{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,5]],"date-time":"2026-04-05T09:35:41Z","timestamp":1775381741634,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,16]],"date-time":"2022-01-16T00:00:00Z","timestamp":1642291200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003246","name":"Dutch Research Council","doi-asserted-by":"publisher","award":["15026"],"award-info":[{"award-number":["15026"]}],"id":[{"id":"10.13039\/501100003246","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A micro-Coriolis mass flow sensor is a resonating device that measures small mass flows of fluid. A large vibration amplitude is desired as the Coriolis forces due to mass flow and, accordingly, the signal-to-noise ratio, are directly proportional to the vibration amplitude. Therefore, it is important to maximize the quality factor Q so that a large vibration amplitude can be achieved without requiring high actuation voltages and high power consumption. This paper presents an investigation of the Q factor of different devices in different resonant modes. Q factors were measured both at atmospheric pressure and in vacuum. The measurement results are compared with theoretical predictions. In the atmospheric environment, the Q factor increases when the resonance frequency increases. When reducing the pressure from 1 bar to 0.1 bar, the Q factor almost doubles. At even lower pressures, the Q factor is inversely proportional to the pressure until intrinsic effects start to dominate, resulting in a maximum Q factor of approximately 7200.<\/jats:p>","DOI":"10.3390\/s22020673","type":"journal-article","created":{"date-parts":[[2022,1,16]],"date-time":"2022-01-16T20:45:21Z","timestamp":1642365921000},"page":"673","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Air Damping Analysis of a Micro-Coriolis Mass Flow Sensor"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6123-6365","authenticated-orcid":false,"given":"Yaxiang","family":"Zeng","sequence":"first","affiliation":[{"name":"Integrated Devices and Systems Group, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands"}]},{"given":"Remco","family":"Sanders","sequence":"additional","affiliation":[{"name":"Integrated Devices and Systems Group, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5571-739X","authenticated-orcid":false,"given":"Remco J.","family":"Wiegerink","sequence":"additional","affiliation":[{"name":"Integrated Devices and Systems Group, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands"}]},{"given":"Joost C.","family":"L\u00f6tters","sequence":"additional","affiliation":[{"name":"Integrated Devices and Systems Group, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands"},{"name":"Bronkhorst High-Tech B.V., Nijverheidsstraat lA, 7261 AK Ruurlo, The Netherlands"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.flowmeasinst.2014.08.015","article-title":"Coriolis flowmeters: A review of developments over the past 20 years, and an assessment of the state of the art and likely future directions","volume":"40","author":"Wang","year":"2014","journal-title":"Flow Meas. Instrum."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"125001","DOI":"10.1088\/0960-1317\/20\/12\/125001","article-title":"Modeling, design, fabrication and characterization of a micro Coriolis mass flow sensor","volume":"20","author":"Haneveld","year":"2010","journal-title":"J. Micromech. Microeng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.sna.2007.01.008","article-title":"Squeeze film air damping in MEMS","volume":"136","author":"Bao","year":"2007","journal-title":"Sens. Actuators A Phys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1437","DOI":"10.1109\/JMEMS.2006.883573","article-title":"Engineering MEMS Resonators with Low Thermoelastic Damping","volume":"15","author":"Duwel","year":"2006","journal-title":"J. Microelectromech. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"085021","DOI":"10.1088\/0960-1317\/21\/8\/085021","article-title":"In-plane acoustic reflectors for reducing effective anchor loss in lateral\u2013extensional MEMS resonators","volume":"21","author":"Harrington","year":"2011","journal-title":"J. Micromech. Microeng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1016\/0042-207X(84)90318-X","article-title":"A bending and stretching mode crystal oscillator as a friction vacuum gauge","volume":"34","author":"Kokubun","year":"1984","journal-title":"Vacuum"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/0924-4247(95)01003-J","article-title":"Damping characteristics of beam-shaped micro-oscillators","volume":"49","author":"Hosaka","year":"1995","journal-title":"Sens. Actuators A Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1115\/1.2893949","article-title":"Theoretical and Experimental Study on Airflow Damping of Vibrating Microcantilevers","volume":"121","author":"Hosaka","year":"1999","journal-title":"J. Vib. Acoust."},{"key":"ref_9","first-page":"19","article-title":"Dependence of the quality factor of micromachined silicon beam resonators on pressure and geometry","volume":"10","author":"Blom","year":"1992","journal-title":"J. Vac. Sci. Technol. B Microelectron. Nanometer Struct."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1063\/1.368002","article-title":"Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope","volume":"84","author":"Sader","year":"1998","journal-title":"J. Appl. