Mixtures and Free Interface Motions

November 22, 2011

Mixtures

Free Interface Motion in Mixtures

  1. (with Sergio A. Alvarez) Motion of a Closed Curve by Minus the Surface Laplacian of Curvature, Differential and Integral Equations, Vol 13, No. 10-12, 1583–1594 (1997).
  2. (with David Kinderlehrer, Florin Manolache and Shlomo Ta’asan) Remarks about Analysis and Simulation of Grain Boundary Systems, Proceeding of Third International Conference of Grain Growth, 437 – 443 (1998).
  3. (with David Kinderlehrer) Evolution of Grain Boundaries, Mathematical Models and Methods in Applied Sciences (M3AS), 11 (4) , 713–729 (2001). abstract
  4. (with Jie Shen) A Phase Field Model for the Mixture of Two Incompressible Fluids and its Approximation by a Fourier-Spectral Method, Physica D, 179, 4, 211–228 (2003). abstract
  5. (with Qiang Du and Xiaoqiang Wang) A Phase Field Approach in the Numerical Study of the Elastic Bending Energy for Vesicle Membranes, Journal of Computational Physics 198, no. 2, 450–468 (2004). abstract
  6. (with Pengtao Yue, Jimmy Feng and Jie Shen) A Diffuse-Interface Method for Simulating Two-Phase Flows of Complex Fluids, Journal of Fluid Mechanics, Vol 515, 293–317 (2004). abstract
  7. (with Qiang Du, Rolf Ryham and Xiaoqiang Wang) A Phase Field Formulation of the Willmore Problem, Nonlinearity, 18, 1249 — 1267 (2005). abstract
  8. (with Qiang Du, Rolf Ryham and Xiaoqiang Wang) Modeling the spontaneous curvature effects in static cell membrane deformation by a phase field formulation, Communications in Pure and Applied Analysis, Vol 4, No 3, 537 — 548 (2005). abstract
  9. (with Qiang Du and Xiaoqiang Wang) Retrieving Topological Information For Phase Field Models, SIAM Journal on Applied Mathematics, Vol 65, No 6, 1913 — 1932 (2005). abstract
  10. (with Pengtao Yue, Jimmy Feng and Jie Shen) Interfacial Forces and Marangoni Flow on a Nematic Drop, Journal of Colloid and Interface Science, 290, 281 — 288 (2005). abstract
  11. (with Pengtao Yue, Jimmy Feng and Jie Shen) Diffuse-Interface Simulations of Drop-Coalescence and Retraction in Viscoelastic Fluids, Journal of Non-Newtonian Fluid Dynamics, Vol 129, 163 — 176 (2005). abstract
  12. (with Pengtao Yue, Jimmy Feng and Jie Shen) Viscoelastic Effects on Drop Deformation in Steady Shear, Journal of Fluid Mechanics, 540, 427 — 437(2005). abstract
  13. (with Qiang Du and Xiaoqiang Wang) Simulating the Deformation of Vesicle Membranes under Elastic Bending Energy in Three Dimensions, Journal of Computational Physics, 212, 2, 757 — 777 (2006). abstract
  14. (with Pengtao Yue, Jimmy Feng and Jie Shen) Transient drop deformation upon startup of shear in viscoelastic fluids, Physics of Fluids, 17, 123101 (2005). abstract
  15. (with Pengtao Yue, Jimmy Feng and Jie Shen) Variational Approach in Two-Phase Flows of Complex Fluids transport and induced elastic stress, in A. Miranville, editor, Mathematical Models and Methods in Phase Transitions,. Nova Publications, (2005). (21 pages)
  16. (with Pengtao Yue, Jimmy Feng and Jie Shen) An Energetic Variational Formulation with Phase Field Methods for Interfacial Dynamics of Complex Fluids: Advantages and Challenges, in M.C. Calderer, E. Terentjev editors, ”Modeling of Soft Matter”, IMA Volumes in Mathematics and its Applications, Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN (2005). (29 pages)
  17. (with Xiaofeng Yang, Jimmy Feng and Jie Shen) Numerical Simulations of Jet Pinching-off and Drop Formation using an Energetic Variational Phase-Field Method, Journal of Computational Physics 218:417-428 (2006). abstract
