{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T11:17:46Z","timestamp":1762341466898,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,5,27]],"date-time":"2020-05-27T00:00:00Z","timestamp":1590537600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100013348","name":"Innosuisse - Schweizerische Agentur f\u00fcr Innovationsf\u00f6rderung","doi-asserted-by":"publisher","award":["27254.1"],"award-info":[{"award-number":["27254.1"]}],"id":[{"id":"10.13039\/501100013348","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper discusses a state-of-the-art inline tubular sensor that can measure the viscosity\u2013density      (   \u03c1 \u03b7   )      of a passing fluid. In this study, experiments and numerical modelling were performed to develop a deeper understanding of the tubular sensor. Experimental results were compared with an analytical model of the torsional resonator. Good agreement was found at low viscosities, although the numerical model deviated slightly at higher viscosities. The sensor was used to measure viscosities in the range of 0.3\u20131000 mPa\u00b7s at a density of 1000 kg\/m3. Above 50 mPa\u00b7s, numerical models predicted viscosity within \u00b15% of actual measurement. However, for lower viscosities, there was a higher deviation between model and experimental results up to a maximum of \u00b121% deviation at 0.3 mPa\u00b7s. The sensor was tested in a flow loop to determine the impact of both laminar and turbulent flow conditions. No significant deviations from the static case were found in either of the flow regimes. The numerical model developed for the tubular torsional sensor was shown to predict the sensor behavior over a wide range, enabling model-based design scaling.<\/jats:p>","DOI":"10.3390\/s20113036","type":"journal-article","created":{"date-parts":[[2020,5,28]],"date-time":"2020-05-28T12:36:58Z","timestamp":1590669418000},"page":"3036","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Analysis of a Tubular Torsionally Resonating Viscosity\u2013Density Sensor"],"prefix":"10.3390","volume":"20","author":[{"given":"Daniel","family":"Brunner","sequence":"first","affiliation":[{"name":"Institute of Computational Physics, Zurich University of Applied Sciences, ZHAW, 8400 Winterthur, Switzerland"},{"name":"Faculty of Engineering Science and Technology, Department of Automation and Process Engineering, The Arctic University of Norway, UiT, P.O. Box 6050 Langnes, 9037 Troms\u00f8, Norway"}]},{"given":"Joe","family":"Goodbread","sequence":"additional","affiliation":[{"name":"Rheonics GmbH, 8406 Winterthur, Switzerland"}]},{"given":"Klaus","family":"H\u00e4usler","sequence":"additional","affiliation":[{"name":"Rheonics GmbH, 8406 Winterthur, Switzerland"}]},{"given":"Sunil","family":"Kumar","sequence":"additional","affiliation":[{"name":"Rheonics GmbH, 8406 Winterthur, Switzerland"}]},{"given":"Gernot","family":"Boiger","sequence":"additional","affiliation":[{"name":"Institute of Computational Physics, Zurich University of Applied Sciences, ZHAW, 8400 Winterthur, Switzerland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0252-3476","authenticated-orcid":false,"given":"Hassan A.","family":"Khawaja","sequence":"additional","affiliation":[{"name":"Faculty of Engineering Science and Technology, Department of Automation and Process Engineering, The Arctic University of Norway, UiT, P.O. Box 6050 Langnes, 9037 Troms\u00f8, Norway"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4102","DOI":"10.1063\/1.2970963","article-title":"Detection of Microviscosity by Using Uncalibrated Atomic Force Microscopy Cantilevers","volume":"93","author":"Papi","year":"2008","journal-title":"Appl. Phys. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1063\/1.2838295","article-title":"Resonating Modes of Vibrating Microcantilevers in Liquid","volume":"92","author":"Ghatkesar","year":"2008","journal-title":"Appl. Phys. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"194102","DOI":"10.1063\/1.2200588","article-title":"Fluid viscosity determination by means of uncalibrated atomic force microscopy cantilevers","volume":"88","author":"Papi","year":"2006","journal-title":"Appl. Phys. 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