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Two-dimensional modelling of transient capillary driven damped micro-oscillations and self-alignment of objects in microassembly

Published online by Cambridge University Press:  08 January 2021

Adam Chafaï Open the ORCID record for Adam Chafaï [Opens in a new window] ,
Y. Vitry ,
S. Dehaeck Open the ORCID record for S. Dehaeck [Opens in a new window] ,
F. Gallaire ,
B. Scheid Open the ORCID record for B. Scheid [Opens in a new window] ,
P. Colinet  and
P. Lambert Open the ORCID record for P. Lambert [Opens in a new window]
Adam Chafaï*
Affiliation:
Transfers, Interfaces and Processes (TIPs), Université Libre de Bruxelles, Avenue F.D. Roosevelt 50, CP 165/67, 1050Brussels, Belgium
Y. Vitry
Affiliation:
Transfers, Interfaces and Processes (TIPs), Université Libre de Bruxelles, Avenue F.D. Roosevelt 50, CP 165/67, 1050Brussels, Belgium
S. Dehaeck
Affiliation:
Transfers, Interfaces and Processes (TIPs), Université Libre de Bruxelles, Avenue F.D. Roosevelt 50, CP 165/67, 1050Brussels, Belgium
F. Gallaire
Affiliation:
Laboratory of Fluid Mechanics and Instabilities (LFMI), Ecole Polytechnique Fédérale de Lausanne, MED 2 2926, Station 9, 1015Lausanne, Switzerland
B. Scheid
Affiliation:
Transfers, Interfaces and Processes (TIPs), Université Libre de Bruxelles, Avenue F.D. Roosevelt 50, CP 165/67, 1050Brussels, Belgium
P. Colinet
Affiliation:
Transfers, Interfaces and Processes (TIPs), Université Libre de Bruxelles, Avenue F.D. Roosevelt 50, CP 165/67, 1050Brussels, Belgium
P. Lambert
Affiliation:
Transfers, Interfaces and Processes (TIPs), Université Libre de Bruxelles, Avenue F.D. Roosevelt 50, CP 165/67, 1050Brussels, Belgium
*
†Email address for correspondence: adam.chafai@ulb.be
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Abstract

In the fields of microgripping and microassembly, the self-alignment motion of a solid micro-object linked by a liquid meniscus to a substrate or a tool is an inexpensive way to overcome the current limitations of the assembly processes at microscale by getting rid of the positioning actuators. Original models providing a dynamical description of the capillary self-alignment of an $L\times D \times d$ chip are reported, as well as experimental results as evidence of their validity. The first two models describe the liquid and the solid physics in two dimensions. Both include nonlinearities and describe the coupling between a laminar flow and a solid structure. The fluid–solid coupling is ensured by the boundary conditions at their surface of contact and by the forces the liquid and the solid apply on each other. Both models yield the shift, lift and tilt modes of deformation of the liquid meniscus. Equations are first numerically solved by using a finite element method (model 1). By approximating the menisci with spherical caps, a geometrical model is then presented (model 2). Next, for small oscillations and thin liquid layers, the equations are linearised. The solution to the semianalytical three degrees of freedom (3-DOF) modal analysis is thus obtained (model 3). Finally, a semianalytical 1-DOF model is presented and numerically solved by considering a one-dimensional motion for the solid object (model 4). Solutions for models 1, 3 and 4 are computed and show good agreement with the experimental measurements. Yet, the remaining deviations are investigated to identify their origin.

