The numerical modeling of cell freezing in binary solution under subcooling conditions

Purpose This paper aims to describe and investigate the mathematical models and numerical modeling of how a cell membrane is affected by a transient ice freezing front combined with the influence of thermal fluctuations and anisotropy. Design/methodology/approach The study consists of mathematical modeling, validation with an analytical solution, and shows the influence of thermal noises on phase front dynamics and how it influences the freezing process of a single red blood cell. The numerical calculation has been modeled in the framework of the phase field method with a Cahn–Hilliard formulation of a free energy functional. Findings The results show an influence scale on directional phase front propagation dynamics and how significant are stochastic thermal noises in micro-scale freezing. Originality/value The numerical calculation has modeled in the framework of the phase field method with a Cahn–Hilliard formulation of a free energy functional.

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Phase-Field Model for Spinodal Decomposition of Dilute Solute Field in Al-Ag Alloy

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.415-417.1168 ◽

2011 ◽

Vol 415-417 ◽

pp. 1168-1170

Author(s):

Ying Jun Gao ◽

Zhi Rong Luo

Keyword(s):

Free Energy ◽

Spinodal Decomposition ◽

Phase Field ◽

Phase Field Model ◽

Free Energy Density ◽

Field Method ◽

Energy Functional ◽

Phase Field Method ◽

Fourth Power ◽

Free Zone

The typical Landau free energy functional with the fourth power of a solute composition field is not suitable for representing spinodal decomposition of a dilute Ag solute field in Al-Ag alloy. Facing this challenge, a new free energy density function is proposed for spinodal decomposition of a dilute Ag solute field of Al-Ag alloy. The evolution of the solute field in Al-4.2% Ag alloy is studied by phase-field method using this new function. The simulated results reveal that the precipitate free zone (PFZ) around the precipitated phase is an ellipse and its width is about two times that of phase, while in the region far from PFZ, a GPZ pattern of Ag solute field appears due to spinodal decomposition.

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Additive Manufacturing of Cementitious Materials by Selective Paste Intrusion: Numerical Modeling of the Flow Using a 2D Axisymmetric Phase Field Method

Materials ◽

10.3390/ma13215024 ◽

2020 ◽

Vol 13 (21) ◽

pp. 5024

Author(s):

Alexandre Pierre ◽

Daniel Weger ◽

Arnaud Perrot ◽

Dirk Lowke

Keyword(s):

Numerical Modeling ◽

3D Printing ◽

Cement Paste ◽

Phase Field ◽

Numerical Approach ◽

Cementitious Materials ◽

Field Method ◽

Phase Field Method ◽

Shape Accuracy ◽

Cement Pastes

The 3D printing of concrete has now entered a new era and a transformation of the construction sector is expected to reshape fabrication with concrete. This work focuses on the selective paste intrusion method, which consists of bonding dry particles of aggregate with a cement paste. This innovative technique could lead to the production of very precise component for specific applications. The main obstacle to tackle in order to reach a high shape accuracy of high mechanical performances of 3D printing elements by selectively activating the material is the control of the distribution of the cement paste through the particle bed. With the aim to better understand the path followed by the solution as it penetrates a cut-section of the granular packing, two-dimensional numerical modeling is carried out using Comsol software. A phase-field method combined with a continuous visco-plastic model has been used to study the influence of the average grain diameter, the contact angle, and the rheological properties of cement pastes on the penetration depth. We compare the numerical modeling results to existing experimental results from 3D experiments and a one-dimensional analytical model. We then highlight that the proposed numerical approach is reliable to predict the final penetration of the cement pastes.

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Thermodynamic Calculation of Al-Cu Eutectic Alloy with Microstructure Simulation Using Phase Field Method

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.295-297.468 ◽

2011 ◽

Vol 295-297 ◽

pp. 468-472 ◽

Cited By ~ 2

Author(s):

Jin Jun Tang ◽

Jian Zhong Jiang ◽

Chun Hua Tang ◽

Da Hui Chen ◽

Li Qun Hou

Keyword(s):

Free Energy ◽

Eutectic Alloy ◽

Phase Field ◽

Regular Solution Model ◽

Field Method ◽

Phase Field Method ◽

Multiple Point ◽

Microstructure Simulation ◽

Thermo Calc Software ◽

New Phase

Phase-field method can be used to describe the complicated morphologies of crystal growth without explicitly tracking the complex phase boundaries. The conformation of volume free energy is very important for microstructure simulation with phase-field method. However, the conformation of volume free energy is still correspondingly simple and ideal at present. In this paper, a new conformation method of free energy is mentioned. Free energy of each phase at appointed states is calculated by Thermo-Calc software. In order to avoided calculation, free energy of each phase is fitted by multiple-point function according to sub- regular solution model. It is obtained that the free energy data and phase graph data of α phase, θ phase and L phase in the extension, temperature (791-841) K and component (0-35)Cu(at.%) with Al-Cu eutectic alloy. The new phase model is also founded, and used to calculate microstructure evolution of Al-Cu eutectic alloy.

