Abstract : Interfacial phenomena are widely observed in nature and play important roles in materials science and fluid mechanics. The dynamics of the interfaces between different phases is of great interest not only because of the associated scientific questions but also due to its various applications. The different phases separated by the interfaces can be both liquids, or liquid-gas phases, or solid-gas phases, etc. Modelling and simulation of such systems is rather challenging, especially in the presence of moving contact lines. This mini-symposium will mainly focus on the mathematical modeling of interface dynamics and the development of efficient numerical methods.
[02231] Competition between viscous flow and diffusion in pinch-off dynamics
Format : Talk at Waseda University
Author(s) :
Tiezheng Qian (Hong Kong University of Science and Technology)
Abstract : We employ the Cahn-Hilliard-Navier-Stokes model to investigate the pinch-off dynamics of a liquid thread surrounded by a viscous fluid. A characteristic length scale is introduced to measure the competition between diffusion and viscous flow. This length scale is adjustable in the model and can approach micrometer scale for aqueous two-phase systems close to the critical point. Numerical examples are presented to show the pinch-off processes in the Stokes regime and the diffusion-dominated regime respectively.
[02273] A phase field model of vesicle growth or shrinkage
Format : Talk at Waseda University
Author(s) :
Shuwang Li (Illinois Institute of Technology)
Xiaoxia Tang (Illinois Institute of Technology)
Steven Wise (University of Tennessee)
Abstract : We present a diffuse interface model for vesicle growth or shrinkage induced by an osmotic pressure. The model consists of an Allen-Cahn equation describing the evolution of phase field and a Cahn-Hilliard equation describing the evolution of concentration field. We establish control conditions for expanding or shrinking vesicles via a common tangent construction. Numerical experiments reveal that the model can capture the main feature of dynamics: formation of circle-like (expanding) and finger-like (shrinking) vesicles.
[03394] A symmetrized parametric finite element method for anisotropic surface diffusion
Format : Talk at Waseda University
Author(s) :
YIFEI LI (National University of Singapore)
Abstract : In this talk, we introduce an energy-stable numerical scheme for 2D closed curve motion under anisotropic surface diffusion using a general anisotropic surface energy γ(n). We propose a symmetric surface energy matrix Z_k(n), derive a symmetrized variational formulation, and discretize it using an structure-preserving parametric finite element method (SP-PFEM). The SP-PFEM is proven unconditionally energy-stable under mild conditions on γ(n). Finally, we report the high performance through numerical results.
[02478] On a diffuse interface model for incompressible viscoelastic two-phase flows
Format : Talk at Waseda University
Author(s) :
Yadong Liu (University of Regensburg)
Dennis Trautwein (University of Regensburg)
Abstract : This talk concerns a diffuse interface model for the flow of two incompressible viscoelastic fluids in a bounded domain. More specifically, the fluids are assumed to be macroscopically immiscible, but with a small transition region, where the two components are partially mixed. Considering the elasticity of both components, one ends up with a coupled Oldroyd-B/Cahn--Hilliard type system, which describes the behavior of two-phase viscoelastic fluids. We prove the existence of weak solutions to the system in two dimensions for general (unmatched) mass densities, variable viscosities, different shear moduli, and a class of physically relevant and singular free energy densities that guarantee that the order parameter stays in the physically reasonable interval. The proof relies on a combination of a novel regularization of the original system and a new hybrid implicit time discretization for the regularized system together with the analysis of an Oldroyd-B type equation.
[03198] Simulating solid-state dewetting of thin films: a phase-field approach
Author(s) :
Wei Jiang (Professor)
Abstract : TBA
[03625] Modeling and simulation for solid-state dewetting problems
Author(s) :
Quan Zhao (University of Regensburg)
Abstract : Deposited thin films are unstable and could dewet to form isolated islands on the substrate in order to minimize the total surface energy. I will introduce a sharp-interface model and a diffuse-interface model for describing the dewetting of solid thin films with anisotropic surface energies. The relationship between the two models is established via the asymptotic analysis. Numerical results are presented to validate the asymptotic results and to demonstrate the anisotropic effects in the evolution.
[02975] Modeling and Energy Stable Numerical Schemes of Network Development in Biology Gels
Author(s) :
BOYI WANG (TU Wien)
Abstract : In this paper, we focus on the modeling and simulation of the network development in biological gels. A thermodynamically consistent model with homogenous Neumann or periodic boundary condition is derived based on the Rayleighian method. Two fully discrete numerical schemes are proposed to solve the problem. Energy stability is achieved at the discrete level for both schemes. Positivity-preserving property can be shown for the model with the Flory—Huggins potential at continuous and discrete level.
[03582] The mixed finite element method applied to cavitation in incompressible nonlinear elasticity
Author(s) :
Weijie Huang (Beijing Jiaotong University)
Abstract : In this talk, I will introduce a mixed finite element method for solving cavitation problem for 2D incompressible nonlinear elastic materials. The method is analytically proved to be locking-free and convergent, and it is also shown to be numerically accurate and efficient by numerical experiments. Furthermore, the newly developed accurate method enables us to find an interesting bifurcation phenomenon in multi-cavity growth.