JFM classification

Micro-/Nano-fluid dynamics: Microfluidics Interfacial Flows (free surface): Contact lines Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 910 , 10 March 2021 , A6
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Apoorva, F., Maccurdy, R. & Lipson, H. 2014 System and methods for electrowetting based pick and place. WO Patent 2014/014892 A2.Google Scholar
Arutinov, G., Edsger, C. P. S., Albert, P., Lambert, P. & Mastrangeli, M. 2014 In-plane mode dynamics of capillary self-alignment. Langmuir 30 (43), 13092–13102.CrossRefGoogle ScholarPubMed
Berthier, J., Brakke, K., Grossi, F., Sanchez, L. & Di Cioccio, L. 2010 Self-alignment of silicon chips on wafers: a capillary approach. J. Appl. Phys. 108 (5), 054905.CrossRefGoogle Scholar
Berthier, J., Brakke, K. A., Mermoz, S., Frétigny, C. & Di Cioccio, L. 2015 Stabilization of the tilt motion during capillary self-alignment of rectangular chips. Sensors Actuators A 234, 180–187.CrossRefGoogle Scholar
Berthier, J., Mermoz, S., Brakke, K., Sanchez, L., Frétigny, C. & Di Cioccio, L. 2013 Capillary self-alignment of polygonal chips: a generalization for the shift-restoring force. Microfluid Nanofluid 14 (5), 845–858.CrossRefGoogle Scholar
Brakke, K. A. 1992 The surface evolver. Expl. Maths 1 (2), 141–165.CrossRefGoogle Scholar
Comsol 2017 COMSOL Multiphysics, Structural Mechanics Module User's Guide.Google Scholar
Comsol 2018 COMSOL Multiphysics, Microfluidics Module User's Guide.Google Scholar
Dehaeck, S., Cavaiani, M., Chafai, A., Tourtit, Y., Vitry, Y. & Lambert, P. 2019 Hybrid two-scale fabrication of sub-millimetric capillary grippers. Micromachines 10 (4), 2–12.CrossRefGoogle ScholarPubMed
Donea, J., Huerta, A., Ponthot, J.-P. & Rodriguez-Ferran, A. 2017 Arbitrary Lagrangian- Eulerian methods. In Encyclopedia of Computational Mechanics, 2nd edn, pp. 1–23. John Wiley & Sons.CrossRefGoogle Scholar
Ellson, R., Stearns, R., Mutz, M., Brown, C., Browning, B., Harris, D., Qureshi, S., Shieh, J. & Wold, D. 2005 In situ DMSO hydration measurements of HTS compound libraries. Comb. Chem. High Throughput Screen. 8 (6), 489–498.CrossRefGoogle ScholarPubMed
Engmann, J., Servais, C. & Burbidge, A. S. 2005 Squeeze flow theory and applications to rheometry: a review. J. Non-Newtonian Fluid Mech. 132 (1–3), 1–27.CrossRefGoogle Scholar
Fantoni, G., Hansen, N. H. & Santochi, M. 2013 A new capillary gripper for mini and micro parts. CIRP Ann. Manuf. Technol. 62 (1), 17–20.CrossRefGoogle Scholar
Goldmann, L. S. 1993 Heuristic force-height equation for molten axisymmetric solder joints. In Proceedings of the Electronic Components and Technology Conference. pp. 1120–1124. IEEE.Google Scholar
Iazzolino, A., Tourtit, Y., Chafaï, A., Gilet, T., Lambert, P. & Tadrist, L. 2020 Pick up and release of micro-objects: a motion-free method to change the conformity of a capillary contact. Soft Matt. 754–763.CrossRefGoogle ScholarPubMed
Jasper, J. J. 2004 The surface tension of pure liquid compounds. J. Colloid Interface Sci. 46 (1), 841–1009.Google Scholar
Kaneda, M., Yamamoto, M., Nakaso, K., Yamamoto, T. & Fukai, J. 2007 Oscillation of a tilted circular pad on a droplet for the self-alignment process. Precis. Engng 31 (2), 177–184.CrossRefGoogle Scholar
Knuesel, R. J. & Jacobs, H. O. 2010 Self-assembly of microscopic chiplets at a liquid-liquid-solid interface forming a flexible segmented monocrystalline solar cell. Proc. Natl Acad. Sci. 107 (3), 993–998.CrossRefGoogle Scholar
