{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T01:39:08Z","timestamp":1772329148447,"version":"3.50.1"},"reference-count":27,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2021,6,29]],"date-time":"2021-06-29T00:00:00Z","timestamp":1624924800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Nature Science Foundation of China","award":["61573312"],"award-info":[{"award-number":["61573312"]}]},{"name":"Project of State Key Laboratory of Industrial Control Technology (Zhejiang University)","award":["ICT2021A09"],"award-info":[{"award-number":["ICT2021A09"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Electrodes are basic components of C4D (capacitively coupled contactless conductivity detection) sensors, and different electrode structures (the configuration pattern or the electrode geometry) can lead to different measurement results. In this work, the effects of electrode geometry of radial configuration on the measurement performance of C4D sensors are investigated. Two geometrical parameters, the electrode length and the electrode angle, are considered. A FEM (finite element method) model based on the C4D method is developed. With the FEM model, corresponding simulation results of conductivity measurement with different electrode geometry are obtained. Meanwhile, practical experiments of conductivity measurement are also conducted. According to the simulation results and experimental results, the optimal electrode geometry of the C4D sensor with radial configuration is discussed and proposed. The recommended electrode length is 5\u201310 times of the pipe inner diameter and the recommended electrode angle is 120\u2013160\u00b0.<\/jats:p>","DOI":"10.3390\/s21134454","type":"journal-article","created":{"date-parts":[[2021,6,29]],"date-time":"2021-06-29T22:39:43Z","timestamp":1625006383000},"page":"4454","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Investigation of the Effects of Electrode Geometry on the Performance of C4D Sensor with Radial Configuration"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7263-9116","authenticated-orcid":false,"given":"Qiang","family":"Huang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Industrial Control Technology, College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0688-2385","authenticated-orcid":false,"given":"Junchao","family":"Huang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Industrial Control Technology, College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1677-4671","authenticated-orcid":false,"given":"Yandan","family":"Jiang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Industrial Control Technology, College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haifeng","family":"Ji","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Industrial Control Technology, College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0045-0576","authenticated-orcid":false,"given":"Baoliang","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Industrial Control Technology, College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1858-5994","authenticated-orcid":false,"given":"Zhiyao","family":"Huang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Industrial Control Technology, College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hauser, P.C., and Kub\u00e1\u0148, P. (2020). Capacitively coupled contactless conductivity detection for analytical techniques\u2014Developments from 2018 to 2020. J. Chromatogr. A, 1632.","DOI":"10.1016\/j.chroma.2020.461616"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1016\/j.talanta.2007.05.058","article-title":"Contactless conductivity detection for microfluidics: Designs and applications","volume":"74","author":"Pumera","year":"2007","journal-title":"Talanta"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2786","DOI":"10.3390\/s130302786","article-title":"Contactless impedance sensors and their application to flow measurements","volume":"13","author":"Opekar","year":"2013","journal-title":"Sensors"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/j.trac.2018.03.007","article-title":"20th Anniversary of Axial Capacitively Coupled Contactless Conductivity Detection in Capillary Electrophoresis","volume":"102","author":"Hauser","year":"2018","journal-title":"TrAC Trends Anal. Chem."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3253","DOI":"10.1109\/TIM.2018.2877825","article-title":"A New Contactless Bubble\/Slug Velocity Measurement Method of Gas-Liquid Two-Phase Flow in Small Channels","volume":"68","author":"Huang","year":"2018","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.aca.2007.11.045","article-title":"A review of the recent achievements in capacitively coupled contactless conductivity detection","volume":"607","author":"Hauser","year":"2008","journal-title":"Anal. Chim. Acta"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.sna.2007.10.047","article-title":"Resonance impedance sensing of human blood cells","volume":"145\u2013146","author":"Zheng","year":"2008","journal-title":"Sens. Actuators A Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/S0021-9673(80)80001-X","article-title":"High-frequency contactless conductivity detection in isotachophoresis","volume":"192","author":"Gas","year":"1980","journal-title":"J. Chromatogr. A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"124001","DOI":"10.1088\/0957-0233\/27\/12\/124001","article-title":"A new contactless impedance sensor for void fraction measurement of gas-liquid two-phase flow","volume":"27","author":"Ji","year":"2016","journal-title":"Meas. Sci. