Precision density and viscosity measurement using two cantilevers with different widths

Abstract

Weintroduceanovelmethodforfastmeasurementofliquidviscosityanddensityusingtwocantilevers withdifferentgeometries.Ourmethodcanbeusedforreal-timemonitoringinlabonchipsystemsand offerhighaccuracyforalargerangeofdensitiesandviscosities.Themeasurementprincipleisbasedon trackingtheoscillationfrequenciesoftwocantileverswithaphase-lockedloop(PLL)andcomparingwith referencemeasurementswithaknownfluid.Asetofequationsandasimplealgorithmisdevelopedto relatethedensityandtheviscositytothefrequencyshiftsofthecantilevers.Wefoundthattheeffectof thedensityandtheviscositycanbewellseparatedifcantilevershavedifferentwidths.Intheexperiments, twoNickelmicrocantilevers(widths25 mand100 m,length:200 m,thickness:1.75 m)werefully immersedintheliquidandthetemperaturewascontrolled.TheactuationwasusinganexternalelectrocoilandtheoscillationsweremonitoredusinglaserDopplervibrometer.Thus,electricalconnectionsto thecantileversarenotrequired,enablingmeasurementsalsoinconductiveliquids.ThePLLisusedto setthephasedifferenceto90◦betweentheactuatorandthesensor.Calibrationmeasurementswere performedusingglycerolandethyleneglycolsolutionswithknowndensitiesandviscosities.Themeasurementerrorwiththenewmethodwaslowerthan3%indensityintherange995–1150kg/m3and 4.6%inviscosityintherange0.935–4mPa.s.Basedonthesignal-to-noiseratio,theminimumdetectable differenceintheviscosityis1 Pa.sandthedensityis0.18kg/m3.Furtherimprovementsintherange andtheaccuracyarepossibleusing3ormorecantileverswithdifferentgeometries.