WO2001022056A1 - Micromechanical transient sensor for measuring viscosity and density of a fluid - Google Patents

Micromechanical transient sensor for measuring viscosity and density of a fluid Download PDF

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Publication number
WO2001022056A1
WO2001022056A1 PCT/US2000/026287 US0026287W WO0122056A1 WO 2001022056 A1 WO2001022056 A1 WO 2001022056A1 US 0026287 W US0026287 W US 0026287W WO 0122056 A1 WO0122056 A1 WO 0122056A1
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Prior art keywords
fluid
viscosity
cantilever
density
microcantilever
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PCT/US2000/026287
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French (fr)
Inventor
Thomas G. Thundat
Patrick Ian Oden
Robert J. Warmack
Eric Laurent Finot
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Ut-Battelle, Llc
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Priority to AU76126/00A priority Critical patent/AU7612600A/en
Publication of WO2001022056A1 publication Critical patent/WO2001022056A1/en

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/02—Analysing fluids
    • G01N29/022—Fluid sensors based on microsensors, e.g. quartz crystal-microbalance [QCM], surface acoustic wave [SAW] devices, tuning forks, cantilevers, flexural plate wave [FPW] devices
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N11/00—Investigating flow properties of materials, e.g. viscosity, plasticity; Analysing materials by determining flow properties
    • G01N11/10—Investigating flow properties of materials, e.g. viscosity, plasticity; Analysing materials by determining flow properties by moving a body within the material
    • G01N11/16—Investigating flow properties of materials, e.g. viscosity, plasticity; Analysing materials by determining flow properties by moving a body within the material by measuring damping effect upon oscillatory body
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/22—Details, e.g. general constructional or apparatus details
    • G01N29/30—Arrangements for calibrating or comparing, e.g. with standard objects
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/34—Generating the ultrasonic, sonic or infrasonic waves, e.g. electronic circuits specially adapted therefor
    • G01N29/341—Generating the ultrasonic, sonic or infrasonic waves, e.g. electronic circuits specially adapted therefor with time characteristics
    • G01N29/343—Generating the ultrasonic, sonic or infrasonic waves, e.g. electronic circuits specially adapted therefor with time characteristics pulse waves, e.g. particular sequence of pulses, bursts
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/44—Processing the detected response signal, e.g. electronic circuits specially adapted therefor
    • G01N29/46—Processing the detected response signal, e.g. electronic circuits specially adapted therefor by spectral analysis, e.g. Fourier analysis or wavelet analysis
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N9/00—Investigating density or specific gravity of materials; Analysing materials by determining density or specific gravity
    • G01N9/002—Investigating density or specific gravity of materials; Analysing materials by determining density or specific gravity using variation of the resonant frequency of an element vibrating in contact with the material submitted to analysis
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N9/00—Investigating density or specific gravity of materials; Analysing materials by determining density or specific gravity
    • G01N9/002—Investigating density or specific gravity of materials; Analysing materials by determining density or specific gravity using variation of the resonant frequency of an element vibrating in contact with the material submitted to analysis
    • G01N2009/006—Investigating density or specific gravity of materials; Analysing materials by determining density or specific gravity using variation of the resonant frequency of an element vibrating in contact with the material submitted to analysis vibrating tube, tuning fork
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00—Indexing codes associated with group G01N29/00
    • G01N2291/02—Indexing codes associated with the analysed material
    • G01N2291/025—Change of phase or condition
    • G01N2291/0256—Adsorption, desorption, surface mass change, e.g. on biosensors
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00—Indexing codes associated with group G01N29/00
    • G01N2291/02—Indexing codes associated with the analysed material
    • G01N2291/028—Material parameters
    • G01N2291/02818—Density, viscosity
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00—Indexing codes associated with group G01N29/00
    • G01N2291/04—Wave modes and trajectories
    • G01N2291/042—Wave modes
    • G01N2291/0427—Flexural waves, plate waves, e.g. Lamb waves, tuning fork, cantilever

