Reactive <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" id="d1e65" altimg="si1.gif"><mml:mi>n</mml:mi></mml:math>-species Cahn–Hilliard system: A thermodynamically-consistent model for reversible chemical reactions

Clavijo, Santiago Pena; Sarmiento, A. F.; Espath, Luis; Dalcín, Lisandro; Cortês, Adriano M. A.; Calo, Victor M.

doi:10.1016/j.cam.2018.10.007

Cited by 14 publications

(19 citation statements)

References 37 publications

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“…Moreover, from Figure 8, one can also infer that there is no formation of the species C until t > 5.6x10 −4 . Therefore, the initial condition, spatially distributed as Figure 7, goes through phase separation during the early stages and is followed by coarsening (Clavijo et al, 2019). These interactions lead to a merging process which eventually forms large and rounded structures as suggested by Figures 8 and 9.…”

Section: Thermodynamic Pressure In Geosystemsmentioning

confidence: 95%

“…At the end of such stage, the system completely consumes the mass of the species A and as expected the interfacial energy of the species C increases as the forward reaction generates more species C and therefore grows the interface. Following Clavijo et al (2019), the reaction term in the chemical process increases the free energy of the system resulting in the growth trend depicted by Figure 13 in the interval 8.02x10 −3 < t < 3.91x10 −2 . Finally, the interleaving between the chemical and mechanical responses of the solid form an elongated structure along the solid primally composed of the species B and surrounded by the species C. Due the large volume changes associated with the chemical process, we can see the stresses all along the solid and thereby the notorious inhomogeneous pressure distribution at the steady state.…”

Section: Thermodynamic Pressure In Geosystemsmentioning

confidence: 99%

“…Spinodal decomposition processes can occur, for example, in plagioclase feldspars and the binary system magnetite-ulvospinel (Carpenter, 1981;Lindsley, 1981;Droubay et al, 2011) Conventionally, the chemical energy can be written asψ ch =ψ ϕ +ψ s whereψ ϕ represents the chemical free energy of the homogeneous system andψ s stands for an interfacial potential which relates the concentration gradients. Herein, we use the definition ofψ ch outlined in Clavijo et al (2019). This functional extends to multicomponent processes of the classical free energy potential used in the Cahn-Hilliard model (Cahn & Hilliard, 1958;Elliott & Garcke, 1997).…”

Section: Chemical Energymentioning

confidence: 99%

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Modelling the chemo-mechanical responses of solid solutions far from equilibrium under heterogeneous stresses

Clavijo¹,

Espath²,

Calo³

2020

Preprint

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We present a coupled thermodynamically-consistent framework for the reactive chemomechanical responses of solid solutions. Specifically, we focus on chemically active solid solutions subject to mechanical effects due to heterogeneous stresses distributions, where the stress generation process (pressure) is driven solely by volume changes associated with the chemical processes. Throughout this paper, we use the model to describe common geological processes. Furthermore, simulation results of a three-phases solid solution provide insights into the phenomena and verify the interleaving between the physical and chemical interactions at solid-state. In particular, we show the evolution of the thermodynamic pressure as the system goes to the steady state.

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Section: Thermodynamic Pressure In Geosystemsmentioning

confidence: 95%

Section: Thermodynamic Pressure In Geosystemsmentioning

confidence: 99%

Section: Chemical Energymentioning

confidence: 99%

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Modelling the chemo-mechanical responses of solid solutions far from equilibrium under heterogeneous stresses

Clavijo¹,

Espath²,

Calo³

2020

Preprint

Self Cite

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“…IGA addresses many scientific and engineering problems (c.f., [2][3][4][5]). Some of its specific applications are in, e.g., structural analysis [6][7][8], fluid mechanics [9][10][11][12], fluid-structure interactions [13,14], chemical physics [15][16][17], and electromagnetics [18,19]. IGA uses spline basis functions, which are standard in computer-aided design (CAD), as shape functions of finite element analysis (FEA).…”

Section: Introductionmentioning

confidence: 99%

Refined isogeometric analysis for generalized Hermitian eigenproblems

Hashemian

Pardo

Calo

2021

Computer Methods in Applied Mechanics and Engineering

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We use refined isogeometric analysis (rIGA) to solve generalized Hermitian eigenproblems (Ku = λMu). rIGA conserves the desirable properties of maximum-continuity isogeometric analysis (IGA) while it reduces the solution cost by adding zero-continuity basis functions, which decrease the matrix connectivity. As a result, rIGA enriches the approximation space and reduces the interconnection between degrees of freedom. We compare computational costs of rIGA versus those of IGA when employing a Lanczos eigensolver with a shift-and-invert spectral transformation. When all eigenpairs within a given interval [λ s , λ e ] are of interest, we select several shifts σ k ∈ [λ s , λ e ] using a spectrum slicing technique. For each shift σ k , the factorization cost of the spectral transformation matrix K − σ k M controls the total computational cost of the eigensolution. Several multiplications of the operator matrix (K − σ k M) −1 M by vectors follow this factorization. Let p be the polynomial degree of the basis functions and assume that IGA has maximum continuity of p − 1. When using rIGA, we introduce C 0 separators at certain element interfaces to minimize the factorization cost. For this setup, our theoretical estimates predict computational savings to compute a fixed number of eigenpairs of up to O(p 2 ) in the asymptotic regime, that is, large problem sizes. Yet, our numerical tests show that for moderate-size eigenproblems, the total observed computational cost reduction is O(p). In addition, rIGA improves the accuracy of every eigenpair of the first N 0 eigenvalues and eigenfunctions, where N 0 is the total number of modes of the original maximum-continuity IGA discretization.

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“…The characteristic long wavelength pattern of the spinodal decomposition wave develops at time step three. Numerical simulations for the Cahn-Hilliard system are performed using a phase-field simulator described inClavijo et al (2019).…”

mentioning

confidence: 99%

Cross-Diffusion Waves as a trigger for multiscale, multiphysics Instabilities: Application to earthquakes

Regenauer‐Lieb

Schrank

et al. 2020

Preprint

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Abstract. Theoretical approaches to earthquake instabilities propose shear-dominated instabilities as a source mechanism. Here we take a fresh look at the role of possible volumetric instabilities preceding a shear instability. We investigate the phenomena that may prepare earthquake instabilities using the coupling of Thermo-Hydro-Mechano-Chemical reaction-diffusion equations in a THMC diffusion matrix. We show that the off-diagonal cross-diffusivities can give rise to a new class of waves known as cross-diffusion waves. Their unique property is that for critical conditions cross-diffusion waves can funnel wave energy into a quasi-stationary wave focus from large to small-scale. The equivalent extreme event in ocean waves and optical fibres leads to the appearance of rogue waves and high energy pulses of light in lasers. In the context of hydromechanical coupling, a rogue wave would appear as a sudden fluid pressure spike on the future fault plane. This is here interpreted as a trigger for the ultimate (shear) seismic moment release.

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Reactive n-species Cahn–Hilliard system: A thermodynamically-consistent model for reversible chemical reactions

Cited by 14 publications

References 37 publications

Modelling the chemo-mechanical responses of solid solutions far from equilibrium under heterogeneous stresses

Modelling the chemo-mechanical responses of solid solutions far from equilibrium under heterogeneous stresses

Refined isogeometric analysis for generalized Hermitian eigenproblems

Cross-Diffusion Waves as a trigger for multiscale, multiphysics Instabilities: Application to earthquakes

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