Phase coexistence in consolidating porous media

Cirillo, Emilio N. M.; Ianiro, Nicoletta; Sciarra, Giulio

doi:10.1103/physreve.81.061121

Cited by 16 publications

(50 citation statements)

References 18 publications

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“…In the papers [8,9] we have studied the stationary version of the problem (2.25) corresponding to the potential energies (2.24) and (6.1) to describe the possible occurance of an interface between two phases differing in fluid content. In fact this model is built in such a way to describe the existence of two states of equilibrium: the fluid-poor phase (ε s , m s ) and the fluid-rich phase (ε f , m f ) corresponding to the two minima of the double-well potential energy Ψ in (6.1).…”

Section: Negativity and Boundedness Of The Strain And Density: Proof mentioning

confidence: 99%

“…In particular, for both figures 6.1-6.2 in the top row we used as initial guess a costant function equal to the fluid-poorphase, while in the central row it has been used a costant function equal to the fluid-rich-phase. Finally, in the bottom row we used as intial guess the solution to the same stationary problem with Dirichlet boundary conditions fixing the two phases at the ends of the sample, namely, (ε(0), m(0)) = (ε s , m s ) and (ε(1), m(1)) = (ε f , m f ) (see [8]).…”

Section: Negativity and Boundedness Of The Strain And Density: Proof mentioning

confidence: 99%

“…In this paper, we study a time-dependent Allen-Cahn-like system modelling the evolution of the macroscopic strain and fluid density in a porous media which is able to produce steady states exhibiting a strong phase separation between fluid-rich and fluid-poor regions; for details see [8][9][10]. The system we are studying (referred to as problem (P) in Section 2.1) has two mathematically challenging components: (i) a coupled flux (a linear combination of strain and fluid density gradients) resembling this way with crossdiffusion problems (see [21], e.g.)…”

Section: Introductionmentioning

confidence: 99%

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Weak solutions to Allen–Cahn-like equations modelling consolidation of porous media

2016

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We study the weak solvability of a system of coupled Allen-Cahn-like equations resembling cross-diffusion which is arising as a model for the consolidation of saturated porous media. Besides using energy like estimates, we cast the special structure of the system in the framework of the Leray-Schauder fixed point principle and ensure this way the local existence of strong solutions to a regularised version of our system. Furthermore, weak convergence techniques ensure the existence of weak solutions to the original consolidation problem. The uniqueness of global-in-time solutions is guaranteed in a particular case. Moreover, we use a finite difference scheme to show the negativity of the vector of solutions.Weak solutions; cross-diffusion system; energy method; Leray-Schauder fixed point theorem; finite differences; consolidation of porous media

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Section: Negativity and Boundedness Of The Strain And Density: Proof mentioning

confidence: 99%

Section: Negativity and Boundedness Of The Strain And Density: Proof mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Weak solutions to Allen–Cahn-like equations modelling consolidation of porous media

2016

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“…In the model which is going to be presented in this paper, on the other hand, the behavior of the solid skeleton is described by means of a strain gradient model, to predict localized strains and fracture, when considering irreversible processes. To the best of author's knowledge, no general model accounting for both the above mentioned items, say localization in fluid flow and strain, can be retrieved from the literature, except a preliminary study by the author [87], stemming from previous results on modeling of porous media saturated by quasi-incompressible fluids, see [42,88,89] and [21,22,23,24,25]. Within this enhanced framework, the hydro-mechanical coupling is therefore responsible not only for the effects of average variations of the hydraulic regime within the RVE on the skeleton deformation, and vice-versa, see among others [78,3,95,19,83,84], but it can also account for the effects of capillary fingering on damaging and fracturing of the skeleton and vice-versa for the effects of strain localization on permeability variations and heterogeneous/anisotropic fluid flow.…”

Section: Introductionmentioning

confidence: 99%

Phase field modeling of partially saturated deformable porous media

Sciarra

2016

Journal of the Mechanics and Physics of Solids

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A poromechanical model of partially saturated deformable porous media is proposed based on a phase field approach at modeling the behavior of the mixture of liquid water and wet air, which saturates the pore space, the phase field being the saturation (ratio). While the standard retention curve is expected still to provide the intrinsic retention properties of the porous skeleton, depending on the porous texture, an enhanced description of surface tension between the wetting (liquid water) and the non-wetting (wet air) fluid, occupying the pore space, is stated considering a regularization of the phase field model based on an additional contribution to the overall free energy depending on the saturation gradient. The aim is to provide a more refined description of surface tension interactions.\ud An enhanced constitutive relation for the capillary pressure is established together with a suitable generalization of Darcy’s law, in which the gradient of the capillary pressure is replaced by the gradient of the so-called generalized chemical potential, which also accounts for the “force” associated to the local free energy of the phase field model. A micro-scale heuristic interpretation of the novel constitutive law of capillary pressure is proposed, in order to compare the envisaged model with that one endowed with the concept of average interfacial area.\ud The considered poromechanical model is formulated within the framework of strain gradient theory in order to account for possible effects, at laboratory scale, of the micro-scale hydro-mechanical couplings between highly-localized flows (fingering) and localized deformations of the skeleton (fracturing)

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“…In this theory two order parameters m and ε are introduced, having respectively the physical meaning of fluid density and solid strain. In [3,7] the interface separating the two coexisting phase has been studied and it has been shown that its localization properties, due to the asymmetry of the potential energy, are not trivial.…”

Section: Introductionmentioning

confidence: 99%

Kink localization under asymmetric double-well potentials

Cirillo

Ianiro²,

Sciarra³

2012

Phys. Rev. E

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We study diffuse phase interfaces under asymmetric double-well potential energies with degenerate minima and demonstrate that the limiting sharp profile, for small interface energy cost, on a finite space interval is in general not symmetric and its position depends exclusively on the second derivatives of the potential energy at the two minima (phases). We discuss an application of the general result to porous media in the regime of solid-fluid segregation under an applied pressure and describe the interface between a fluid-rich and a fluid-poor phase.

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Phase coexistence in consolidating porous media

Cited by 16 publications

References 18 publications

Weak solutions to Allen–Cahn-like equations modelling consolidation of porous media

Weak solutions to Allen–Cahn-like equations modelling consolidation of porous media

Phase field modeling of partially saturated deformable porous media

Kink localization under asymmetric double-well potentials

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