Lambert, P., Borno, R. T., Lendersand, C., Malharbizand, M., Mastrangeli, M., Ondarçuhu, T., Takei, A., Valsamis, J.-B. & De Volder, M. 2013 Surface Tension in Microsystems Engineering Below the Capillary Length. Springer.CrossRefGoogle Scholar
Lambert, P., Mastrangeli, M., Valsamis, J. B. & Degrez, G. 2010 Spectral analysis and experimental study of lateral capillary dynamics for flip-chip applications. Microfluid Nanofluid 9 (4–5), 797–807.CrossRefGoogle Scholar
Lienemann, J., Greiner, A., Korvink, J. G., Xiong, X., Hanein, Y. & Böhringer, K. F. 2003 Modeling, Simulation, and Experimentation of a Promising New Packaging Technology: Parallel Fluidic Self-Assembly of Microdevices, vol. 13, pp. 3–43. Wiley-VCH.Google Scholar
Lin, C., Tseng, F. & Kan, H. C. 2009 Numerical studies on micropart self-alignment using surface tension forces. Microfluid Nanofluid 6 (1), 63–75.CrossRefGoogle Scholar
Lu, H. & Bailey, C. 2005 Dynamic analysis of flip-chip self-alignment. IEEE Trans. Adv. Packag. 28 (3), 475–480.CrossRefGoogle Scholar
Mastrangeli, M., Valsamis, J. B., Van Hoof, C., Celis, J. P. & Lambert, P. 2010 Lateral capillary forces of cylindrical fluid menisci: a comprehensive quasi-static study. J. Micromech. Microengng 20 (7), 075041.CrossRefGoogle Scholar
Meurisse, M.-H. & Querry, M. 2006 Squeeze effects in a flat liquid bridge between parallel solid surfaces. J. Tribol. 128 (3), 575–584.CrossRefGoogle Scholar
Najib, A. M., Abdullah, M. Z., Saad, A. A., Samsudin, Z. & Che Ani, F. 2017 Numerical simulation of self-alignment of chip resistor components for different silver content during reflow soldering. Microelectron. Reliab. 79 (April), 69–78.CrossRefGoogle Scholar
Park, S. C., Fang, J., Biswas, S., Mozafari, M., Stauden, T. & Jacobs, H. O. 2015 Approaching roll-to-roll fluidic self-assembly: relevant parameters, machine design, and applications. J. Microelectromech. Syst. 24 (6), 1928–1937.CrossRefGoogle Scholar
Patra, S. K. & Lee, Y. C. 1991 Quasi-static modeling of the self-alignment mechanism in flip-chip soldering — part I: single solder joint. Trans. ASME: J. Electron. Packag. 113 (4), 337–342.Google Scholar
Roman, B. & Bico, J. 2010 Elasto-capillarity: deforming an elastic structure with a liquid droplet. J. Phys.: Condens. Matter 22 (49), 493101.Google ScholarPubMed
Shi, J. & Tomasi, C. 1994 Good features to track. In IEEE Conference on Computer Vision and Patttern Recognition. IEEE.Google Scholar
Takei, A., Matsumoto, K. & Shimoyama, I. 2010 Capillary torque caused by a liquid droplet sandwiched between two plates. Langmuir 26 (4), 2497–2504.CrossRefGoogle ScholarPubMed
Uran, S., Safaric, R. & Bratina, B. 2017 Reliable and accurate release of micro-sized objects with a gripper that uses the capillary-force method. Micromachines 8 (6), 182.Google Scholar
Valsamis, J. B., Mastrangeli, M. & Lambert, P. 2013 Vertical excitation of axisymmetric liquid bridges. Eur. J. Mech. B/Fluids 38, 47–57.CrossRefGoogle Scholar
Vasudev, A., Jagtiani, A., Du, L. & Zhe, J. 2009 A low-voltage droplet microgripper for micro-object manipulation. J. Micromech. Microengng 19 (7), 075005.CrossRefGoogle Scholar
van Veen, N. 1999 Analytical derivation of the self-alignment motion of flip chip soldered components. Trans. ASME: J. Electron. Packag. 121, 116–121.Google Scholar

Chafaï et al. supplementary movie

Movie presenting the experimental set-up and validation steps for the measurement of the capillary driven micro-oscillations.

Download Chafaï et al. supplementary movie(Video)
Video 19.9 MB