{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:26:43Z","timestamp":1760232403178,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2022,11,2]],"date-time":"2022-11-02T00:00:00Z","timestamp":1667347200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union","award":["842147"],"award-info":[{"award-number":["842147"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This work presents a feedback closed-loop platform to be used for viscosity or viscoelasticity sensing of Newtonian or non-Newtonian fluids. The system consists of a photothermally excited microcantilever working in a digital Phase-Locked Loop, in which the phase between the excitation signal to the cantilever and the reference demodulating signals is chosen and imposed in the loop. General analytical models to describe the frequency and amplitude of oscillation of the cantilever immersed in viscous and viscoelastic fluids are derived and validated against experiments. In particular, the sensitivity of the sensor to variations of viscosity of Newtonian fluids, or to variations of elastic\/viscous modulus of non-Newtonian fluids, are studied. Interestingly, it is demonstrated the possibility of controlling the sensitivity of the system to variations of these parameters by choosing the appropriate imposed phase in the loop. A working point with maximum sensitivity can be used for real-time detection of small changes of rheological parameters with low-noise and fast-transient response. Conversely, a working point with zero sensitivity to variations of rheological parameters can be potentially used to decouple the effect of simultaneous external factors acting on the resonator.<\/jats:p>","DOI":"10.3390\/s22218421","type":"journal-article","created":{"date-parts":[[2022,11,3]],"date-time":"2022-11-03T03:53:07Z","timestamp":1667447587000},"page":"8421","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Photothermal Self-Excitation of a Phase-Controlled Microcantilever for Viscosity or Viscoelasticity Sensing"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2572-0974","authenticated-orcid":false,"given":"Jo\u00e3o","family":"Mouro","sequence":"first","affiliation":[{"name":"Institute for Complex Systems, National Research Council (ISC-CNR), 50019 Florence, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6131-0377","authenticated-orcid":false,"given":"Paolo","family":"Paoletti","sequence":"additional","affiliation":[{"name":"School of Engineering, University of Liverpool, Liverpool L69 3GH, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marco","family":"Sartore","sequence":"additional","affiliation":[{"name":"Elbatech Srl, 57030 Marciana, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3063-4376","authenticated-orcid":false,"given":"Massimo","family":"Vassalli","sequence":"additional","affiliation":[{"name":"School of Engineering, University of Glasgow, Glasgow G12 8LT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9851-1850","authenticated-orcid":false,"given":"Bruno","family":"Tiribilli","sequence":"additional","affiliation":[{"name":"Institute for Complex Systems, National Research Council (ISC-CNR), 50019 Florence, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1449","DOI":"10.1039\/b706004c","article-title":"Microrheology: A review of the method and applications","volume":"3","author":"Cicuta","year":"2007","journal-title":"Soft Matter"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"968","DOI":"10.1021\/acsmacrolett.8b00498","article-title":"Optical Tweezers Microrheology: From the Basics to Advanced Techniques and Applications","volume":"7","year":"2018","journal-title":"ACS Macro Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.cocis.2019.02.006","article-title":"Microrheology with optical tweezers: Peaks & troughs","volume":"43","author":"Tassieri","year":"2019","journal-title":"Curr. Opin. Colloid Interface Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2749","DOI":"10.1039\/c005065b","article-title":"Development of a MEMS based dynamic rheometer","volume":"10","author":"Christopher","year":"2010","journal-title":"Lab Chip"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"719898","DOI":"10.1155\/2012\/719898","article-title":"The Microcantilever: A Versatile Tool for Measuring the Rheological Properties of Complex Fluids","volume":"2012","author":"Dufour","year":"2012","journal-title":"J. Sens."},{"key":"ref_6","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_7","doi-asserted-by":"crossref","first-page":"6262","DOI":"10.1063\/1.1512318","article-title":"Torsional frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope","volume":"92","author":"Green","year":"2002","journal-title":"J. Appl. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2731","DOI":"10.1063\/1.1368856","article-title":"Measurement of solution viscosity by atomic force microscopy","volume":"72","author":"Ahmed","year":"2001","journal-title":"Rev. Sci. Instrum."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1122\/1.1475978","article-title":"Rheological measurements using microcantilevers","volume":"46","author":"Boskovic","year":"2002","journal-title":"J. Rheol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"041907","DOI":"10.1063\/1.2837181","article-title":"Rheological behavior probed by vibrating microcantilevers","volume":"92","author":"Belmiloud","year":"2008","journal-title":"Appl. Phys. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.sna.2007.07.010","article-title":"Analysis of resonating microcantilevers operating in a viscous liquid environment","volume":"141","author":"Dufour","year":"2008","journal-title":"Sens. Actuators A Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"043106","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_13","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.snb.2008.08.012","article-title":"Multi-parameter microcantilever sensor for comprehensive characterization of Newtonian fluids","volume":"135","author":"Ghatkesar","year":"2008","journal-title":"Sens. Actuators B Chem."