A multicomponent flow model in deformable porous media

Detmann, Bettina; Krejčı́, Pavel

doi:10.1002/mma.5482

Cited by 4 publications

(2 citation statements)

References 8 publications

(12 reference statements)

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“…In addition to describing electrical and magnetic effects, the Preisach model has proven to be a very convenient tool for mathematical modeling of fluid transport processes in porous media [221][222][223][224][225][226][227][228][229][230][231][232]. In general, the pressure-saturation relation has a nonlinear hysteresis character.…”

Section: Continuous Media and Processes In Porous Mediamentioning

confidence: 99%

The Preisach model of hysteresis: fundamentals and applications

Semenov,

Borzunov,

Meleshenko

et al. 2024

Phys. Scr.

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The Preisach model is a well-known model of hysteresis in the modern nonlinear science. This paper provides an overview of works that are focusing on the study of dynamical systems from various areas (physics, economics, biology), where the Preisach model plays a key role in the formalization of hysteresis dependencies. Here we describe the input-output relations of the classical Preisach operator, its basic properties, methods of constructing the output using the demagnetization function formalism, a generalization of the classical Preisach operator for the case of vector input-output relations. Various generalizations of the model are described here in relation to systems containing ferromagnetic and ferroelectric materials. The main attention we pay to experimental works, where the Preisach model has been used for analytic description of the experimentally observed results. Also, we describe a wide range of the technical applications of the Preisach model in such fields as energy storage devices, systems under piezoelectric effect, models of systems with long-term memory. The properties of the Preisach operator in terms of reaction to stochastic external impacts are described and a generalization of the model for the case of the stochastic threshold numbers of its elementary components is given.

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Section: Continuous Media and Processes In Porous Mediamentioning

confidence: 99%

The Preisach model of hysteresis: fundamentals and applications

Semenov,

Borzunov,

Meleshenko

et al. 2024

Phys. Scr.

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“…This relation is further coupled with the phase dynamics through the elasticity modulus depending on the proportion of healthy and tumor phases. We refer to [19] for a mathematical model of a multicomponent flow in deformable porous media, from which we take inspiration. The mass balance relations are derived from a free energy functional F D F .'…”

Section: Introductionmentioning

confidence: 99%

Analysis of a tumor model as a multicomponent deformable porous medium

Krejčı́

Rocca

Sprekels

2022

Interfaces Free Bound.

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We propose a diffuse interface model to describe a tumor as a multicomponent deformable porous medium. We include mechanical effects in the model by coupling the mass balance equations for the tumor species and the nutrient dynamics to a mechanical equilibrium equation with phase-dependent elasticity coefficients. The resulting PDE system couples two Cahn-Hilliard type equations for the tumor phase and the healthy phase with a PDE linking the evolution of the interstitial fluid to the pressure of the system, a reaction-diffusion type equation for the nutrient proportion, and a quasistatic momentum balance. We prove here that the corresponding initial-boundary value problem has a solution in appropriate function spaces.

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Numerical study of mass transfer and desorption behaviors in deformable porous media using a coupling lattice Boltzmann model

Zhao

et al. 2020

Phys. Rev. E

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A multicomponent flow model in deformable porous media

Cited by 4 publications

References 8 publications

The Preisach model of hysteresis: fundamentals and applications

The Preisach model of hysteresis: fundamentals and applications

Analysis of a tumor model as a multicomponent deformable porous medium

Numerical study of mass transfer and desorption behaviors in deformable porous media using a coupling lattice Boltzmann model

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