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1002\/elps.201800248","article-title":"Contactless conductivity detection for analytical techniques: Developments from 2016 to 2018","volume":"40","author":"Hauser","year":"2019","journal-title":"Electrophoresis"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1007\/s41208-018-0093-y","article-title":"Measuring Method of Solid-Liquid Two-Phase Flow in Slurry Pipeline for Deep-Sea Mining","volume":"34","author":"Yang","year":"2018","journal-title":"Thalassas"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Zhu, H.T., Chen, Y., Xiong, Y.F., Xu, F., and Lu, Y.Q. (2020). A flexible wireless dielectric sensor for noninvasive fluid monitoring. Sensors, 20.","DOI":"10.3390\/s20010174"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.sna.2014.03.024","article-title":"Design and implementation of an industrial C4D sensor for conductivity detection","volume":"213","author":"Ji","year":"2014","journal-title":"Sens. Actuators A Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3387","DOI":"10.1002\/elps.200406059","article-title":"Fundamental aspects of contactless conductivity detection for capillary electrophoresis. Part I: Frequency behavior and cell geometry","volume":"25","author":"Hauser","year":"2004","journal-title":"Electrophoresis"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3718","DOI":"10.1002\/1522-2683(200211)23:21<3718::AID-ELPS3718>3.0.CO;2-U","article-title":"A contactless conductivity detector for capillary electrophoresis: Effects of the detection cell geometry on the detector performance","volume":"23","author":"Opekar","year":"2002","journal-title":"Electrophoresis"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1602","DOI":"10.1109\/TIM.2019.2890921","article-title":"A Capacitive-Coupled Noncontact Probe for the Measurement of Conductivity of Liquids","volume":"68","author":"Tejaswini","year":"2019","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1181","DOI":"10.1002\/elan.200403232","article-title":"The effects of the electrode system geometry on the properties of contactless conductivity detectors for capillary electrophoresis","volume":"17","author":"Opekar","year":"2005","journal-title":"Electroanalysis"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1153","DOI":"10.1109\/JSEN.2006.881390","article-title":"Capacitance sensors for void-fraction measurements and flow-pattern identification in air-oil two-phase flow","volume":"6","author":"Ahmed","year":"2006","journal-title":"IEEE Sens. J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1016\/j.sna.2010.08.018","article-title":"A capacitive sensor system for the analysis of two-phase flows of oil and conductive water","volume":"163","author":"Demori","year":"2010","journal-title":"Sens. Actuators A Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"22431","DOI":"10.3390\/s141222431","article-title":"Measurement of gas-liquid two-phase flow in micro-pipes by a capacitance sensor","volume":"14","author":"Ji","year":"2014","journal-title":"Sensors"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1088\/0957-0233\/1\/1\/012","article-title":"Design of capacitance electrodes for concentration measurement of two-phase flow","volume":"1","author":"Xie","year":"1990","journal-title":"Meas. Sci. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1673","DOI":"10.1007\/s00216-011-5233-7","article-title":"Comparison of the performance characteristics of two tubular contactless conductivity detectors with different dimensions and application in conjunction with HPLC","volume":"401","author":"Mark","year":"2011","journal-title":"Anal. Bioanal. Chem."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"7826","DOI":"10.1021\/ac800380g","article-title":"Reduction of the impedance of a contactless conductivity detector for microchip capillary electrophoresis: Compensation of the electrode impedance by addition of a series inductance from a piezoelectric quartz crystal","volume":"80","author":"Kang","year":"2008","journal-title":"Anal. Chem."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/j.snb.2009.08.032","article-title":"A new method of capacitively coupled contactless conductivity detection based on series resonance","volume":"143","author":"Huang","year":"2009","journal-title":"Sens. Actuators B Chem."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"6371","DOI":"10.1109\/JSEN.2019.2908179","article-title":"Development of a Passive Capacitively Coupled Contactless Conductivity Detection (PC4D) Sensor System for Fluidic Channel Analysis toward Point-of-Care Applications","volume":"19","author":"Bui","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/S0955-5986(03)00019-0","article-title":"Design and optimisation of impedance probes for void fraction measurements","volume":"14","author":"Devia","year":"2003","journal-title":"Flow Meas. Instrum."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.aca.2011.03.038","article-title":"A simple contactless impedance probe for determination of ethanol in gasoline","volume":"694","author":"Opekar","year":"2011","journal-title":"Anal. Chim. 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