A ternary Cahn–Hilliard–Navier–Stokes model for two-phase flow with precipitation and dissolution

Rohde, Christian; Wolff, Lars von

doi:10.1142/s0218202521500019

Cited by 16 publications

(41 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…With this, an overview of the PF approaches to the solute precipitation [ 180 , 220 ] and precipitation in binary alloys [ 179 , 221 , 222 ] is provided that are instructive for simulating self-healing mechanisms of concrete. The following models are presented in chronological order ( Table 2 ).…”

Section: Phase-field Modeling Of Precipitation Reaction Mechanismsmentioning

confidence: 99%

See 1 more Smart Citation

A Review on Cementitious Self-Healing and the Potential of Phase-Field Methods for Modeling Crack-Closing and Fracture Recovery

et al. 2020

View full text Add to dashboard Cite

Improving the durability and sustainability of concrete structures has been driving the enormous number of research papers on self-healing mechanisms that have been published in the past decades. The vast developments of computer science significantly contributed to this and enhanced the various possibilities numerical simulations can offer to predict the entire service life, with emphasis on crack development and cementitious self-healing. The aim of this paper is to review the currently available literature on numerical methods for cementitious self-healing and fracture development using Phase-Field (PF) methods. The PF method is a computational method that has been frequently used for modeling and predicting the evolution of meso- and microstructural morphology of cementitious materials. It uses a set of conservative and non-conservative field variables to describe the phase evolutions. Unlike traditional sharp interface models, these field variables are continuous in the interfacial region, which is typical for PF methods. The present study first summarizes the various principles of self-healing mechanisms for cementitious materials, followed by the application of PF methods for simulating microscopic phase transformations. Then, a review on the various PF approaches for precipitation reaction and fracture mechanisms is reported, where the final section addresses potential key issues that may be considered in future developments of self-healing models. This also includes unified, combined and coupled multi-field models, which allow a comprehensive simulation of self-healing processes in cementitious materials.

show abstract

Section: Phase-field Modeling Of Precipitation Reaction Mechanismsmentioning

confidence: 99%

“…Redeker and Rohde [ 221 , 222 ] extended the Noorden–Eck model by incorporating curvature effects between two fluid phases to simulate precipitation in a porous medium. The model contains two immiscible fluids and one solid phase.…”

Section: Phase-field Modeling Of Precipitation Reaction Mechanismsmentioning

confidence: 99%

A Review on Cementitious Self-Healing and the Potential of Phase-Field Methods for Modeling Crack-Closing and Fracture Recovery

et al. 2020

View full text Add to dashboard Cite

show abstract

“…Phase-field formulations for two-phase flow with phase transitions and chemical reactions were developed in Refs. [3], [17], [39] and [34], where sharp-interface limits for certain regimes were found. However, all the above models are isothermal.…”

Section: Introductionmentioning

confidence: 99%

A phase-field approach to model evaporation in porous media: Upscaling from pore to Darcy scale

Ghosh¹,

Bringedal²

2021

Preprint

View full text Add to dashboard Cite

We develop a phase-field model for evaporation in a porous medium by explicitly considering a vapor component together with the liquid and gas phases in the system. The phase-field model consists of the conservation of mass (for phases and vapor component), momentum, and energy. In addition, the evolution of the phase field is described by the Allen-Cahn equation. In the limit of vanishing interface width, matched asymptotic expansions reveal that the phase-field model reduces to the sharp-interface model with all the relevant transmission conditions at the moving interface. An energy estimate is derived, which suggests that for the diffusiondominated regime, energy always decreases with time. However, this is not always the case for other regimes. The phase-field model is upscaled to the Darcy scale using periodic homogenization for the diffusion-dominated regime. The effective parameters at the Darcy scale are connected to the pore scale through corresponding cell problems.

show abstract

“…Kinetic reactions at phase boundaries have been introduced in [27,23]. More recently, phase-field models that couple precipitation and dissolution with fluid flow have been developed [11,24].…”

Section: Introductionmentioning

confidence: 99%

“…In this work we upscale the Cahn-Hilliard-Navier-Stokes model of [24] from pore scale to REV scale using asymptotic expansions. We consider the simplified geometry of a thin strip.…”

Section: Introductionmentioning

confidence: 99%

Upscaling of a Cahn-Hilliard Navier-Stokes Model with Precipitation and Dissolution in a Thin Strip

von Wolff,

Pop

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We consider a phase-field model for the incompressible flow of two immiscible fluids. This model extends widespread models for two fluid phases by including a third, solid phase, which can evolve due to e.g. precipitation and dissolution.We consider a simple, two-dimensional geometry of a thin strip, which can still be seen as the representation of a single pore throat in a porous medium. Under moderate assumptions on the Peclet number and the capillary number, we investigate the limit case when the ratio between the width and the length of the strip is going to zero. In this way and employing transversal averaging, we derive an upscaled model. The result is a multi-scale model consisting of the upscaled equations for the total flux and the ion transport, while the phase-field equation has to be solved in cell-problems at the pore scale to determine the position of interfaces. We also investigate the sharp interface limit of the multi-scale model, in which the phase-field parameter approaches 0. The resulting sharp interface model consists only of Darcy-scale equations, as the cell-problems can be solved explicitly. Notably we find asymptotic consistency, that is the upscaling process and the sharp interface limit commute. We use numerical results to investigate the validity of the upscaling when discontinuities are formed in the upscaled model.

show abstract

A ternary Cahn–Hilliard–Navier–Stokes model for two-phase flow with precipitation and dissolution

Cited by 16 publications

References 27 publications

A Review on Cementitious Self-Healing and the Potential of Phase-Field Methods for Modeling Crack-Closing and Fracture Recovery

A Review on Cementitious Self-Healing and the Potential of Phase-Field Methods for Modeling Crack-Closing and Fracture Recovery

A phase-field approach to model evaporation in porous media: Upscaling from pore to Darcy scale

Upscaling of a Cahn-Hilliard Navier-Stokes Model with Precipitation and Dissolution in a Thin Strip

Contact Info

Product

Resources

About