Two-phase flows with bulk-surface interaction described by a Navier–Stokes–Cahn–Hilliard model with dynamic boundary conditions

通过具有动态边界条件的 NavierâStokesâCahnâHilliard 模型描述具有体表面相互作用的两相流

• 批准号: 524694286
• 负责人: Dr. Patrik Knopf
• 金额: --
• 依托单位: Lehrstuhl für Mathematik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/524694286?language=en
• 关键词: Two; phase; flows; bulk; surface

We are planning to investigate a thermodynamically consistent diffuse interface model for two-phase flows with possibly unmatched densities that was recently derived by A. Giorgini and the applicant in [arXiv:2208.09695]. The model consists of a Navier-Stokes equation, which describes the time evolution of the velocity field associated with the two fluids, and a convective Cahn-Hilliard system describing the location of the two fluids in the considered domain via a phase-field function. These two subsystems are coupled in a nonlinear way by means of a phase-field depending source term in the Navier-Stokes equation as well as convection terms in the Cahn-Hilliard subsystem. In the case of unmatched densities, meaning that the individual constant densities of the two fluids are different, there is an additional nonlinear coupling as the density function appearing in the Navier-Stokes equation does also depend on the phase-field. In contrast to previous phase-field models for two-phase flows in the literature (e.g., the well-known Abels-Garcke-Grün model), our new model introduced in [arXiv:2208.09695] allows for dynamic changes of the contact angle between the diffuse interface separating the fluids and the boundary, and is also capable of describing the situation of absorption of material by the boundary. This is achieved by the usage of a class of dynamic boundary conditions for the Cahn-Hilliard subsystem that has previously been introduced for the Cahn-Hilliard equation by K.F. Lam, C. Liu, S. Metzger and the applicant in [ESAIM: Mathematical Modelling and Numerical Analysis 55(1): 229-282, 2021]. In order to make the model (thermodynamically) consistent, we impose a certain Navier slip boundary condition on the velocity field. The model derivation for our new Navier-Stokes-Cahn-Hilliard model as well as some first analytical results in the case of matched densities were presented in [arXiv:2208.09695]. The goal of the proposed project is to further investigate the model in terms of mathematical analysis first in the case of matched densities but later also in the much more difficult case of unmatched densities where the two fluids may have a different individual density.

我们正计划研究一个适用于密度可能不匹配的两相流的扩散界面模型，该模型最近由A。Giorgini和申请人在[arXiv：2208.09695]中。该模型包括一个Navier-Stokes方程，它描述了与两种流体相关联的速度场的时间演化，和一个对流Cahn-Hilliard系统，通过相场函数描述了两种流体在所考虑的域中的位置。这两个子系统通过Navier-Stokes方程中的相场依赖源项以及Cahn-Hilliard子系统中的对流项以非线性方式耦合。在密度不匹配的情况下，这意味着两种流体的个体恒定密度不同，存在额外的非线性耦合，因为出现在Navier-Stokes方程中的密度函数也依赖于相场。与文献中先前的两相流相场模型（例如，众所周知的Abels-Garcke-Grün模型），我们在[arXiv：2208.09695]中引入的新模型允许分离流体的扩散界面和边界之间的接触角动态变化，并且还能够描述材料的吸收情况边界。这是通过对Cahn-Hilliard子系统使用K.F.兰姆角，澳-地Liu，S. Metzger和申请人在[ESAIM：Mathematical Modeling and Numerical Analysis 55（1）：229-282，2021]中。为了使模型的一致性，我们在速度场上施加了一定的Navier滑移边界条件。我们新的Navier-Stokes-Cahn-Hilliard模型的模型推导以及匹配密度情况下的一些初步分析结果在[arXiv：2208.09695]中给出。拟议项目的目标是进一步研究模型的数学分析，首先在匹配密度的情况下，但后来也在更困难的情况下，不匹配的密度，其中两种流体可能有不同的个体密度。