Definitions

  • This invention relates to apparatus and methods for the accurate determination of viscosity, density or both of very small volumes of fluids.
  • MEMS microelectromechanical sensors
  • U.S. Patent No. 5,130,257 to Bear et al. discloses a viscosity sensor fabricated using a surface transverse wave device for use in the measurement of viscosity.
  • microcantilevers having typical dimensions of 50-200 ⁇ m in length, 10-40 ⁇ m in width, and 0.3-3 ⁇ m in thickness.
  • the resonance frequency, amplitude and Q-value varies with the viscosity and the density of the medium surrounding the cantilever.
  • the cantilever is excited into resonance by an external means for a finite amount of time until a stable resonance amplitude is established. After that period, the external excitation is switched off and the transient behavior (decay) of the vibration is recorded.
  • the resonance frequency, amplitude and Q factor are determined from the transient spectrum.
  • the decay in amplitude of vibration can be used to determine the density of the material. Numerous methods for measuring the vibration of the cantilever are available and a multiplicity of cantilevers can be used for the determination of a wide range of densities.
  • Fig. 1 is a schematic diagram illustrating the components of this invention.
  • Fig. 2 is an illustration of the signal which is used to discern the viscosity and density of a fluid medium.
  • Fig. 3(a) shows a square wave signal used to excite a cantilever
  • Fig. 3(b) shows the corresponding transient response of a cantilever.
  • Fig. 4 is a trace of the transient response of a cantilever.
  • a MEMS device can be constructed using available or easily fabricated components.
  • the microcantilevers used are commercially available from several sources, and may include those conventionally used in scanning force microscopy.
  • the microcantilever may be prepared from various ceramics metals and semiconductor materials by methods well known to those familiar with the fabrication of microelectronic devices and according to the method of the aforementioned Albrecht et al. reference.
  • a mounting block with an inventive piezoelectric exciting device is commercially available, as is a mounting stage for the cantilever and laboratory base.
  • Detection methods may be optical beam deflection, interference, capacitance, piezoresistance, or electron tunneling. On the basis of familiarity, we prefer optical methods such as those described in the Wachter et al.
  • the technique involve exciting the cantilever into resonance frequency by an external means such as a piezoelectric crystal or by electrostatic means, or electromagnetic, or photoinduced, or the like as are known in the art.
  • the microcantilevers can also be excited using a photothermal technique where the light source is used in a pulse mode to impart energy to the cantilever.
  • Microcantilevers can also be excited using acoustic waves. It may take many pulses to excite the microcantilevers into resonance. Because the square pulses contain all the Fourier components, a cantilever of any natural resonance frequency can be excited using square pulse excitation.
  • the form of the excitation amplitude can be periodic at or near the resonant frequency of the cantilever and can be pure harmonic, square, or other arbitrary waveform.
  • a pure harmonic waveform to induce the maximum amplitude resonance of the cantilever may be used.
  • An impulse or rectangular pulse can also be used.
  • the mathematical expression for viscosity and density of the fluid can be derived as follows. Let L, W, and T be the length, width, and thickness of the cantilever. The density of the cantilever is taken as p c . The cantilever resonates in vacuum with a resonance frequency, ⁇ 0 (2 ⁇ f°) and a quality factor Q 0 . The finite Q-factor in vacuum is mainly due to internal energy loss. However, when operated in a fluid, the resonance frequency and Q-factor change due to energy loss due to viscosity.
  • the equation of motion of the cantilever in a medium can be written as:
  • E the Young's modulus
  • I the moment of inertia
  • b 0 the intrinsic damping of the cantilever
  • M 0 the mass per unit length of the cantilever
  • M f us the induced mass (mass of fluid moving along with the cantilever per unit length)
  • u is the cantilever displacement at distance x from the fixed end of the cantilever.
  • the intrinsic damping b 0 can be determined from the resonance characteristics of the cantilever in vacuum (w 0 and Q 0 .
  • the intrinsic damping, b 0 can be written as:
  • Equation 8 is a complex number of form, X + iY.
  • the measured angular frequency is:
  • R x can be calculated using the resonance frequency, Q-factor, and the amplitude of vibration in vacuum and in the medium, the length, width, and the thickness of the cantilever as well as the density of the cantilever material is known apriori. Once the Reynold's number and M f are known, the density and the viscosity of the medium can be calculated as follows:
  • Density of the medium can be written as:
  • the viscosity of the medium is given by:
  • the cantilever is calibrated in vacuum or a fluid with known properties for determining its intrinsic resonance properties. Later the cantilever can be resonated in unknown fluids. Or the cantilever can be calibrated in vacuum and a fluid of known viscosity and density to determine the relative changes in viscosity and density with respect to a fluid of known viscosity and density.
