Galerkin Lattice Boltzmann Methods for Direct Simulation of Liquid Slip on Superhydrophobic Surfaces

本研究的目的是发展一种基于Galerkin公式的非结构格子Boltzmann方法(LBM)，用于直接模拟超疏水表面上的液体滑移，并确定在实际条件下最大有效滑移的重要设计因素。由于捕获在纳米结构中的液体和气体之间的粘度差异很大，预计超疏水表面上会有很大的有效滑移。一个成功的数值模型应该能够处理超疏水表面的复杂形状和流体之间较大的粘度差。非结构网格上的两相GLBM将克服结构网格上的两相GLBM作为超疏水表面建模工具所固有的一些不良特性，即在大密度/粘度差下的不稳定性和网格施加的几何限制。这将使在复盖着复杂纳米结构的超疏水表面上进行详细的流动物理研究成为可能。本文的研究内容是：(1)在非结构网格上采用隐式时间推进法，发展适用于大密度、大粘度不混溶两相流动的GLBM；(2)基于自由能最小化原则，在液-固-气边界上建立适当的边界条件，并将其纳入GLBM框架；(3)研究具有复杂纳米结构的超疏水表面上连续和分散(液滴)流动的物理特性；超疏水表面由于具有防粘、防污染、自清洁等性能，在许多工业和生物领域具有广泛的应用前景。当液滴在污染物上滚动时，它从表面收集颗粒，并从表面去除污染物颗粒。在微流体和生物医学应用中，超疏水表面减少了壁面的流体动力阻力，并防止了一滴在同一表面上移动的另一滴的交叉污染。这项拟议的研究探索了一种新的建模能力，可以显着改变现有的微流控器件设计方法，并帮助预先筛选设计备选方案，降低设计成本。从拟议项目中获得的研究经验也将增强高级计算流体力学课程的课程材料。

The objective of the proposed research is to develop an unstructured lattice Boltzmann method (LBM) based on the Galerkin formulation (GLBM) for the direct simulation of liquid slip on superhydrophobic surfaces and identify important design factors that maximize the effective slip under practical conditions. The large effective slip on superhydrophobic surfaces is expected due to the sizable difference in viscosity between liquid and gas that is trapped in the nanostructures. A successful numerical model should be able to deal with complex shape of superhydrophobic surfaces and large viscosity difference between fluids. The proposed two-phase GLBM on the unstructured mesh will overcome several undesirable properties inherent to the LBM on the structured mesh as a modeling tool for superhydrophobic surfaces; namely, instability at large density/viscosity difference and geometrical restriction imposed by the mesh. It will enable investigation of detailed flow physics on superhydrophobic surfaces covered with complex nanostructures. The proposed research is to: (1) Develop GLBM for immiscible two phase flows having a large density and viscosity ratio, using implicit time marching on unstructured mesh; (2) Establish appropriate boundary conditions at the liquid-solid-gas boundary based on the minimization of the free energy and incorporate them into GLBM framework; (3) Examine the physics of continuous and dispersed (droplets) liquid flows on superhydrophobic surfaces with complex nanostructures; and (4) Find the optimum profile and distribution of nanostructures for the maximum superhydrophobicity and effective slip.Superhydrophobic surfaces are of great interest in many industrial and biological applications, because properties such as anti-sticking, anti-contamination, and self-cleaning are expected. When a droplet rolls over a contamination, it collects the particles from the surface and the contaminant particles are removed from the surface. In microfluidic and biomedical applications, superhydrophobic surfaces reduce the hydrodynamic drag at the wall, and prevent cross-contamination of one drop by another one moving on the same surface. The proposed research explores a new modeling capability that could significantly change existing approaches to designing microfluidic devices and help prescreen design alternatives reducing the design cost. The research experience acquired from the proposed project will also enhance the course materials for the advanced computational fluid dynamics courses.