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Linearized analysis of the deformation of ultra-thin lubricant films under gas pressures by the long wave equation

机译：用长波方程线性分析超薄润滑膜在气压下的变形

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Long wave theory was employed to examine the deformations of ultra-thin but continuum liquid films produced by applied pressures and shearing stresses. Long wave theory is based on the time-evolution equation for the shape and deformation of thin liquid films and includes surface tension and surface forces such as van der Waals forces. As the deformations caused by gas pressures are usually very small, the linearized long wave equation, which is applicable to infinitesimal deformations, was derived and employed to predict the steady-state liquid surface deformations of a non-polar lubricant produced by concentrated or distributed gas pressures. It was found that the results obtained using the linearized equation agree well with those obtained using the nonlinear long wave equation.
机译：长波理论被用来研究超薄但连续的液膜在施加压力和剪切应力作用下的变形。长波理论基于时间演化方程来确定薄膜的形状和变形，包括表面张力和表面力，例如范德华力。由于由气压引起的变形通常很小，因此推导了适用于极小变形的线性长波方程，并将其用于预测由浓缩或分布气体产生的非极性润滑剂的稳态液态表面变形压力。发现使用线性化方程获得的结果与使用非线性长波方程获得的结果非常吻合。

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