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**1 - 4**of**4**### DOI: 10.2478/s11600-013-0149-6 From Slots to Tubes: The Influence of Dimensionality on Fracture Dissolution Models

"... We briefly review the models of fracture dissolution process, discussing the experimental and numerical evidence showing that this phenomenon is inherently two-dimensional and hence cannot be accurately described by one-dimensional models. The physical reason for this incompatibility is that a disso ..."

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We briefly review the models of fracture dissolution process, discussing the experimental and numerical evidence showing that this phenomenon is inherently two-dimensional and hence cannot be accurately described by one-dimensional models. The physical reason for this incompatibility is that a dissolution front in a single rock fracture is potentially unstable to small variations in local permeability, leading to spontaneous formation of dissolution channels in the rock. This leads to a dramatic increase of fissure opening rates, which must be taken into account not only in the estimation of karstification times but also in the assessment of ground subsidence, dam collapse or toxic seepage risks. Key words: dissolution, karst formation, hydrology. 1.

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### 1 Simulations of Particle-Fluid Suspensions with the Lattice-Boltzmann Equation

"... The lattice-Boltzmann model [1,2] has become a popular method for modeling fluid-dynamical behavior, because of its robustness and simplicity. In essence, we follow the time evolution of a discrete velocity distribution, which describes the number of particles moving in a given direction at a given ..."

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The lattice-Boltzmann model [1,2] has become a popular method for modeling fluid-dynamical behavior, because of its robustness and simplicity. In essence, we follow the time evolution of a discrete velocity distribution, which describes the number of particles moving in a given direction at a given space and time point. Because the model lives on a regular lattice, the

### Journal of Computational Physics

, 2010

"... Porous media space is mapped explicitly. Chemical reactions at the solidâ€“fluid boundaries lead to disso-which are well suited to complex geometries. In this paper we propose a number of algorithmic improvements, and in par-ticular a more accurate representation of the interface between the solid mat ..."

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Porous media space is mapped explicitly. Chemical reactions at the solidâ€“fluid boundaries lead to disso-which are well suited to complex geometries. In this paper we propose a number of algorithmic improvements, and in par-ticular a more accurate representation of the interface between the solid matrix and the fluid. The simplest representation of a porous material is to divide the system into cells, with each cell being either solid or fluid [14,15]. However, the accuracy of such a scheme is limited, unless a very large number of grid points are used. Such simu-lations have so far been limited to two-dimensional systems [16]. We have previously developed a lattice-Boltzmann model 0021-9991/ $- see front matter 2010 Elsevier Inc. All rights reserved.