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Squeeze Film Force Modeling with Considering Slip and Inertia Effects Between Hydrophobic Surfaces Within Submillimeter Clearance

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Abstract

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.

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Abbreviations

b :

Slip length, m

f :

Frequency of squeeze, Hz

F in :

Squeeze film force in the region 0 ≤ r ≤ Rs, N

F outer :

Squeeze film force in the region Rs ≤ r ≤ R, N

F exp :

Amplitude of experimental squeeze film force, N

F pre :

Amplitude of predicted squeeze film force, N

h :

Dynamic film thickness (h0 + εsin(ωt)), m

\(\dot{h}\) :

Velocity of squeeze, m/s

\(\ddot{h}\) :

Accelerate of squeeze, m/s2

h 0 :

Initial film thickness, m

P :

Pressure in the film region, Pa

r, z :

Radial and axial coordinates

R :

Radius of the circular plate, m

R s :

Internal radius of slip region, m

R sm :

Minimum value of Rs, m

u s :

Slip velocity, m/s

Vr, Vz :

Velocity in r and z direction, respectively, m/s

α :

Damping correction coefficient

β :

Inertial correction coefficient

γ :

Predicted error of squeeze film force

ε :

Amplitude of squeeze, m

η :

Dynamic viscosity of lubricant, Pa·s

ρ :

Density of lubricant, kg/m3

σ :

Accumulated fitting error, N

τ co :

Critical surface shear stress, Pa

\(\tilde{\tau }_{{{\text{co}}}}\) :

Critical surface shear stress with sign of us, Pa

τs, τc :

Shear stress at the bottom surface, Pa

ω :

Angular frequency of squeeze, rad/s

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Acknowledgements

The work is supported by the National Natural Science Foundation of China (Nos. 51675195, 51721092) and the National Major Science and Technology Projects of China (No. 2017ZX02101007-002). The authors also thank Micro and Nano Fabrication and Measurement Laboratory of Huazhong University of Science and Technology.

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Authors and Affiliations

  1. State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Luoyu Road 1037, Wuhan, 430074, China

    Xueping Li, Bin Han, Xuedong Chen, Xinhao Luo & Wei Jiang

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  1. Xueping Li
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  2. Bin Han
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  3. Xuedong Chen
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  4. Xinhao Luo
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  5. Wei Jiang
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Contributions

[XL] and [WJ] contributed to the study conception and design. Material preparation, data collection and analysis were performed by [XL], [BH] and [XL]. The first draft of the manuscript was written by [XL] and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript. The funding was acquired by [XC] and [WJ].

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Correspondence to Wei Jiang.

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Li, X., Han, B., Chen, X. et al. Squeeze Film Force Modeling with Considering Slip and Inertia Effects Between Hydrophobic Surfaces Within Submillimeter Clearance. Tribol Lett 68, 78 (2020). https://doi.org/10.1007/s11249-020-01320-x

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