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Periodic structures of clean, normal, and superconducting material II: order parameter and free-energy functions

Canadian Journal of Physics ◽

10.1139/p86-281 ◽

1986 ◽

Vol 64 (12) ◽

pp. 1581-1583 ◽

Cited By ~ 1

Author(s):

Robert Cleary

Keyword(s):

Free Energy ◽

Numerical Calculation ◽

Critical Temperature ◽

Order Parameter ◽

Periodic Structures ◽

Energy Functional ◽

Normal Metal ◽

Fermi Velocity ◽

Energy Functions ◽

Free Energy Functional

The critical temperature of a clean, normal (n) and superconducting (s) material is calculated and found to differ very slightly from its bulk value. The order parameter at 0°, Δ(0), is found to be modified much more than its bulk value for periodic structures of various cell widths, superconducting-to-normal metal length ratios, and Fermi-velocity differences in the normal and superconducting regions. At intermediate temperatures, an expression for Δ(T)/Δ(0) as a function of T/Tc and Δ(0)/Tc is given. The free-energy functional Fs − Fn is calculated. As in the case of Δ(T)/Δ(0), numerical calculations are necessary. These integrands are carried out to the point where numerical quadrature is simple and straightforward. Because of the great number of parameters describing our system, we do not perform any numerical calculation. These are left to the interested experimentalist for his particular structure.

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Phase Field Calculations with CVM Free Energy within Square Approximation

Materials Science Forum ◽

10.4028/www.scientific.net/msf.561-565.1935 ◽

2007 ◽

Vol 561-565 ◽

pp. 1935-1940

Author(s):

Tetsuo Mohri ◽

Nao Fujihashi ◽

Ying Chen

Keyword(s):

Free Energy ◽

Phase Field ◽

Stoichiometric Composition ◽

Sharp Decrease ◽

Cluster Variation Method ◽

Field Method ◽

Phase Field Method ◽

Square Lattice ◽

Variation Method ◽

Cluster Variation

Phase Field Method is combined with the Cluster Variation Method within the square approximation, and the multiscale ordering behavior from atomistic to microstructural evolution process of ordered domains in the two dimensional square lattice is investigated. The transition temperature is determined at 1:1 stoichiometric composition and it is confirmed that the transition is of the second order. The growth process of the ordered domains is visualized and it is revealed that the sharp decrease of the free energy takes place during the process.

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Numerical research of solidification dynamics with anisotropy and thermal fluctuations

MATEC Web of Conferences ◽

10.1051/matecconf/201824005028 ◽

2018 ◽

Vol 240 ◽

pp. 05028

Author(s):

Przemysław Smakulski ◽

Jun Ishimoto ◽

Sławomir Pietrowicz

Keyword(s):

Phase Field ◽

Front Propagation ◽

Solidification Process ◽

Thermal Fluctuations ◽

Field Method ◽

Pure Component ◽

Phase Field Method ◽

Freezing Process ◽

Variable Order ◽

Phase Front

The influence of thermal fluctuations and anisotropy on the solidification process of a pure component is analyzed. It helps to understand the unstable freezing process where complicated structures such as dendrites could be formed due to a supercooling event reached during the cooling of the biological material. The study consists of mathematical modeling, validation with an analytical solution, and shows the influence of thermal noises on phase front dynamics. The analysis has been modeled in the framework of the Phase Field Method with Cahn-Hilliard formulation of a free energy functional [1]. The phase front is described by the Eulerian approach of fluid fields and formulated as a Phase Field scalar variable (order parameter) with a predefined, diffused boundary thickness. The results describe an influence scale onto directional phase front propagation dynamics, and how significant are stochastic thermal noises in micro-scale freezing.

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A Phase-Field Model for the Formation of Martensite and Bainite

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.922.31 ◽

2014 ◽

Vol 922 ◽

pp. 31-36 ◽

Cited By ~ 4

Author(s):

Tansel T. Arif ◽

Rong Shan Qin

Keyword(s):

Free Energy ◽

Phase Field ◽

Materials Science ◽

Current Model ◽

Phase Field Model ◽

Field Method ◽

Field Variable ◽

Phase Field Method ◽

Cubic Symmetry ◽

Chemical Free Energy

The phase field method is rapidly becoming the method of choice for simulating the evolution of solid state phase transformations in materials science. Within this area there are transformations primarily concerned with diffusion and those that have a displacive nature. There has been extensive work focussed upon applying the phase field method to diffusive transformations leaving much desired for models that can incorporate displacive transformations. Using the current model, the formation of martensite, which is formed via a displacive transformation, is simulated. The existence of a transformation matrix in the free energy expression along with cubic symmetry operations enables the reproduction of the 24 grain variants of martensite. Furthermore, upon consideration of the chemical free energy term, the model is able to utilise both the displacive and diffusive aspects of bainite formation, reproducing the autocatalytic nucleation process for multiple sheaves using a single phase field variable. Transformation matrices are available for many steels, one of which is used within the model.

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