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2487","DOI":"10.1063\/1.1150640","article-title":"Viscosity measurements based on experimental investigations of composite cantilever beam eigenfrequencies in viscous media","volume":"71","author":"Bergaud","year":"2000","journal-title":"Rev. Sci. Instrum."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"074907","DOI":"10.1063\/1.1873060","article-title":"Hydrodynamics of oscillating atomic force microscopy cantilevers in viscous fluids","volume":"97","author":"Maali","year":"2005","journal-title":"J. Appl. Phys."},{"key":"ref_13","first-page":"1803","article-title":"Silicon resonant microcantilevers for absolute pressure measurement","volume":"24","author":"Bianco","year":"2006","journal-title":"J. Vac. Sci. Technol. B Microelectron. Nanometer Struct."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1016\/j.snb.2011.08.020","article-title":"Application of piezoelectric tuning forks in liquid viscosity and density measurements","volume":"160","author":"Waszczuk","year":"2011","journal-title":"Sens. Actuators B Chem."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"24318","DOI":"10.3390\/s150924318","article-title":"Measurement and Evaluation of the Gas Density and Viscosity of Pure Gases and Mixtures Using a Micro-Cantilever Beam","volume":"15","author":"Badarlis","year":"2015","journal-title":"Sensors"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.triboint.2010.10.001","article-title":"An investigation of the damping effects of various gas environments on a vibratory MEMS device","volume":"44","author":"Kim","year":"2011","journal-title":"Tribol. Int."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.microrel.2016.05.007","article-title":"Experimental investigation of temperature and relative humidity effects on resonance frequency and quality factor of CMOS-MEMS paddle resonator","volume":"63","author":"Jan","year":"2016","journal-title":"Microelectron. Reliab."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1088\/0960-1317\/17\/1\/018","article-title":"Comments on the size effect on the microcantilever quality factor in free air space","volume":"17","author":"Lee","year":"2007","journal-title":"J. Micromech. Microeng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.jsv.2007.04.013","article-title":"Investigation of the effects of air on the dynamic behavior of a small cantilever beam","volume":"305","author":"Nouira","year":"2007","journal-title":"J. Sound Vib."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/j.ultramic.2003.12.014","article-title":"Hydrodynamic damping of a magnetically oscillated cantilever close to a surface","volume":"100","author":"Rankl","year":"2004","journal-title":"Ultramicroscopy"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"174904","DOI":"10.1063\/1.4803681","article-title":"Study of the out-of-plane vibrational modes in thin-film amorphous silicon micromechanical disk resonators","volume":"113","author":"Gualdino","year":"2013","journal-title":"J. Appl. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1109\/JMEMS.2021.3107744","article-title":"Design, Fabrication, and Characterization of a Micro Coriolis Mass Flow Sensor Driven by PZT Thin Film Actuators","volume":"30","author":"Zeng","year":"2021","journal-title":"J. Microelectromech. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"228103","DOI":"10.1103\/PhysRevLett.102.228103","article-title":"Nonmonotonic Energy Dissipation in Microfluidic Resonators","volume":"102","author":"Burg","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_24","unstructured":"Karniadakis, G., Beskok, A., and Aluru, N. (2005). Microflows and Nanoflows: Fundamentals and Simulation, Springer."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Landau, L.D., and Lifshitz, E.M. (1987). Viscous fluids. Fluid Mechanics, Elsevier. [2nd ed.].","DOI":"10.1016\/B978-0-08-033933-7.50010-6"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"114906","DOI":"10.1063\/1.2202232","article-title":"Hydrodynamic loading of microcantilevers vibrating in viscous fluids","volume":"99","author":"Basak","year":"2006","journal-title":"J. Appl. Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"056313","DOI":"10.1103\/PhysRevE.85.056313","article-title":"Nanoelectromechanical devices in a fluidic environment","volume":"85","author":"Svitelskiy","year":"2012","journal-title":"Phys. Rev. E"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/BF01540828","article-title":"Calculation of unsteady flows due to small motions of cylinders in a viscous fluid","volume":"3","author":"Tuck","year":"1969","journal-title":"J. Eng. Math."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/0042-207X(66)91162-6","article-title":"The theory of oscillating-vane vacuum gauges","volume":"16","author":"Christian","year":"1966","journal-title":"Vacuum"},{"key":"ref_30","unstructured":"(2021, November 09). Laser Doppler Vibrometry\u2014Technology from Polytec\u2014Polytec. Available online: https:\/\/www.polytec.com\/eu\/vibrometry\/technology\/laser-doppler-vibrometry."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/2\/673\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T14:15:10Z","timestamp":1760364910000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/2\/673"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,16]]},"references-count":30,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,1]]}},"alternative-id":["s22020673"],"URL":"https:\/\/doi.org\/10.3390\/s22020673","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,16]]}}}