scholarly journals Time-Fractional Phase Field Model of Electrochemical Impedance

2021 ◽  
Vol 5 (4) ◽  
pp. 191
Author(s):  
Pavel E. L’vov ◽  
Renat T. Sibatov ◽  
Igor O. Yavtushenko ◽  
Evgeny P. Kitsyuk
Keyword(s):  
Phase Field ◽  
Chemical Potential ◽  
Electrochemical Impedance ◽  
Phase Field Model ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary ◽  
Warburg Impedance ◽  
Cahn Hilliard Equation ◽  
Dimensional Cell ◽  
Additional Calculation

In this paper, electrochemical impedance responses of subdiffusive phase transition materials are calculated and analyzed for one-dimensional cell with reflecting and absorbing boundary conditions. The description is based on the generalization of the diffusive Warburg impedance within the fractional phase field approach utilizing the time-fractional Cahn–Hilliard equation. The driving force in the model is the chemical potential of ions, that is described in terms of the phase field allowing us to avoid additional calculation of the activity coefficient. The derived impedance spectra are applied to describe the response of supercapacitors with polyaniline/carbon nanotube electrodes.

scholarly journals Phase field model with a variable chemical potential

2002 ◽  
Vol 132 (4) ◽  
pp. 993-1019 ◽  
Author(s):  
Yoshihiro Tonegawa
Keyword(s):  
Phase Field ◽  
Hausdorff Distance ◽  
Mean Curvature ◽  
Field Model ◽  
Chemical Potential ◽  
Phase Field Model ◽  
Hilliard Equation ◽  
Variable Chemical ◽  
Energy Bound ◽  
Cahn Hilliard Equation

We study some asymptotic behaviour of phase interfaces with variable chemical potential under the uniform energy bound. The problem is motivated by the Cahn-Hilliard equation, where one has a control of the total energy and chemical potential. We show that the limit interface is an integral varifold with generalized Lp mean curvature. The convergence of interfaces as 0 is in the Hausdorff distance sense.

scholarly journals Optimal control of stochastic phase-field models related to tumor growth

2020 ◽  
Vol 26 ◽  
pp. 104
Author(s):  
Carlo Orrieri ◽  
Elisabetta Rocca ◽  
Luca Scarpa
Keyword(s):  
Optimal Control ◽  
Tumor Growth ◽  
Phase Field ◽  
Phase Field Model ◽  
Growth Dynamics ◽  
Necessary Optimality Conditions ◽  
Reaction Diffusion ◽  
Adjoint System ◽  
Reaction Diffusion Equation ◽  
Cahn Hilliard Equation

We study a stochastic phase-field model for tumor growth dynamics coupling a stochastic Cahn-Hilliard equation for the tumor phase parameter with a stochastic reaction-diffusion equation governing the nutrient proportion. We prove strong well-posedness of the system in a general framework through monotonicity and stochastic compactness arguments. We introduce then suitable controls representing the concentration of cytotoxic drugs administered in medical treatment and we analyze a related optimal control problem. We derive existence of an optimal strategy and deduce first-order necessary optimality conditions by studying the corresponding linearized system and the backward adjoint system.

Suppression of Anomalous Interface Effects by Localization of Solute Redistribution in Thin Interface Phase-Field Modeling of Solidification

2005 ◽  
Vol 475-479 ◽  
pp. 3197-3202
Author(s):  
Won Tae Kim ◽  
Seong Gyoon Kim
Keyword(s):  
Phase Field ◽  
Chemical Potential ◽  
Phase Field Model ◽  
Field Calculation ◽  
Solute Redistribution ◽  
Grid Spacing ◽  
Potential Jump ◽  
Narrow Region ◽  
Enhanced Surface ◽  
Interface Effects

A phase field model for alloy solidification was developed to suppress the anomalous interface effects such as enhanced surface diffusion, chemical potential jump and surface stretching by localizing the solute redistribution into a narrow region within the phase-field interface. Application of this model to a free dendritic growth in an undercooled liquid yields quantitatively the same results as previously reported anti-trapping model. By localization of the solute redistribution into a region of single grid spacing the anomalous interfacial effects can be effectively suppressed. This model can be used for quantitative phase field calculation with an enhanced computational efficiency.