  18. (with C. Zhou, P. Yue, J Feng and Jie Shen) Heart-shaped bubbles rising in anisotropic liquids, Physics of Fluids, 19, 041703 (2007). abstract
  19. (with Qiang Du, Rolf Ryham and Xiaoqiang Wang) Diffusive Interface Energies Capturing the Euler Number: Relaxation and Renormalization, Communications of Mathematical Sciences 5, pp.233-242 (2007). article
  20. (with Xiaobing Feng and Yinnian He) Analysis of finite element approximations of a phase field model for two phase fluids, Mathematics of Computation 76, no. 258, 539–571 (2007). abstract
  21. (with Noel J. Walkington) Convergence of Numerical Approximations of the Incompressible Navier Stokes Equations with Variable Density and Viscosity, SIAM Journal of Numerical Analysis 45, no. 3, 1287–1304 (2007). abstract
  22. (with Qiang Du and Manlin Li) Analysis of a Phase Field Navier-Stokes Vesicle-Fluid Interaction Model, Discrete and Continuous Dynamical Systems B, 8, No 3, pp.539-556, (2007). abstract
  23. (with Rolf Ryham and Ludmil Zikatanov) Mathematical Models for the Deformation of Electrolyte Droplets, Discrete and Continuous Dynamical Systems B, Volume 8, Number 3, 649 — 661 (2007). abstract
  24. (with Ping Lin and Hui Zhang) An energy law preserving C0 finite element scheme for simulating the kinematic effects in liquid crystal dynamics, Journal of Computational Physics, Volume 227, Issue 2, 1411 —1427 (2007). abstract
  25. (with Aaron Naber, Jimmy Feng and Christopher A. Bertelo) The Nucleation and Growth of Gas Bubbles in a Newtonian Fluid: An Energetic Variational Phase Field Approach, in Moving Interface Problems and Applications in Fluid Dynamics (AMS Contemporary Mathematics Series, Vol. 466, eds. K. B. Cheong, Z. Li and P. Lin). pp. 95-120. American Mathematics Society (2008).
  26. (with Qiang Du, Rolf Ryham and Xiaoqiang Wang) Energetic Variational Approaches to Modeling Vesicle and Fluid Interactions, Physica D, 238, 923—930 (2009). abstract
  27. (with Pengtao Sun and Jinchao Xu) Phase Field Model of Thermo-Induced Marangoni Effects in the Mixtures and its Numerical Simulations with Mixed Finite Element Methods, Communications in Computational Physics, 6, 1095 — 1117(2009). abstract
  28. (with Yunkyong Hyon and Do Young Kwak) Energetic Variational Approach in Complex Fluids : Maximum Dissipation Principle, Discrete and Continuous Dynamical Systems, Volume 26, Number 4, 1291 — 1304 (2010). abstract
  29. (with Xiang Xu and Liyun Zhao) Axisymmetric Solutions to a coupled Navier-Stokes/Allen-Cahn Equations, SIAM Journal of Mathematical Analysis, Volume 41, Issue 6, 2246-2282 (2010). abstract
  30. (with Norifumi Sato and Yoshihiro Tonegawa) On the Existence of Mean Curvature Flow with Transport Term, Interfaces and Free Boundaries 12, No 2, 251-277 (2010). abstract
  31. (with Jinsong Hua, Ping Lin and Qi Wang) Energy Law Preserving C0 Finite Element Schemes for Phase Field Models in Two-Phase Flow Computations, Journal of Computational Physics 230, 7115 – 7131 (2011). abstract
  32. (with James H. Adler, James Brannick, Thomas Manteuffel and Ludmil Zikatanov) First-order system least squares and the energetic variational approach for two-phase flow, Journal of Computational Physics 230(17):6647-6663 (2011). abstract
  33. (with Xiaofeng Yang, M. Gregory Forest and Jie Shen) Shear Cell Rupture of Nematic Droplets in Viscous Fluids, Journal of Non-Newtonian Fluid Mechanics 166:487499 (2011). abstract
  34. (with Huan Sun, James Brannick and Tiezheng Qian) Diffuse Interface Method for Multiple Phase Materials: An Energetic Variational Approach, submitted to Journal of Computational Physics (2011).