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A non-isothermal phase field model that captures both displacive and diffusive phase transformations in a unified framework is presented. The model is developed in a formal thermodynamic setting, which provides guidance on admissible…

Materials Science · Physics 2011-12-02 Mirko Maraldi , Garth N. Wells , Luisa Molari

Multiphase systems are ubiquitous in engineering, biology, and materials science, where understanding their complex interactions and rheological behavior is crucial for advancing applications ranging from emulsion stability to cellular…

Fluid Dynamics · Physics 2025-10-27 Andres Santiago Espinosa-Moreno , Nicolas Moreno , Marco Ellero

Phase-field methods offer a versatile computational framework for simulating large-scale morphological evolution. However, the applicability and predictability of phase-field models are inherently limited by their ad hoc nature, and there…

Materials Science · Physics 2025-10-30 Jaehyeok Jin , David R. Reichman

The diffuse medium in and around galaxies can exist in a multi-phase state: small, cold gas clouds contributing significantly to the total mass embedded in pressure equilibrium with a hotter, more diffuse volume-filling component. Modeling…

Astrophysics of Galaxies · Physics 2022-12-28 Rainer Weinberger , Lars Hernquist

Phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems. Here, we develop a new analytical approach based on bifurcation analysis to explore…

Numerical Analysis · Mathematics 2022-10-14 Xinyue Evelyn Zhao , Long-Qing Chen , Wenrui Hao , Yanxiang Zhao

We further develop a recently introduced phase-field model of rapid alloy solidification [Ji et al., PRL 2023]. This model utilizes enhanced solute diffusivity within the spatially diffuse interface region to quantitatively capture solute…

Materials Science · Physics 2025-08-11 Kaihua Ji , Mingwang Zhong , Alain Karma

Multiscale modelling is a new paradigm that has emerged in recent times to study the well-known problem of the process-structure-property relationship in the area of materials science and engineering. For obtaining the desired performance…

Materials Science · Physics 2023-10-10 Rupesh Chafle , Vishal Panwar , Kaushik Das , Somnath Bhowmick , Rajdip Mukherjee

Amorphization during severe plastic deformation has been observed in various crystalline materials, yet its underlying mechanisms remain poorly understood. This study introduces a novel phase-field model at the mesoscale, integrating…

Materials Science · Physics 2025-10-10 Yuntong Huang , Shuyang Dai , Chuqi Chen , Yang Xiang

Detailed understanding of the coupling between fluid flow and solid deformation in porous media is crucial for the development biomedical devices and novel energy technologies relating to a wide range of geological and biological processes.…

Fluid Dynamics · Physics 2021-09-22 Francisco J. Carrillo

A diffuse-interface model for microstructure with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and formalized within a variational framework. The model includes a composition…

Materials Science · Physics 2011-07-28 Daniel A. Cogswell , W. Craig Carter

We consider the problem of heterogeneous nucleation and growth. The system is described by a phase field model in which the temperature is included through thermal noise. We show that this phase field approach is suitable to describe…

Statistical Mechanics · Physics 2009-11-07 Mario Castro

Most of the commercially important alloys are multicomponent, producing multiphase microstructures as a result of processing. When the coexisting phases are elastically coherent, the elastic interactions between these phases play a major…

Materials Science · Physics 2019-04-17 Sandeep Sugathan , Saswata Bhattacharya

We present a hybrid Volume-of-Fluid (VoF) Phase-Field method for general soluble surfactant-laden interfacial flows. The scheme retains the VoF method for interface tracking and momentum solution, while a diffused Phase-Field serves as a…

Fluid Dynamics · Physics 2026-05-28 Ilies Haouche , Benjamin Reichert , Michaël Baudoin , Palas Kumar Farsoiya

We review how phase-field models contributed to the understanding of various aspects of crystal nucleation including homogeneous and heterogeneous processes, and their role in microstructure evolution. We recall results obtained both by the…

A body $\Theta$ containing two phases, which may form a periodic composite with microstructure much smaller that the body, or which may have structure on a length scale comparable to the body, is subjected to slowly time varying boundary…

Mathematical Physics · Physics 2023-04-26 Ornella Mattei , Graeme W. Milton , Mihai Putinar

We study existence of solutions in the variational sense for a class of stochastic phase-field models describing moving boundary problems. The models consist of stochastic reaction-diffusion equations with singular diffusion forced by a…

Probability · Mathematics 2026-01-12 Amjad Saef , Wilhelm Stannat

We present a pedagogical review of the swelling thermodynamics and phase transitions of polymer gels. In particular, we discuss how features of the volume phase transition of the gel's osmotic equilibrium is analogous to other transitions…

Soft Condensed Matter · Physics 2019-06-13 Michael S. Dimitriyev , Ya-Wen Chang , Paul M. Goldbart , Alberto Fernández-Nieves

Granular flow problems characterized by large deformations are widespread in various applications, including coastal and geotechnical engineering. The paper deals with the application of a rigid-perfectly plastic two-phase model extended by…

Fluid Dynamics · Physics 2024-02-02 Wibke Düsterhöft-Wriggers , Svenja Schubert , Thomas Rung

In the present study, the multiphase volume distribution problem, where there can be an arbitrary number of phases, is addressed using a consistent and conservative volume distribution algorithm. The proposed algorithm satisfies the…

Computational Physics · Physics 2021-06-24 Ziyang Huang , Guang Lin , Arezoo M. Ardekani

Particle-stabilised emulsions are a cornerstone of soft matter science due to their broad application and fundamental relevance. Computer simulations provide key insights into the formation and behaviour of these emulsions, yet current…

Soft Condensed Matter · Physics 2026-02-19 Elisabeth C. Eij , Joost de Graaf , Martin F. Haase , Jesse M. Steenhoff