Squeeze film force exists but is undesirable in some engineering applications such as immersion lithography and micro-electro mechanical systems. The dynamic characteristics of such systems can be improved by adopting hydrophobic surfaces. In addition to squeeze film damping effects, slip effects are prominent and the inertial effects can be neglected with small film thickness, while inertial effects are prominent and slip effects can be neglected with large film thickness. Existing squeeze film force models that ignore inertia effects will cause unacceptable deviations between hydrophobic surfaces with clearance from dozens to hundreds of microns. In this paper, the squeeze film force model is formulated based on Navier–Stokes equations and two parameters slip boundary conditions while simultaneously considering slip and inertia effects. Experiments using different squeeze film thicknesses and squeeze amplitudes are conducted with parallelism between two specimen surfaces of less than 0.01°. The experimental results show that the slip and inertia effects are critical for accurately predicting the squeeze film force between hydrophobic surfaces under moderate film thickness. The predicted errors of the proposed model can be significantly reduced to less than 0.5% after proper fitting of the two slip parameters under all the test conditions. The method can be adopted for the identification of slip parameters and derivation of kinetic models for systems with squeeze film.

中文翻译：

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考虑亚毫米间隙内疏水表面之间的滑动和惯性效应的挤压膜力建模

存在挤压膜力，但在某些工程应用中（例如浸没式光刻和微机电系统）是不理想的。通过采用疏水性表面可以改善此类系统的动态特性。除了挤压薄膜的阻尼作用外，在薄膜厚度小的情况下，滑动作用也很明显，而惯性作用可以被忽略；而在薄膜厚度大的情况下，惯性作用则很明显，而滑动作用可以被忽略。现有的忽略惯性效应的挤压膜力模型将导致疏水表面之间的间隙从数十微米到数百微米不可接受的偏差。在本文中，基于Navier-Stokes方程和两个参数滑移边界条件，同时考虑滑移和惯性效应，构造了挤压膜力模型。在两个样品表面之间的平行度小于0.01°的情况下，使用不同的挤压膜厚度和挤压幅度进行了实验。实验结果表明，滑移和惯性效应对于准确预测中等膜厚下疏水表面之间的挤压膜力至关重要。在所有测试条件下正确拟合两个滑移参数后，所提出模型的预测误差可以显着降低至小于0.5％。该方法可用于识别滑动参数和推导带膜系统的动力学模型。实验结果表明，滑移和惯性效应对于准确预测中等膜厚下疏水表面之间的挤压膜力至关重要。在所有测试条件下正确拟合两个滑移参数后，所提出模型的预测误差可以显着降低至小于0.5％。该方法可用于识别滑动参数和推导带膜系统的动力学模型。实验结果表明，滑动和惯性效应对于准确预测中等膜厚下疏水性表面之间的挤压膜力至关重要。在所有测试条件下正确拟合两个滑移参数后，所提出模型的预测误差可以显着降低至小于0.5％。该方法可用于识别滑动参数和推导带膜系统的动力学模型。