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

本研究的目的是开发一种基于伽辽金公式（GLBM）的非结构晶格玻尔兹曼方法（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化有效滑移的重要设计因素。由于被困在纳米结构中的液体和气体之间粘度的巨大差异，预计超疏水表面上的有效滑移会很大。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的大粘度差。所提出的非结构化网格上的两相GLBM将克服结构化网格上的LBM固有的一些不良特性，作为超疏水表面的建模工具；即在大密度/粘度差和网格施加的几何限制下的不稳定性。它将使研究复杂纳米结构覆盖的超疏水表面的详细流动物理成为可能。提出的研究方向是：(1)利用非结构化网格上的隐式时间推进技术，开发大密度黏度比非混相两相流的GLBM；(2)在自由能最小化的基础上，在液固气边界处建立合适的边界条件，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）液体流动的物理特性；(4)找到纳米结构的最佳轮廓和分布，以获得最大的超疏水性和有效滑移。超疏水表面由于具有抗粘、抗污染和自清洁等特性，在许多工业和生物应用中引起了人们的极大兴趣。当液滴在污染物上滚动时，它从表面收集颗粒，污染物颗粒从表面去除。在微流体和生物医学应用中，超疏水表面减少了壁面的水动力阻力，并防止在同一表面上移动的另一个液滴的交叉污染。提出的研究探索了一种新的建模能力，可以显著改变现有的设计微流控装置的方法，并有助于预先筛选设计方案，降低设计成本。从计划项目中获得的研究经验也将增强高级计算流体动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.