{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T18:47:41Z","timestamp":1772045261158,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2012,3,14]],"date-time":"2012-03-14T00:00:00Z","timestamp":1331683200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Micromachines"],"abstract":"<jats:p>In this paper, a general methodology for the dynamic study of electrostatically actuated droplets is presented. A simplified 1D transient model is developed to investigate the transient response of a droplet to an actuation voltage and to study the effect of geometrical and fluid-thermal properties and electrical parameters on this behavior. First, the general approach for the dynamic droplet motion model is described. All forces acting on the droplet are introduced and presented in a simplified algebraic expression. For the retentive force, the empirically extracted correlations are used, and for the electrostatic actuation force, results from electrostatic finite element simulations are used. The dynamic model is applied to electrowetting induced droplet motion between parallel plates in the case of a single actuation electrode and for an array of electrodes. Using this methodology, the influence of the switching frequency and actuation voltage is studied. Furthermore, a linearized equivalent damped mass\u2014spring model is presented to approximate the dynamic droplet motion. It is shown that the optimal switching frequency can be estimated by twice the natural frequency of the linearized damped mass\u2014spring system.<\/jats:p>","DOI":"10.3390\/mi3010150","type":"journal-article","created":{"date-parts":[[2012,3,14]],"date-time":"2012-03-14T14:17:19Z","timestamp":1331734639000},"page":"150-167","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Modeling and Control of Electrowetting Induced Droplet Motion"],"prefix":"10.3390","volume":"3","author":[{"given":"Herman","family":"Oprins","sequence":"first","affiliation":[{"name":"IMEC, Kapeldreef 75, B3001 Leuven, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bart","family":"Vandevelde","sequence":"additional","affiliation":[{"name":"IMEC, Kapeldreef 75, B3001 Leuven, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martine","family":"Baelmans","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, KULeuven, Celestijnenlaan 300A, B-3001 Leuven, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,3,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"R705","DOI":"10.1088\/0953-8984\/17\/28\/R01","article-title":"Electrowetting: From basics to applications","volume":"17","author":"Mugele","year":"2005","journal-title":"J. Phys. Condens. Matter."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"De Gennes, P.-G., Brochard-Wyart, F., and Quere, D. (2004). Capillarity and Wetting Phenomena, Springer.","DOI":"10.1007\/978-0-387-21656-0"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/s10404-007-0164-5","article-title":"Digital microfluidic design and optimization of classic and new fluidic functions for lab on a chip systems","volume":"4","author":"Fouillet","year":"2007","journal-title":"Microfluid. Nanofluid."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1039\/b110474h","article-title":"Electrowetting-based actuation of droplets for integrated microfluidics","volume":"2","author":"Pollack","year":"2002","journal-title":"Lab Chip"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1109\/JMEMS.2002.807467","article-title":"Creating, transporting, cutting, and merging liquid droplets by electrowetting-based actuation for digital microfluidic circuits","volume":"12","author":"Cho","year":"2003","journal-title":"J. Microelectromechan. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Chakrabarty, K., and Su, F. (2006). Digital Microfluidic Biochips: Synthesis, Testing, and Reconfiguration Technique, CRC Press.","DOI":"10.1201\/9781420008302"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/s101890070029","article-title":"Variable focal lens controlled by an external voltage: An application of electrowetting","volume":"3","author":"Berge","year":"2000","journal-title":"Eur. Phys. J. E"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"940","DOI":"10.1002\/adma.200304745","article-title":"Tunable and latchable liquid microlens with photopolymerizable components","volume":"15","author":"Yang","year":"2003","journal-title":"Adv. Mater."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1128","DOI":"10.1063\/1.1779954","article-title":"Variable-focus liquid lens for miniature cameras","volume":"85","author":"Kuiper","year":"2004","journal-title":"Appl. Phys. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1038\/nature01988","article-title":"Video-speed electronic paper based on electrowetting","volume":"425","author":"Hayes","year":"2003","journal-title":"Nature"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Heikenfeld, J., and Steckl, A.J. (2005). High-transmission electrowetting light valves. Appl. Phys. Lett.","DOI":"10.1063\/1.1901816"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"732","DOI":"10.1109\/28.703965","article-title":"Electrostatic actuation of liquid droplets for microreactor applications","volume":"34","author":"Washizu","year":"1998","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1109\/84.846697","article-title":"Surface-tension-driven microactuation based on continuous electrowetting","volume":"9","author":"Lee","year":"2000","journal-title":"J. Microelectromech. Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1109\/JMEMS.2002.803286","article-title":"A surface-tension driven micropump for low-voltage and low-power operations","volume":"11","author":"Yun","year":"2002","journal-title":"J. Microelectromech. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/S1359-0294(00)00085-6","article-title":"Electrowetting: A recent outbreak","volume":"6","author":"Quilliet","year":"2001","journal-title":"Curr. Opin. Colloid Interface Sci."