Analysis of Laminar Flow Over a Non-Conventional Random Rough Surface Based on Lattice Boltzmann Method

The average flow model offers a great convenience for the analysis of laminar flow over rough surfaces and is widely used in simulation studies. Flow factors used in the average flow model are generally expressed as a function of statistical properties of a single level rough surface with gentle slopes. However, for a nonconventional surface with multilevel roughness or high local surface slopes, such as polishing pads used in chemical mechanical planarization (CMP), it has not been verified whether this model is still applicable as expected. Generally, computations based on the Reynolds equation are carried out repeatedly for the same problem regarding different but statistically identical rough surfaces, and the average flow model is applicable if stable flow factors (statistical average) are obtained. However, due to the complex topography and high local surface slopes of polishing pads used in CMP, the Reynolds equation is no longer valid, and thus a new method needs to be developed to estimate the applicability of the average flow model and to calculate the flow factors accurately. In this study, aiming to research the flow over a nonconventional random rough surface such as the slurry flow in CMP, a new strategy is developed to research the incompressible laminar flow through a narrow gap between various nonconventional rough surfaces by combining the lattice Boltzmann method (LBM) and numerical simulation of random rough surface. With this strategy, it is convenient to simulate the flow field in a narrow gap between various random rough surfaces and obtain the flow factors. In addition, an analytical formula for calculating the flow factors of a dual-level rough surface, i.e., surface composed of two different types of microstructure, is introduced and verified through a comparison with the results obtained using the presented numerical simulation strategy.