A Class of Conservative Phase Field Models for Multiphase Fluid Flows

[1]  P. Flory.  Principles of polymer chemistry , 1953 .

[2]  J. E. Hilliard,et al.  Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .

[3]  John E. Hilliard,et al.  Free Energy of a Nonuniform System. III. Nucleation in a Two‐Component Incompressible Fluid , 1959 .

[4]  R. Kobayashi.  Modeling and numerical simulations of dendritic crystal growth , 1993 .

[5]  Wheeler,et al.  Phase-field models for anisotropic interfaces. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  Chen,et al.  Computer simulation of the domain dynamics of a quenched system with a large number of nonconserved order parameters: The grain-growth kinetics. , 1994, Physical review. B, Condensed matter.

[7]  David Coates,et al.  Polymer-dispersed liquid crystals , 1995 .

[8]  Michael Ortiz,et al.  Mixed Atomistic and Continuum Models of Deformation in Solids , 1996 .

[9]  Yunzhi Wang,et al.  The continuum field approach to modeling microstructural evolution , 1996 .

[10]  Masao Doi,et al.  Introduction to Polymer Physics , 1996 .

[11]  Geoffrey B. McFadden,et al.  Phase-field model for solidification of a eutectic alloy , 1996, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[12]  J. Lowengrub,et al.  Quasi–incompressible Cahn–Hilliard fluids and topological transitions , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[13]  R. Larson.  The Structure and Rheology of Complex Fluids , 1998 .

[14]  A. Karma,et al.  Phase-field model of dendritic sidebranching with thermal noise. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[15]  Zhigang Suo,et al.  Dynamics of nanoscale pattern formation of an epitaxial monolayer , 2001 .

[16]  Noel J. Walkington,et al.  Digital Object Identifier (DOI) 10.1007/s002050100158 An Eulerian Description of Fluids Containing Visco-Elastic Particles , 2022 .

[17]  L. Chen,et al.  Phase-field model of domain structures in ferroelectric thin films , 2001 .

[18]  Long-Qing Chen.  Phase-Field Models for Microstructure Evolution , 2002 .

[19]  Jie Shen,et al.  Computer simulation of spinodal decomposition in constrained films , 2003 .

[20]  Jie Shen,et al.  Three-dimensional phase-field modeling of spinodal decomposition in constrained films , 2003 .

[21]  Jie Shen,et al.  A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method , 2003 .

[22]  James J. Feng,et al.  A diffuse-interface method for simulating two-phase flows of complex fluids , 2004, Journal of Fluid Mechanics.

[23]  Q. Du,et al.  A phase field approach in the numerical study of the elastic bending energy for vesicle membranes , 2004 .

[24]  Steven M. Wise,et al.  EFFICIENT PHASE-FIELD SIMULATION OF QUANTUM DOT FORMATION IN A STRAINED HETEROEPITAXIAL FILM , 2004 .

[25]  Qiang Du,et al.  Modeling the spontaneous curvature effects in static cell membrane deformations by a phase field formulation , 2005 .

[26]  Qiang Du,et al.  Retrieving Topological Information for Phase Field Models , 2005, SIAM J. Appl. Math..

[27]  Jie Shen,et al.  Transient drop deformation upon startup of shear in viscoelastic fluids , 2005 .

[28]  Junseok Kim,et al.  Phase field modeling and simulation of three-phase flows , 2005 .

[29]  Qiang Du,et al.  A phase field formulation of the Willmore problem , 2005 .

[30]  James J. Feng,et al.  Diffuse-interface simulations of drop coalescence and retraction in viscoelastic fluids , 2005 .

[31]  Qiang Du,et al.  Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions , 2006, J. Comput. Phys..

[32]  Jie Shen,et al.  Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method , 2006, J. Comput. Phys..

[33]  Qi Wang,et al.  PHASE-FIELD MODELS FOR BIOFILMS. I. THEORY AND 1-D SIMULATIONS ∗ , 2008 .

[34]  Qi Wang,et al.  Phase Field Models for Biofilms. I. Theory and One-Dimensional Simulations , 2008, SIAM J. Appl. Math..

[35]  Jie Shen,et al.  An efficient moving mesh spectral method for the phase-field model of two-phase flows , 2009, J. Comput. Phys..

[36]  Qi Wang,et al.  A 2-D Kinetic Theory for Flows of Monodomain Polymer-rod Nanocomposites , 2009 .

[37]  Tianyu Zhang,et al.  Cahn-Hilliard Vs Singular Cahn-Hilliard Equations in Phase Field Modeling , 2009 .

[38]  Qi Wang,et al.  A multicomponent model for biofilm-drug interaction , 2010 .

[39]  Xiaofeng Yang,et al.  Energy stable schemes for Cahn-Hilliard phase-field model of two-phase incompressible flows , 2010 .

[40]  Jie Shen,et al.  A Phase-Field Model and Its Numerical Approximation for Two-Phase Incompressible Flows with Different Densities and Viscosities , 2010, SIAM J. Sci. Comput..

[41]  Qi Wang,et al.  Energy law preserving C0 finite element schemes for phase field models in two-phase flow computations , 2011, J. Comput. Phys..

[42]  Xiaofeng Yang,et al.  Mass and Volume Conservation in Phase Field Models for Binary Fluids , 2013 .