A new lubrication model is derived for solving ultra-thin gas lubrication problems encountered in the analysis of a magnetic head slider flying over a magnetic disk coated with giant-molecule lubricant film. In this model, the liquid lubricant film is replaced with a permeable material, and the boundary between the gas and liquid is subject to two kinds of velocity slippage: one due to the rarefaction effect and the other to the porous effect. Using this model, a rarefaction-modified Reynolds equation is derived considering the permeability of the running surface. This equation is then applied to the lubrication of head sliders flying over a magnetic medium. An interesting condition is found to arise wherein total apparent slippage seems to disappear due to the cancellation of the two slippages and the permeability effects are larger for a slider having a steeper pressure gradient.

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