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"154102","DOI":"10.1063\/1.3387753","article-title":"Longitudinal vibration mode of piezoelectric thick-film cantilever-based sensors in liquid media","volume":"96","author":"Castille","year":"2010","journal-title":"Appl. Phys. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/j.sna.2011.02.025","article-title":"A straightforward determination of fluid viscosity and density using microcantilevers: From experimental data to analytical expressions","volume":"172","author":"Youssry","year":"2011","journal-title":"Sens. Actuators A Phys."},{"key":"ref_16","first-page":"753","article-title":"Vibrating Microcantilever used as Viscometer and Microrheometer","volume":"4","author":"Belmiloud","year":"2006","journal-title":"Proc. IEEE Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1016\/j.sna.2013.07.022","article-title":"High-frequency viscoelastic measurements of fluids based on microcantilever sensing: New modeling and experimental issues","volume":"201","author":"Lemaire","year":"2013","journal-title":"Sens. Actuators A Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"125306","DOI":"10.1088\/0957-0233\/23\/12\/125306","article-title":"On-chip characterization of the viscoelasticity of complex fluids using microcantilevers","volume":"23","author":"Youssry","year":"2012","journal-title":"Meas. Sci. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"065001","DOI":"10.1063\/5.0047631","article-title":"Multimodal real-time frequency tracking of cantilever arrays in liquid environment for biodetection: Comprehensive setup and performance analysis","volume":"92","author":"Padovani","year":"2021","journal-title":"Rev. Sci. Instrum."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"022136","DOI":"10.1063\/1.3601872","article-title":"Comparison of photothermal and piezoacoustic excitation methods for frequency and phase modulation atomic force microscopy in liquid environments","volume":"1","author":"Labuda","year":"2011","journal-title":"AIP Adv."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"103703","DOI":"10.1063\/1.3238484","article-title":"Spurious-free cantilever excitation in liquid by piezoactuator with flexure drive mechanism","volume":"80","author":"Asakawa","year":"2009","journal-title":"Rev. Sci. Instrum."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"144101","DOI":"10.1063\/1.4995386","article-title":"Measuring viscosity with nonlinear self-excited microcantilevers","volume":"111","author":"Mouro","year":"2017","journal-title":"Appl. Phys. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Mouro, J., Paoletti, P., Basso, M., and Tiribilli, B. (2021). Measuring Viscosity Using the Hysteresis of the Non-Linear Response of a Self-Excited Cantilever. Sensors, 21.","DOI":"10.3390\/s21165592"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"124305","DOI":"10.1063\/1.4896487","article-title":"Self-excited vibrational viscometer for high-viscosity sensing","volume":"116","author":"Yabuno","year":"2014","journal-title":"J. Appl. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"061009","DOI":"10.1115\/1.4030975","article-title":"Self-Excited Vibrational Cantilever-Type Viscometer Driven by Piezo-Actuator","volume":"137","author":"Higashino","year":"2015","journal-title":"J. Vib. Acoust."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Urasaki, S., Yabuno, H., Yamamoto, Y., and Matsumoto, S. (2021). Sensorless Self-Excited Vibrational Viscometer with Two Hopf Bifurcations Based on a Piezoelectric Device. Sensors, 21.","DOI":"10.3390\/s21041127"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"8676","DOI":"10.1021\/ac4014918","article-title":"Real-Time Viscosity and Mass Density Sensors Requiring Microliter Sample Volume Based on Nanomechanical Resonators","volume":"85","author":"Bircher","year":"2013","journal-title":"Anal. Chem."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"124904","DOI":"10.1063\/1.2205409","article-title":"Photothermal excitation of microcantilevers in liquids","volume":"99","author":"Ramos","year":"2006","journal-title":"J. Appl. Phys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"173108","DOI":"10.1063\/1.2917718","article-title":"Phototermal self-excitation of nanomechanical resonators in liquids","volume":"92","author":"Ramos","year":"2008","journal-title":"Appl. Phys. Lett."},{"key":"ref_30","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_31","doi-asserted-by":"crossref","unstructured":"Mouro, J., Pinto, R., Paoletti, P., and Tiribilli, B. (2020). Microcantilever: Dynamical Response for Mass Sensing and Fluid Characterization. Sensors, 21.","DOI":"10.3390\/s21010115"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"095008","DOI":"10.1088\/1361-6439\/aa7a6f","article-title":"Nonlinear behaviour of self-excited microcantilevers in viscous fluids","volume":"27","author":"Mouro","year":"2017","journal-title":"J. Micromech. Microeng."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/21\/8421\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:09:14Z","timestamp":1760144954000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/21\/8421"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,2]]},"references-count":32,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["s22218421"],"URL":"https:\/\/doi.org\/10.3390\/s22218421","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,11,2]]}}}