论文标题
在不可压缩的粘弹性两相流的扩散界面模型上
On a diffuse interface model for incompressible viscoelastic two-phase flows
论文作者
论文摘要
本文涉及一个弥漫性界面模型，用于在一个有界结构域中两种不可压缩的粘弹性流体的流动。更具体地说，假定流体在宏观上不混溶，但是在一个小的过渡区域，其中两个组件部分混合了。考虑到这两个组件的弹性，最终都带有耦合的Oldroyd-B/Cahn--Hilliard型系统，该系统描述了两相粘弹性流体的行为。我们证明了系统在二维中的存在较弱的解决方案，用于一般（无与伦比的）质量密度，可变粘度，不同的剪切模量以及一类具有物理相关和奇异的自由能密度，以保证订单参数保持在物理合理的间隔中。证明依赖于原始系统的正则化和正规化系统的新混合隐式时间离散化以及对OldRoyd-B类型方程的分析的组合。
This paper 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 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.