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Pamula, V.K., and Chakrabarty, K. (2003, January 28\u201329). Cooling of integrated circuits using droplet-based microfluidics. Proceedings of the 13th ACM Great Lakes Symposium on VLSI 2003, Washington, DC, USA.","DOI":"10.1145\/764808.764831"},{"key":"ref_17","unstructured":"Paik, P.Y., Pamula, V.K., and Chakrabarty, K. (2004, January 1\u20134). Thermal effects on droplets transport in digital microfluidics with application to chip cooling. Proceedings of theInter Society Conference on Thermal Phenomena, Las Vegas, NV, USA."},{"key":"ref_18","unstructured":"Paik, P.Y., Pamula, V.K., and Chakrabarty, K. (2005, January 27\u201330). Droplet-based hot spot cooling using topless digital microfluidics on a printed circuit board. Proceedings of the IEEE International Workshop on Thermal Investigations of ICs and Systems, Belgirate, Italy."},{"key":"ref_19","unstructured":"Mohseni, K. (2005, January 15\u201317). Effective cooling of integrated circuits using liquid alloy electrowetting. Proceedings of the 21st Semi-Therm Symposium, San Jose, CA, USA."},{"key":"ref_20","unstructured":"Nicole, C., Lasance, C.J.M., Prins, M.W.J., Baret, J.-C., and Decre, M.M.J. (2005). A Cooling System for Electronic Substrates. (WO 2006\/016293 A1), WIPO Patent."},{"key":"ref_21","unstructured":"Garimella, S.V., and Bahadur, V. (2007). Electrowetting Based Heat Spreader. (11\/752702), U.S. Patent."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"966","DOI":"10.1016\/j.mejo.2007.11.024","article-title":"Convection heat transfer in electrostatic actuated liquid droplets for electronics cooling","volume":"39","author":"Oprins","year":"2008","journal-title":"Microelectron. J."},{"key":"ref_23","unstructured":"Oprins, H., Vandevelde, B., Fiorini, P., Beyne, E., de Vos, J., and Majeed, B. (2011). Device for cooling integrated circuits. (20110304987 A1), U.S. Patent."},{"key":"ref_24","unstructured":"Oprins, H., Fiorini, P., de Vos, J., Majeed, B., Vandevelde, B., and Beyne, E. (December, January 30). Modeling, design and fabrication of a novel electrostatically actuated droplet based impingement cooler. Proceedings of the 10th PowerMEMS, Leuven, Belgium."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Majeed, B., Jones, B., Oprins, H., Vandevelde, B., Sabuncogolu, D., and Fiorini, P. (2011, January 9\u201313). Fabrication of an electrostatically actuated impingement cooling device. Proceedings of the 44th International Symposium on Microelectronics, Long Beach, CA, USA.","DOI":"10.4071\/isom-2011-TP5-Paper1"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/S0925-4005(02)00223-X","article-title":"Dynamics of electrowetting droplet transport","volume":"87","author":"Ren","year":"2002","journal-title":"Sens. Actuat. B"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1494","DOI":"10.1088\/0960-1317\/16\/8\/009","article-title":"An energy-based model for electrowetting-induced droplet actuation","volume":"16","author":"Bahadur","year":"2006","journal-title":"J. Micromech. Microeng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/j.snb.2003.09.030","article-title":"Automated on-chip droplet dispensing with volume control by electro-wetting actuation and capacitance metering","volume":"98","author":"Ren","year":"2004","journal-title":"Sens. Actuat. B"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1016\/j.sna.2006.04.050","article-title":"Actuation potentials and capillary forces in electrowetting based microsystems","volume":"134","author":"Berthier","year":"2007","journal-title":"Sens. Actuat. A"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"5794","DOI":"10.1063\/1.1563828","article-title":"Equilibrium behaviour of sessile drops under surface tension, applied external fields, and material variations","volume":"93","author":"Shapiro","year":"2003","journal-title":"J. Appl. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1080\/15567260701337555","article-title":"Digitized heat transfer using electrowetting on dielectric","volume":"11","author":"Mohseni","year":"2007","journal-title":"Nanoscale Microscale Thermophys. Eng."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jcis.2006.03.051","article-title":"The physics of moving wetting lines","volume":"299","author":"Blake","year":"2006","journal-title":"J. Colloid Interface Sci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1103\/RevModPhys.81.739","article-title":"Wetting and spreading","volume":"81","author":"Bonn","year":"2009","journal-title":"Rev. Mod. Phys."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1006\/jcis.1995.1130","article-title":"Liquid drops on an inclined plane: The relation between contact angles, drop shape and retentive force","volume":"170","author":"Extrand","year":"1995","journal-title":"J. Colloid Interface Sci."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1016\/j.jcis.2005.08.048","article-title":"Electrowetting-induced capillary flow in a parallel-plate channel","volume":"296","author":"Chen","year":"2006","journal-title":"J. Colloid Interface Sci."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Chen, N., Kuhl, T., Tadmor, R., Lin, Q., and Israelachvili, J. (2004). Large deformations during the coalescence of fluid interfaces. Phys. Rev. Lett.","DOI":"10.1103\/PhysRevLett.92.024501"}],"container-title":["Micromachines"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-666X\/3\/1\/150\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:49:23Z","timestamp":1760219363000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-666X\/3\/1\/150"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3,14]]},"references-count":36,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2012,3]]}},"alternative-id":["mi3010150"],"URL":"https:\/\/doi.org\/10.3390\/mi3010150","relation":{},"ISSN":["2072-666X"],"issn-type":[{"value":"2072-666X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,3,14]]}}}