{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:34:55Z","timestamp":1760243695281,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2012,8,3]],"date-time":"2012-08-03T00:00:00Z","timestamp":1343952000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper a multi-disciplinary simulation of a capacitive droplet sensor based on an open plate capacitor as transducing element is presented. The numerical simulations are based on the finite volume method (FVM), including calculations of an electric field which changes according to the presence of a liquid droplet. The volume of fluid (VOF) method is applied for the simulation of the ejection process of a liquid droplet out of a dispenser nozzle. The simulations were realised using the computational fluid dynamic (CFD) software CFD ACE+. The investigated capacitive sensing principle enables to determine the volume of a micro droplet passing the sensor capacitor due to the induced change in capacity. It could be found that single droplets in the considered volume range of 5 nL &lt; Vdrop &lt; 100 nL lead to a linear change of the capacity up to \u0394Q &lt; 30 fC. The sensitivity of the focused capacitor geometry was evaluated to be Si = 0.3 fC\/nL. The simulation results are validated by experiments which exhibit good agreement.<\/jats:p>","DOI":"10.3390\/s120810550","type":"journal-article","created":{"date-parts":[[2012,8,3]],"date-time":"2012-08-03T11:02:44Z","timestamp":1343991764000},"page":"10550-10565","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Numerical Investigations on Electric Field Characteristics with Respect to Capacitive Detection of Free-Flying Droplets"],"prefix":"10.3390","volume":"12","author":[{"given":"Andreas","family":"Ernst","sequence":"first","affiliation":[{"name":"Laboratory for MEMS Applications, Department of Microsystems Engineering (IMTEK), University of Freiburg, 79110 Freiburg, Germany"},{"name":"Biofluidix GmbH, Georges-Koehler-Allee 103, 79110 Freiburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Klaus","family":"Mutschler","sequence":"additional","affiliation":[{"name":"Laboratory for MEMS Applications, Department of Microsystems Engineering (IMTEK), University of Freiburg, 79110 Freiburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Laurent","family":"Tanguy","sequence":"additional","affiliation":[{"name":"Laboratory for MEMS Applications, Department of Microsystems Engineering (IMTEK), University of Freiburg, 79110 Freiburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nils","family":"Paust","sequence":"additional","affiliation":[{"name":"Laboratory for MEMS Applications, Department of Microsystems Engineering (IMTEK), University of Freiburg, 79110 Freiburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roland","family":"Zengerle","sequence":"additional","affiliation":[{"name":"Laboratory for MEMS Applications, Department of Microsystems Engineering (IMTEK), University of Freiburg, 79110 Freiburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter","family":"Koltay","sequence":"additional","affiliation":[{"name":"Laboratory for MEMS Applications, Department of Microsystems Engineering (IMTEK), University of Freiburg, 79110 Freiburg, Germany"},{"name":"Biofluidix GmbH, Georges-Koehler-Allee 103, 79110 Freiburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,8,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1109","DOI":"10.1007\/s00216-007-1335-7","article-title":"The dosage of small volumes for chromatographic quantifications using drop-on-demand dispenser system","volume":"388","author":"Engelmann","year":"2007","journal-title":"Anal. Bioanal. Chem."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"544","DOI":"10.1177\/1087057102238630","article-title":"A standard operation procedure for assessing liquid handler performance in high-throughput screening","volume":"7","author":"Taylor","year":"2002","journal-title":"J. Biomol. Screen."},{"key":"ref_3","first-page":"37","article-title":"In-line processing trends for lateral-flow immunoassay manufacturing","volume":"13","author":"Tisone","year":"2007","journal-title":"IVD Technol."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Thurow, K., Kr\u00fcger, T., and Stoll, N. (2009). An optical approach for the determination of droplet volumes in nanoliterdispensing. J. Autom. Methods Manag. Chem.","DOI":"10.1155\/2009\/198732"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"490","DOI":"10.1002\/qj.49707934204","article-title":"A photoelectric raindrop spectrometer","volume":"79","author":"Mason","year":"1953","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1016\/j.sna.2010.01.023","article-title":"Non-contact optical sensor to detect free flying droplets in the nanolitre range","volume":"158","author":"Ernst","year":"2010","journal-title":"Sens. Actuators A"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"929","DOI":"10.1175\/1520-0450(1968)007<0929:AETFIW>2.0.CO;2","article-title":"An electrostatic theory for instruments which measure the radii of water drops by detecting a change in capacity due to the presence of a drop","volume":"7","author":"Winn","year":"1968","journal-title":"J. Appl. Meteor."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1736","DOI":"10.1109\/JSEN.2010.2095837","article-title":"Noncontact determination of velocity and volume of nanoliter droplets on the fly","volume":"11","author":"Ernst","year":"2011","journal-title":"IEEE Sens. J."},{"key":"ref_9","first-page":"300","article-title":"PipeJet: A simple disposable dispenser for the nanoliter- and microliter range","volume":"9","author":"Streule","year":"2004","journal-title":"JALA"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2121","DOI":"10.1126\/science.1056991","article-title":"Autoionization in liquid water","volume":"291","author":"Geissler","year":"2001","journal-title":"Science"},{"key":"ref_11","unstructured":"Anderson, J.D. (1995). Computational Fluid Dynamics\u2014The Basics with Applications, McGraw-Hill."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/0021-9991(81)90145-5","article-title":"Volume of fluid (VOF) method for the dynamics of free boundaries","volume":"39","author":"Hirt","year":"1981","journal-title":"J. Comp. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1006\/jcph.1998.5906","article-title":"Reconstruction volume tracking","volume":"141","author":"Rider","year":"1998","journal-title":"J. Comp. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"690","DOI":"10.1016\/j.ijmultiphaseflow.2007.08.008","article-title":"3-D numerical simulation of contact angle hysteresis for microscale two phase flow","volume":"34","author":"Fang","year":"2008","journal-title":"Int. J. Multiph. Flow"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1016\/0021-9991(92)90240-Y","article-title":"A continuum method for modeling surface tension","volume":"100","author":"Brackbill","year":"1992","journal-title":"J. Comput. Phys."},{"key":"ref_16","unstructured":"ESI-Group Available online: http:\/\/www.esi-group.com (accessed on 29 June 2010)."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/12\/8\/10550\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:51:36Z","timestamp":1760219496000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/12\/8\/10550"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,8,3]]},"references-count":16,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2012,8]]}},"alternative-id":["s120810550"],"URL":"https:\/\/doi.org\/10.3390\/s120810550","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2012,8,3]]}}}