous medium by nonwetting liquid is suggested.
In accordance with this mechanism, the absorption of mechanical energy is a
result expenditure of energy for the formation of menisci in the pores on the
shell of the infinite cluster and expenditure of energy for the formation of
liquid-porous medium interface in the pores belonging to the infinite cluster
of filled pores. It was found that in dependences on the porosity and,
consequently, in dependences on the number of filled pores neighbors, the
thermal effect of filling can be either positive or negative and the cycle of
infiltration-defiltration can be closed with full outflow of liquid. It can
occur under certain relation between percolation properties of porous medium
and the energy characteristics of the liquid-porous medium interface and the
liquid-gas interface. It is shown that a consecutive account of these
correlation effects and percolation properties of the pores space during
infiltration allow to describe all experimental data under discussion

### Anisotropic Mesh Adaptation for Finite Element Solution of Anisotropic Porous Medium Equation

Anisotropic Porous Medium Equation (APME) is developed as an extension of the
Porous Medium Equation (PME) for anisotropic porous media. A special analytical
solution is derived for APME for time-independent diffusion. Anisotropic mesh
adaptation for linear finite element solution of APME is discussed and
numerical results for two dimensional examples are presented. The solution
errors using anisotropic adaptive meshes show second order convergence.Comment: 18 pages, 13 figure

### Dispersion and Dispersivity Tensors in Saturated Porous Media with Uniaxial Symmetry

The coefficients of dispersion, D_{ij}, and the dispersivity, a_{ijkl},
appear in the expression for the flux of a solute in saturated flow through
porous media. We present a detailed analysis of these tensors in an axially
symmetric porous medium and show that in such a medium, the dispersivity is
governed by 6 independent moduli. We present also the constraints that have to
be satisfied by these moduli. We also show that at least two independent
experiments are required in order to obtain the values of these coefficients
for any three-dimensional porous medium domain.Comment: 1

### Mean survival times of absorbing triply periodic minimal surfaces

Understanding the transport properties of a porous medium from a knowledge of
its microstructure is a problem of great interest in the physical, chemical and
biological sciences. Using a first-passage time method, we compute the mean
survival time $\tau$ of a Brownian particle among perfectly absorbing traps for
a wide class of triply-periodic porous media, including minimal surfaces. We
find that the porous medium with an interface that is the Schwartz P minimal
surface maximizes the mean survival time among this class. This adds to the
growing evidence of the multifunctional optimality of this bicontinuous porous
medium. We conjecture that the mean survival time (like the fluid permeability)
is maximized for triply periodic porous media with a simply connected pore
space at porosity $\phi=1/2$ by the structure that globally optimizes the
specific surface. We also compute pore-size statistics of the model
microstructures in order to ascertain the validity of a "universal curve" for
the mean survival time for these porous media. This represents the first
nontrivial statistical characterization of triply periodic minimal surfaces.Comment: 14 pages, 5 figures, 1 tabl

### The optimal system, similarity reduction and group-invariant solutions to the Fractional Porous Medium equation and Fractional Dual Porous Medium equation

In this paper, we developed the group analysis to the time Fractional Porous
Medium Equation (FPME) and the time Fractional Dual Porous Medium Equation
(FDPME). The symmetry groups and the corresponding optimal systems of these two
equations are obtained. Based on the above results, similarity reductions are
performed and some explicit group invariant solutions are constructed

### A reducing mechanism on wave speed for chemotaxis systems with degenerate diffusion

This paper is concerned with traveling wave solutions for a chemotaxis model
with degenerate diffusion of porous medium type. We establish the existence of
semi-finite traveling waves, including the sharp type and $C^1$ type
semi-finite waves. Our results indicate that chemotaxis slows down the wave
speed of semi-finite traveling wave, that is, the traveling wave speed for
chemotaxis with porous medium (degenerate) diffusion is smaller than that for
the porous medium equation without chemotaxis. As we know, this is a new result
not shown in the existing literature. The result appears to be a little
surprising since chemotaxis is a connective force. We prove our results by the
Schauder's fixed point theorem and estimate the wave speed by a variational
approach

### Physically consistent simulation of transport of inertial particles in porous media

A new numerical approach is presented for simulating the movement of test particles suspended in an incompressible fluid flowing through a porous matrix. This two-phase particle-laden flow is based on the Navier-Stokes equations for incompressible fluid flow and equations of motion for the individual particles in which Stokes drag is dominant. The Immersed Boundary method is applied to incorporate the geometric complexity of the porous medium. A symmetry-preserving finite volume discretization method in combination with a volume penalization method resolves the flow within the porous material. The new Lagrangian particle tracking is such that for mass-less test particles no (numerical) collision with the coarsely represented porous medium occurs at any spatial resolution

### Dispersion of imbibition fronts

We have studied the dispersive behaviour of imbibition fronts in a porous
medium by X-ray tomography. Injection velocities were varied and the porous
medium was initially prewetted or not. At low velocity in the prewetted medium,
the imbibition profiles are found to be distinctly hyperdispersive. The
profiles are anomalously extended when compared to tracer fronts exhibiting
conventional (Gaussian) dispersion. We observe a strong velocity dependence of
the exponent characterizing the divergence of the dispersion coefficient for
low wetting-fluid saturation. Hyperdispersion is absent at high imbibition
velocities or when the medium is not prewetted.Comment: 8 pages, 5 figures; submitted to Europhysics Letter

### A general fractional porous medium equation

We develop a theory of existence and uniqueness for the following porous
medium equation with fractional diffusion, \{ll} \dfrac{\partial u}{\partial
t} + (-\Delta)^{\sigma/2} (|u|^{m-1}u)=0, & \qquad x\in\mathbb{R}^N,\; t>0,
[8pt] u(x,0) = f(x), & \qquad x\in\mathbb{R}^N.%. We consider data $f\in
L^1(\mathbb{R}^N)$ and all exponents $00$. Existence and
uniqueness of a weak solution is established for $m> m_*=(N-\sigma)_+ /N$,
giving rise to an $L^1$-contraction semigroup. In addition, we obtain the main
qualitative properties of these solutions. In the lower range $0<m\le m_*$
existence and uniqueness of solutions with good properties happen under some
restrictions, and the properties are different from the case above $m_*$. We
also study the dependence of solutions on $f,m$ and $\sigma$. Moreover, we
consider the above questions for the problem posed in a bounded domain.Comment: 43 pages, 2 figure

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