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In this paper, we numerically study the lubricant migration on a flying slider air-bearing surface in a hard disk drive. The lubricant dynamics is based on a continuum thin film lubrication theory with inter-molecular forces and a precursor film model. It includes air-bearing pressure, air-bearing shear stress, the Laplace pressure, the disjoining pressure, and the shear stress caused by the surface free energy gradient. Using this model we investigate the lubricant migration behavior on a modern negative pressure type slider surface. We also reveal the correlation between the lubricant migration behavior and the air-bearing shear stress. We further perform the lubricant migration analysis for various different slider designs, radii, and skew angles.