Variational Theories of Two-Phase Continuum Poroelastic Mixtures: A Short Survey

Serpieri, Roberto; Corte, Alessandro Della; Travascio, Francesco; Rosati, Luciano

doi:10.1007/978-3-319-31721-2_17

Cited by 11 publications

(14 citation statements)

References 71 publications

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“…31,32 Additional details can be found in the Supporting Information and elsewhere. 28,29,33 Ultrasonic systems require temperature control 34 because they are susceptible to erroneous measurements induced by thermal fluctuations. For example, localized heat gains result from mechanical vibrations at solid−solid interfaces (friction), nonisothermal deformations (dampening), and cavitation.…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Reduction of Dispersion in Ultrasonically-Enhanced Micropacked Beds

Navarro-Brull

Teixeira

Zhang

et al. 2017

Ind. Eng. Chem. Res.

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Section: Methodsmentioning

confidence: 99%

“…The simulation results were obtained using our previously described model 29 , using Biot's equations to capture the propagation of ultrasound within the porous bed medium 31,32 . Additional details can be found in the Supporting Information and elsewhere 28,29,33 .…”

Section: Us-reactor Designmentioning

confidence: 99%

Reduction of Dispersion in Ultrasonically-Enhanced Micropacked Beds

Navarro-Brull

Teixeira

Zhang

et al. 2017

Ind. Eng. Chem. Res.

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“…Out of many microscopic variables presented in the solid, the geometric shape of pores, and their connectivity are most important for computing the volume occupied by the fluid. In this paper, just like in [46], as well as several papers before us [42,44,45] and others, the internal 'microscopic' volume of the pores is chosen as an important variable affecting the potential energy of the solid. This choice is true for the case when the pores' geometry will be roughly similar throughout the material.…”

Section: Definition Of Variablesmentioning

confidence: 99%

“…Furthermore, [32,33] derive the equations of porous media using additional terms in the Lagrangian coming from the kinetic energy of the microscopic fluctuations. Of particular interest to us are the works on the Variational Macroscopic Theory of Porous Media (VMTPM) which was formulated in its present form in [34][35][36][37][38][39][40][41][42][43], also summarized in a recent book [44]. In these works, the microscopic dynamics of capillary pores is modelled by a second-grade material, where the internal energy of the fluid depends on both the deformation gradient of the elastic media and the gradients of local fluid content.…”

Section: Introductionmentioning

confidence: 99%

Actively deforming porous media in an incompressible fluid: a variational approach

Farkhutdinov,

Gay-Balmaz,

Putkaradze

2021

Preprint

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Many parts of biological organisms are comprised of deformable porous media. The biological media is both pliable enough to deform in response to an outside force and can deform by itself using the work of an embedded muscle. For example, the recent work [1] has demonstrated interesting 'sneezing' dynamics of a freshwater sponge, when the sponge contracts and expands to clear itself from surrounding polluted water. We derive the equations of motion for the dynamics of such an active porous media (i.e., a deformable porous media that is capable of applying a force to itself with internal muscles), filled with an incompressible fluid. These equations of motion extend the earlier derived equation for a passive porous media filled with an incompressible fluid. We use a variational approach with a Lagrangian written as the sum of terms representing the kinetic and potential energy of the elastic matrix, and the kinetic energy of the fluid, coupled through the constraint of incompressibility. We then proceed to extend this theory by computing the case when both the active porous media and the fluid are incompressible, with the porous media still being deformable, which is often the case for biological applications. For the particular case of a uniform initial state, we rewrite the equations of motion in terms of two coupled telegraph-like equations for the material (Lagrangian) particles expressed in the Eulerian frame of reference, particularly suitable for numerical simulations, formulated for both the compressible media/incompressible fluid case and the doubly incompressible case. We derive interesting conservation laws for the motion, perform numerical simulations in both cases and show the possibility of self-propulsion of a biological organism due to particular running wave-like application of the muscle stress.

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“…Furthermore, [28,29] derive the equations of porous media using additional terms in the Lagrangian coming from the kinetic energy of the microscopic fluctuations. Of particular interest to us are the works on the Variational Macroscopic Theory of Porous Media (VMTPM) which was formulated in its present form in [30,31,32,33,34,35,36,37,38,39], also summarized in a recent book [40]. In these works, the microscopic dynamics of capillary pores is modelled by a second grade material, where the internal energy of the fluid depends on both the deformation gradient of the elastic media, and the gradients of local fluid content.…”

Section: Introductionmentioning

confidence: 99%

Geometric variational approach to the dynamics of porous medium, filled with incompressible fluid

Farkhutdinov

Gay–Balmaz²,

Putkaradze

2020

Acta Mech

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We derive the equations of motion for the dynamics of a porous media filled with an incompressible fluid. We use a variational approach with a Lagrangian written as the sum of terms representing the kinetic and potential energy of the elastic matrix, and the kinetic energy of the fluid, coupled through the constraint of incompressibility. As an illustration of the method, the equations of motion for both the elastic matrix and the fluid are derived in the spatial (Eulerian) frame. Such an approach is of relevance e.g. for biological problems, such as sponges in water, where the elastic porous media is highly flexible and the motion of the fluid has a 'primary' role in the motion of the whole system. We then analyze the linearized equations of motion describing the propagation of waves through the media. In particular, we derive the propagation of S-waves and P-waves in an isotropic media. We also analyze the stability criteria for the wave equations and show that they are equivalent to the physicality conditions of the elastic matrix. Finally, we show that the celebrated Biot's equations for waves in porous media are obtained for certain values of parameters in our models.

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Variational Theories of Two-Phase Continuum Poroelastic Mixtures: A Short Survey

Cited by 11 publications

References 71 publications

Reduction of Dispersion in Ultrasonically-Enhanced Micropacked Beds

Reduction of Dispersion in Ultrasonically-Enhanced Micropacked Beds

Actively deforming porous media in an incompressible fluid: a variational approach

Geometric variational approach to the dynamics of porous medium, filled with incompressible fluid

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