Liquid phase stratification induced by large temperature gradient during spinodal decomposition in Fe–Cr alloys: A phase-field study

2021 ◽  
pp. 2150374
Author(s):  
Lifei Du ◽  
Runbo Tian ◽  
Tiantian Shi ◽  
Youqi Cao
Keyword(s):  
Liquid Phase ◽  
Temperature Gradient ◽  
Spinodal Decomposition ◽  
Phase Field ◽  
Anisotropic Diffusion ◽  
Phase Field Model ◽  
Solute Diffusion ◽  
Large Temperature ◽  
Cahn Hilliard Equation ◽  
Kinetics Of

The spinodal decomposition in Fe-40at.%Cr binary alloy is numerically studied by implementing the phase-field model based on Cahn–Hilliard equation. Effects of different temperature gradients on the solute distributing characteristics during the spinodal decomposition are investigated. In the system with a temperature gradient, the phase decomposition happens gradually from low temperature to high temperature, and a metastable stratification is achieved with specified temperature distribution. The critical temperature and corresponding temperature gradient are specified for the obvious solute stratification in the binary Fe–Cr alloy. The kinetics of the solute diffusion during the spinodal decomposition is discussed to reveal the liquid phase stratification induced by the anisotropic diffusion with the nonuniform temperature field. Therefore, tailoring the heat treatment during the spinodal decomposition in Fe–Cr binary alloys might be an efficient way to obtain nanometer coherent microstructures with specified solute distribution.

scholarly journals Effect of the Particle Size Distribution on the Cahn-Hilliard Dynamics in a Cathode of Lithium-Ion Batteries

Batteries ◽  
2020 ◽  
Vol 6 (2) ◽  
pp. 29
Author(s):  
Pavel L’vov ◽  
Renat Sibatov
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Phase Field ◽  
Single Phase ◽  
Field Model ◽  
Phase Field Model ◽  
Hilliard Equation ◽  
Wide Range ◽  
Cahn Hilliard Equation

The phase-field model based on the Cahn-Hilliard equation is employed to simulate lithium intercalation dynamics in a cathode with particles of distributed size. We start with a simplified phase-field model for a single submicron particle under galvanostatic condition. We observe two stages associated with single-phase and double-phase patterns typical for both charging and discharging processes. The single-phase stage takes approximately 10–15% of the process and plays an important role in the intercalation dynamics. We establish the laws for speed of front propagation and evolution of single-phase concentration valid for different sizes of electrode particles and a wide range of temperatures and C-rates. The universality of these laws allows us to formulate the boundary condition with time-dependent flux density for the Cahn-Hilliard equation and analyze the phase-field intercalation in a heterogeneous cathode characterized by the particle size distribution.

Convergence of the phase field model to its sharp interface limits

1998 ◽  
Vol 9 (4) ◽  
pp. 417-445 ◽  
Author(s):  
GUNDUZ CAGINALP ◽  
XINFU CHEN
Keyword(s):  
Surface Tension ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Field Equations ◽  
Two Phase ◽  
Cahn Equation ◽  
Phase Field Equations ◽  
Cahn Hilliard Equation ◽  
Surface Tension Model

We consider the distinguished limits of the phase field equations and prove that the corresponding free boundary problem is attained in each case. These include the classical Stefan model, the surface tension model (with or without kinetics), the surface tension model with zero specific heat, the two phase Hele–Shaw, or quasi-static, model. The Hele–Shaw model is also a limit of the Cahn–Hilliard equation, which is itself a limit of the phase field equations. Also included in the distinguished limits is the motion by mean curvature model that is a limit of the Allen–Cahn equation, which can in turn be attained from the phase field equations.

Phase Field Model of Electrochemical Impedance Spectroscopy

2019 ◽  
Vol 35 (1) ◽  
pp. 1077-1085 ◽  
Author(s):  
William Gathright ◽  
Michael Jensen ◽  
Dan Lewis
Keyword(s):  
Electrochemical Impedance Spectroscopy ◽  
Impedance Spectroscopy ◽  
Phase Field ◽  
Field Model ◽  
Electrochemical Impedance ◽  
Phase Field Model

On a SAV-MAC scheme for the Cahn–Hilliard–Navier–Stokes phase-field model and its error analysis for the corresponding Cahn–Hilliard–Stokes case

2020 ◽  
Vol 30 (12) ◽  
pp. 2263-2297
Author(s):  
Xiaoli Li ◽  
Jie Shen
Keyword(s):  
Error Analysis ◽  
Phase Field ◽  
Field Model ◽  
Chemical Potential ◽  
Phase Field Model ◽  
Auxiliary Variable ◽  
Field Variable ◽  
Second Order ◽  
Navier Stokes ◽  
Order Error

We construct a numerical scheme based on the scalar auxiliary variable (SAV) approach in time and the MAC discretization in space for the Cahn–Hilliard–Navier–Stokes phase- field model, prove its energy stability, and carry out error analysis for the corresponding Cahn–Hilliard–Stokes model only. The scheme is linear, second-order, unconditionally energy stable and can be implemented very efficiently. We establish second-order error estimates both in time and space for phase-field variable, chemical potential, velocity and pressure in different discrete norms for the Cahn–Hilliard–Stokes phase-field model. We also provide numerical experiments to verify our theoretical results and demonstrate the robustness and accuracy of our scheme.

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