- Open Access
Drops on architected elastic substrates: A repertoire of regimes at the turn of a knob
Phys. Rev. Research 7, 033095 – Published 28 July, 2025
DOI: https://doi.org/10.1103/9ssq-gjhv
Abstract
Drops on a vibrating substrate can experience a variety of motion regimes, including directional motion and climbing. The key ingredient to elicit these regimes is simultaneously activating the in-plane and out-of-plane degrees of freedom of the substrate with the proper phase difference. This is typically achieved by imposing a prescribed rigid-body motion of the entire substrate. However, this framework is unable to establish different motion conditions in different regions of the substrate, thus lacking the precious spatial selectivity necessary to elicit complex drop control patterns. Challenging this paradigm, we leverage the inherent elasticity of the substrate to provide the required in-plane and out-of-plane modal characteristics and spatial diversity. To this end, we design architected substrates exhibiting a rich landscape of deformation modes, and we exploit their multimodal response to switch between drop motion regimes and select desired spatial patterns, using the excitation frequency as our tuning parameter.
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References (40)
- I. Shestopalov, J. D. Tice, and R. F. Ismagilov, Multi-step synthesis of nanoparticles performed on millisecond time scale in a microfluidic droplet-based system, Lab Chip 4, 316 (2004).
- R. Seemann, M. Brinkmann, T. Pfohl, and S. Herminghaus, Droplet based microfluidics, Rep. Prog. Phys. 75, 016601 (2012).
- H. Stone, A. Stroock, and A. Ajdari, Engineering flows in small devices: Microfluidics toward a lab-on-a-chip, Annu. Rev. Fluid Mech. 36, 381 (2004).
- T. M. Squires and S. R. Quake, Microfluidics: Fluid physics at the nanoliter scale, Rev. Mod. Phys. 77, 977 (2005).
- P. Calvert, Inkjet printing for materials and devices, Chem. Mater. 13, 3299 (2001).
- C. Modak, A. Kumar, A. Tripathy, and P. Sen, Drop impact printing, Nat. Commun. 11, 4327 (2020).
- J. Whitehill, A. Neild, T. W. Ng, and M. Stokes, Collection of suspended particles in a drop using low frequency vibration, Appl. Phys. Lett. 96, 053501 (2010).
- F. Mugele and J.-C. Baret, Electrowetting: From basics to applications, J. Phys.: Condens. Matter 17, R705 (2005).
- X. Li, P. Bista, A. Z. Stetten, H. Bonart, M. T. Schür, S. Hardt, F. Bodziony, H. Marschall, A. Saal, X. Deng, R. Berger, S. A. L. Weber, and H.-J. Butt, Spontaneous charging affects the motion of sliding drops, Nat. Phys. 18, 713 (2022).
- R. Blossey and A. Bosio, Contact line deposits on cdna microarrays: A “twin-spot effect”, Langmuir 18, 2952 (2002).
- J. Yu, E. Berthier, A. Craig, T. de Groot, S. Sparks, P. Ingram, D. Jarrard, W. Huang, D. Beebe, and A. Theberge, Reconfigurable open microfluidics for studying the spatiotemporal dynamics of paracrine signalling, Nat. Biomed. Eng. 3, 830 (2019).
- D. Zwicker, O. W. Paulin, and C. ter Burg, Physics of droplet regulation in biological cells, arXiv:2501.13639.
- Y. Zeng, J. Khor, T. Neel, W.-c. Tu, J. Berthier, S. Thongpang, E. Berthier, and A. Theberge, Miniaturizing chemistry and biology using droplets in open systems, Nat. Rev. Chem. 7, 439 (2023).
- M. Costalonga and P. Brunet, Directional motion of vibrated sessile drops: A quantitative study, Phys. Rev. Fluids 5, 023601 (2020).
- J. F. Joanny and P. G. de Gennes, A model for contact angle hysteresis, J. Chem. Phys. 81, 552 (1984).
- P. G. de Gennes, Wetting: Statics and dynamics, Rev. Mod. Phys. 57, 827 (1985).
- B. Eral, D. 't Mannetje, and J. Oh, Contact angle hysteresis: A review of fundamentals and applications, Colloid Polym. Sci. 291, 247 (2013).
