不可压缩两相流中可溶表面活性剂的热力学一致性稀疏界面模型的全局弱解

我们研究了一个热力学一致性的稀疏界面模型，用于描述在二维或三维有界域内，两个粘性不可压缩牛顿流体（密度不匹配）及其可溶表面活性剂的运动。 resulting hydrodynamic system consists of a nonhomogeneous Navier-Stokes system for the (volume averaged) velocity $\mathbf{u}$ and a coupled Cahn-Hilliard system for the phase-field variables $\phi$ and $\psi$ that represent the difference in volume fractions of the binary fluids and the surfactant concentration, respectively. For the initial boundary value problem with physically relevant singular potentials subject to a no-slip boundary condition for the fluid velocity and homogeneous Neumann boundary conditions for the phase-field variables and the chemical potentials, we first establish the existence of global weak solutions in the case of non-degenerate mobilities based on a suitable semi-implicit time discretization. Next, we prove the existence of global weak solutions for a class of general degenerate mobilities, with the aid of a new type of approximations for both the mobilities and the singular parts of the potential densities.