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arXiv 2504.09024physics.flu-dynphysics.comp-ph
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一种用于界面约束被动标量输运的鲁棒格子玻尔兹曼方法：在含表面活性剂多相流中的应用

A Robust Lattice Boltzmann Method for Interface-Bound Transport of a Passive Scalar: Application to Surfactant-Laden Multiphase Flows

William Schupbach, Kannan Premnath

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30 pages, 12 figures
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AI总结：

本文提出一种鲁棒中心矩格子玻尔兹曼方法，结合Jain-Mani变量变换求解界面约束标量输运方程，并与CACE及两流体流动求解器耦合，成功模拟了含表面活性剂液滴在剪切流中的变形与破碎。

摘要：

受流体运动平流输运且被限制在界面上的被动标量的输运在多相输运现象中具有众多应用。一个典型例子是不溶性表面活性剂浓度场沿界面的平流-扩散。Stone（Phys. Fluids A, 1990）提出的界面上表面活性剂输运的尖锐界面模型已被Teigen等人（in Comm. Math. Sci., 2009）基于delta函数正则化扩展为扩散界面形式。然而，后一种方法包含奇异项，这可能损害其数值实现。最近，Jain和Mani（in Annual Research Briefs, CTR, Stanford University, 2022）通过应用变量变换绕开了这一问题，该变换有效地导出了一个带有附加界面约束通量项的广义界面约束标量输运方程。所得公式与用于追踪界面的保守Allen-Cahn方程（CACE）具有相似之处。在本文中，我们将讨论一种新颖的鲁棒中心矩格子玻尔兹曼（LB）方法，通过应用Jain和Mani的变换来模拟Teigen等人提出的标量场的界面约束平流-扩散输运方程。该方法与另一个用于CACE的LB格式耦合以计算演化界面，所得算法已针对文献中可用的一些基准问题进行了验证。作为进一步扩展，我们将其与我们的中心矩LB流动求解器耦合以求解两流体运动，该运动受由局部表面活性剂浓度变化引起的表面张力变化所调制的Marangoni应力控制，其中表面张力变化通过Langmuir等温线建模。随后通过模拟不同毛细数下剪切流中含不溶性表面活性剂的液滴变形和破碎对该方法进行了验证。

英文摘要：

The transport of a passive scalar restricted on interfaces, which is advected by the fluid motions have numerous applications in multiphase transport phenomena. A prototypical example is the advection-diffusion of the concentration field of an insoluble surfactant along interfaces. A sharp-interface model of the surfactant transport on the interface (Stone, Phys. Fluids A, 1990) has been extended to a diffuse-interface formulation based on a delta-function regularization by Teigen et al. (in Comm. Math. Sci., 2009). However, the latter approach involves singular terms which can compromise its numerical implementation. Recently, Jain and Mani (in Annual Research Briefs, CTR, Stanford University, 2022) circumvented this issue by applying a variable transformation, which effectively leads to a generalized interface-bound scalar transport equation with an additional interfacial confining flux term. The resulting formulation has similarities with the conservative Allen-Cahn equation (CACE) used for tracking of interfaces. In this paper, we will discuss a novel robust central moment lattice Boltzmann (LB) method to simulate the interface-bound advection-diffusion transport equation of a scalar field proposed in Teigen et al. by applying Jain and Mani's transformation. It is coupled with another LB scheme for the CACE to compute the evolving interfaces, and the resulting algorithm is validated against some benchmark problems available in the literature. As further extension, we have coupled it with our central moment LB flow solver for the two-fluid motions, which is modulated by the Marangoni stresses resulting from the variation of the surface tension with the local surfactant concentration modeled via the Langmuir isotherm. This is then validated by simulating insoluble surfactant-laden drop deformation and break-up in a shear flow at various capillary numbers.

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