- J.-J. Huang, H. Huang, and X. Wang, Numerical study of drop motion on a surface with stepwise wettability gradient and contact angle hysteresis, Phys. Fluids 26, 062101 (2014).
- S. Varagnolo, V. Schiocchet, D. Ferraro, M. Pierno, G. Mistura, M. Sbragaglia, A. Gupta, and G. Amati, Tuning drop motion by chemical patterning of surfaces, Langmuir 30, 2401 (2014).
- C. Lin, S. Chen, L. Xiao, and Y. Liu, Tuning drop motion by chemical chessboard-patterned surfaces: A many-body dissipative particle dynamics study, Langmuir 34, 2708 (2018).
- A. Buguin, L. Talini, and P. Silberzan, Ratchet-like topological structures for the control of microdops, Appl. Phys. A 75, 207 (2002).
- O. Sandre, L. Gorre-Talini, A. Ajdari, J. Prost, and P. Silberzan, Moving droplets on asymmetrically structured surfaces, Phys. Rev. E 60, 2964 (1999).
- P.-B. Bintein, H. Lhuissier, A. Mongruel, L. Royon, and D. Beysens, Grooves accelerate dew shedding, Phys. Rev. Lett. 122, 098005 (2019).
- S. Daniel and M. K. Chaudhury, Rectified motion of liquid drops on gradient surfaces induced by vibration, Langmuir 18, 3404 (2002).
- S. Daniel, S. Sircar, J. Gliem, and M. K. Chaudhury, Ratcheting motion of liquid drops on gradient surfaces, Langmuir 20, 4085 (2004).
- S. Daniel, M. K. Chaudhury, and P.-G. de Gennes, Vibration-actuated drop motion on surfaces for batch microfluidic processes, Langmuir 21, 4240 (2005).
- P. Sartori, D. Quagliati, S. Varagnolo, M. Pierno, G. Mistura, F. Magaletti, and C. M. Casciola, Drop motion induced by vertical vibrations, New J. Phys. 17, 113017 (2015).
- X. Noblin, R. Kofman, and F. Celestini, Ratchetlike motion of a shaken drop, Phys. Rev. Lett. 102, 194504 (2009).
- P. Brunet, J. Eggers, and R. D. Deegan, Vibration-induced climbing of drops, Phys. Rev. Lett. 99, 144501 (2007).
- L. Dong, A. Chaudhury, and M. Chaudhury, Lateral vibration of a water drop and its motion on a vibrating surface, Eur. Phys. J. E: Soft Matter Biol. Phys. 21, 231 (2006).
- F. Celestini and R. Kofman, Vibration of submillimeter-size supported droplets, Phys. Rev. E 73, 041602 (2006).
- P. Brunet, J. Eggers, and R. Deegan, Motion of a drop driven by substrate vibrations, Eur. Phys. J.: Spec. Top. 166, 11 (2009).
- K. John and U. Thiele, Self-ratcheting stokes drops driven by oblique vibrations, Phys. Rev. Lett. 104, 107801 (2010).
- R. D. Deegan, Climbing a slippery slope, J. Fluid Mech. 882, F1 (2020).
- S. Mettu and M. K. Chaudhury, Vibration spectroscopy of a sessile drop and its contact line, Langmuir 28, 14100 (2012).
- M. Charara, Z. Kujala, S. Lee, and S. Gonella, Spatially selective drop-motion programming using metamaterials, Proc. R. Soc. London, Ser. A 481, 20240429 (2025).
- T. Tóth, D. Ferraro, E. Chiarello, M. Pierno, G. Mistura, G. Bissacco, and C. Semprebon, Suspension of water droplets on individual pillars, Langmuir 27, 4742 (2011).
- J. Oliver, C. Huh, and S. Mason, Resistance to spreading of liquids by sharp edges, J. Colloid Interface Sci. 59, 568 (1977).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/9ssq-gjhv for drop size selection and modes, drop experimental velocities, details on experiments, alternative two-cell case, and drop motion supporting videos.
- P. H. Steen, C.-T. Chang, and J. B. Bostwick, Droplet motions fill a periodic table, Proc. Natl. Acad. Sci. USA 116, 4849 (2019).