Abstract
This chapter presents a study on the dynamics of lateral motion of a liquid meniscus confined by a circular pad and a circular chip moving parallely to the pad. This problem is a typical flip-chip case study, whose use is wide-spread in industrial assembly. The proposed model describing this dynamics is made of two coupled physics: the Navier-Stokes equation governing the liquid flow between the pad and the chip, and the Newton’s law describing the motion of the chip. This coupled problem is solved with a spectral method based on Chebyshev polynomials, by assuming an analytical expression of the lateral stiffness of the meniscus in the cases of circular and square pads. The theoretical results are benchmarked with literature results and thoroughly experimentally validated. From these results, we propose a map giving the characteristic time of the chip dynamics according to only two non-dimensional parameters, constructed with the physical (density, surface tension, viscosity), geometrical (pad area, gap) or dynamical (chip mass) parameters of the problem. These results have been published in [8].
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Notes
- 1.
This conclusion has been very recently extended to whatever polygonal shapes [1].
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Acknowledgments
This work is conducted with financial support from the project Hybrid Ultra Precision Manufacturing Process Based on Positional and Self assembly for Complex Micro-Products (HYDROMEL NMP2-CT-2006-026622) funded by the European Commission. A special thanks to B. Tartini. Thanks to Bruno Tartini for manufacturing the mechanical components of the experimental set up, and thanks to my students for their help in these developments, especially Jeanne Boute and Carsten Engel.
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Lambert, P. (2013). Lateral Capillary Forces (Dynamics). In: Lambert, P. (eds) Surface Tension in Microsystems. Microtechnology and MEMS. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37552-1_8
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DOI: https://doi.org/10.1007/978-3-642-37552-1_8
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