Abstract
To fulfil the need of research minded audience, modern viscometers using various physical phenomena are described. The viscometers discussed are based on tuning fork, ultrasonic, plate waves, Love waves, cantilevers and use of optical fibres. A tuning fork generates sound using the phenomenon of resonance at a constant frequency. Similarly a tuning fork-type viscometer resonate its sensor plates at a natural frequency and measures viscosity from the driving force (electromagnetic force) required to maintain constant amplitude. Measurement of acoustic and shear impedances of ultrasonic longitudinal waves are functions of viscosity of the liquid. A viscometer based on aforesaid principle has been described. Martin et al. showed that the attenuation of the plate waves propagating on thin silicon-nitride membranes in contact with viscous liquids depends upon the viscosity of the liquid while the decrease in frequency of maximum transmission depends upon the density of the liquid. Thus an ultrasonic plate wave viscometer along with its basic theory is briefly described. Love wavesâplain polarised shear waves using micro devices have been profitably used for viscosity measurement. The Change in frequency of a PZT crystal is a function of the product of viscosity and density of the liquid around it. Piezoelectric resonator has a good potential to measure viscosity and density of the liquids. Such a device is also given. Similarly the micro-cantilevers used for measurement of very small forces can be used to determine density and viscosity of liquids. The change in amplitude and velocity of a vibrating optical fibres partially immersed in a liquid depends upon the viscosity of the liquid. The change in intensity of the diffraction pattern is proportional to the small changes in amplitude of the vibrating optical fibre. This phenomenon has been used to determine viscosity of liquids available in very small amount.
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Sader JE (1998) Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscopy. J. Appl. Phys. 84, 64 (1998); Abstract: The vibrational characteristics of a cantilever beam are well known tostrongly depend on the fluid in which the beam is immersed. In this paper, wepresent a detailed theoretical analysis of the frequency response of a cantilever beam, that is immersed in a viscous fluid and excited by an arbitrary driving force. Due to its practical importance in application to the atomic force microscope (AFM), we consider in detail the special case of a cantilever beam that is excited by a thermal driving force. This will incorporate the presentation of explicit analytical formulae and numerical results, which will be of value to the users and designers of AFM cantilever beams.
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John E. Sader, James W. M. Chon, and Paul Mulvaney (1999) âCalibration of rectangular atomic force microscope cantileversâ, Rev. Sci. Instrum. 70, 3967 Abstract: A method to determine the spring constant of a rectangular atomic forcemicroscope cantilever is proposed that relies solely on the measurement of the resonant frequency and quality factor of the cantilever in fluid (typically air), and knowledge of its plan view dimensions. This method gives very good accuracy and improves upon the previous formulation by Sader et al. [Rev. Sci. Instrum. 66, 3789 (1995)] which, unlike the present method, requires knowledge of both the cantilever density and thickness.
Nabil Ahmed, Diego F. Nino, and Vincent T. Moy, 2001, âMeasurement of solution viscosity by atomic force microscopyâ Rev. Sci. Instrum. 72, 2731, (4 pages) Abstract: We report on studies aimed at employing the atomic force microscope (AFM) to measure the viscosity of aqueous solutions. At ambient temperature, the AFM cantilever undergoes thermal fluctuations that are highly sensitive to the local environment. Here, we present measurements of the (cantileverâs resonant frequency in aqueous solutions of glycerol, sucrose, ethanol, sodium chloride, polyethylene glycol, and bovine plasma albumin). The measurements revealed that variations in the resonant frequency of the cantilever in the different solutions are largely dependent on the viscosity of the medium. An application of this technique is to monitor the progression of a chemical reaction where a change in viscosity is expected to occur. An example is demonstrated through monitoring of the hydrolysis of double stranded deoxyribonucleic acid by DNase.
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G. Y. Chen1, R. J. Warmack1, T. Thundat1, D. P. Allison1, and A. Huang2, 1994 âResonance response of scanning force microscopy cantileversâ Rev. Sci. Instrum. 65, 2532 Abstract: A variational method is used to calculate the deflection and the fundamental and harmonic resonance frequencies of commercial Vâshaped and rectangular atomic force microscopy cantilevers. The effective mass of Vâshaped cantilevers is roughly half that calculated for the equivalent rectangular cantilevers. Damping by environmental gases, including air, nitrogen, argon, and helium, affects the frequency of maximum response and to a much greater degree the quality factor Q. Helium has the lowest viscosity, resulting in the highest Q, and thus provides the best sensitivity in non-contact force microscopy. Damping in liquids is dominated by an increase in effective mass of the cantilever due to an added mass of the liquid being dragged with that cantilever.
Abdelhamid Maali1, Cedric Hurth2, Rodolphe Boisgard1, Cedric Jai1, Touria Cohen-Bouhacina1, and Jean-Pierre Aim1, 2005, âHydrodynamics of oscillating atomic force microscopy cantilevers in viscous fluidsâ J. Appl. Phys. 97, 074907, 6 pages Abstract: We present a study of thermal noise of commercially available atomic force microscopy (AFM) cantilevers in air and in water. The purpose of this work is to investigate the oscillation behavior of a clamped AFM microlever in liquids. Up to eight vibration modes are recorded. The experimental results are compared to theoretical predictions from the hydrodynamic functions corresponding to rigid transverse oscillations of an infinitely long rectangular beam. Except for the low-frequency modes, the known hydrodynamic functions cannot describe the amount of dissipated energy due to the liquid motion induced by the cantilever oscillation. The observed variation of the damping coefficient is smaller than the one predicted. The difference at higher modes between the mentioned theoretical description and experimental results is discussed with the help of numerical solutions of the three-dimensional Navierâs Stokes equation.
Lippert F, Parker D, Jandt K (2004) Caries Res 38:464
Perry J, Neville A, Hodgkiess T (2002) J Therm Spray Technol 11:536
Bergauda C, Nicu L (2000) Rev Sci Instrum 71:2487
Landau, Lifshitz F (1995) Fluid mechanics, 2nd ed. _Pergamon, New York
Sader JE (1998) J Appl Phys 84: 64
Sader JE (2000) J Appl Phys 87:3978
Boskovic S, Chon JWM, Mulvaney P, Sader JE (2002) J Rheol 46:891
Sader JE, Chon JWM, Mulvaney P (2002) Rev Sci Instrum 70
Ahmed N, Nino DF, Moy VT (2001) Rev Sci Instrum 72:2731
Oden PI, Chen GY, Steele RA, Warmack RJ, Thundat T (1996) Appl Phys Lett 68:3814
Chen GY, Warmack RJ, Thundat T, Allison DP, Huang A (1994) Rev Sci Instrum 65:2532
Chu WH Southwest Research Institute, Technical Report No. 2, 963
Maali A, Hurth C, Boisgard R, Jai C, Cohen-Bouhacina T, Aima J-P (2005) J Appl Phys 97:074907
Buenviaje CK, Ge SR, Rafallovich MH, Overney RM (1998) Mater Res Soc Symp Proc 552:187
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Gupta, S.V. (2014). New Trends in Viscometers. In: Viscometry for Liquids. Springer Series in Materials Science, vol 194. Springer, Cham. https://doi.org/10.1007/978-3-319-04858-1_6
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