  • Another advantage is that this technique is the speed by which measurements can be carried out.
  • the typical time involved is in the range of sub milliseconds to sub microseconds.
  • the method has two inherent advantages.
  • the cantilever can be recalibrated as needed by testing in a vacuum or a fluid of known properties. Any drift in the instrument can be immediately identified.
  • different cantilevers can be compared to each other so that there is no instrumental error resulting from the fabrication of the devices.
  • a second advantage is that, for a given device, comparisons between fluids can be readily made. As noted earlier, for most industrial uses, it is not the absolute viscosity but the viscosity relative to another fluid which is important.
  • a third advantage is magnetic excitation.
  • Magnetic excitation can be achieved by attaching a magnetic particle or evaporating a magnetic film such as Cr or Co or their alloys to the apex of the cantilever.
  • this device quickly senses the direction and the magnitude of any change in viscosity. Since viscosity is affected by temperature, the device may be used to identify a process or operational change before a bulk viscosity or density change could be quickly measured.
  • cantilevers can be readily fabricated in one- or two- dimensional arrays, inhomogeneities of viscosity or density in the monitored fluid can be sensed. Individual cantilevers in the arrays sense physical properties in their immediate vicinity.
  • a one-dimensional array could be placed in a fluid stream, such as a pipe, to measure any inhomogeneities or gradients in viscosity or density of the fluid flow.
  • Microcantilevers can be excited and their movement measured in a variety of manners.
  • Excitation may be by piezoelectric, piezoresistive methods, by capacitive, photothermal, electrostatic, or acoustic techniques. Movement of the cantilever is preferably measured by reflection of light from the tip of the microcantilever but may also be measured piezoelectricly, piezoresistively, and by the methods disclosed in U.S. Patent Nos. 5,440,008 and 5,719,324.
  • An exemplary device for measuring viscosity and density is shown in Fig. 1.
  • An oscillator circuit 1 generates a square wave signal 2 which energizes a device 4 such as a piezoelectric transducer to cause a cantilever 3 to resonate.
  • the resonance is detected, in the example, by shinning a light from laser diode 5 onto the tip of cantilever 3.
  • the reflected light impinges upon position sensitive diode 6.
  • the signal from PSD 6 is amplified (7) and analyzed at amplitude measuring circuit 8.
  • the display of the result form the measurement is shown in Fig. 2 as a plot of amplitude versus time for the decay of resonance when the stimulation is interrupted.
  • Fig. 3 illustrates the relationship between the square wave signal and cantilever response.
  • the method of this invention may be used to determine many physical parameters and for process and quality control.
  • the sensors are very small and may be located in remote and even hazardous locations. Viscosity/specific density provides a good indication of the completeness of a chemical reaction and provides a nearly instantaneous indication of when a process stream condition changes. Leaks, especially gas leaks, are quickly identified at the source.
  • the devices are also useful in kinetic studies, especially using shock tubes to study reaction process. Because this method is based on relative changes in the successive amplitudes rather than absolute amplitudes, this method can be used for measuring viscosity and density in noisy environments.
  • a reference cantilever can be used to avoid transients caused by noises. For example, acoustic noises in the environments can produce transient motion of a cantilever. Using a reference cantilever the noise contribution from the transient can be filtered using wavelet or Fourier transform analysis. The same approach can be used for other interference such as noise introduced by temperature variation.
  • a microcantilever may be fabricated to specify length, width and thickness.
  • the microcantilever is attached, at its base, to a piezoelectric device which is energized by a square wave generator.
  • the microcantilever may be first characterized in a vacuum to determine the resonance frequency and Q-factor by observing the transient response of the cantilever. This is the calibration of the cantilever.
  • the chamber is then opened to admit a gas, pure nitrogen, and allowed to equilibrate at a pressure of 760mm of Hg.
  • the decay curve of the microcantilever is determined as before and plotted as illustrated in Fig. 4. It is noted that the absolute magnitude of the amplitude is not critical, only the decrement.
  • the experiment was repeated using Argon and He.
  • the logarithmic decrement of the amplitude ⁇ is given by equation (16).
  • the value of Q can be determined from the decay curve of the amplitude.
  • the value of the resonance frequency can be determined from the center crossing of the decay curve.
  • the logarithmic decrement of the amplitude ⁇ is given by

Abstract

A method and apparatus for measuring the viscosity and/or specific density of a fluid utilizes a microcantilever vibrated in the analyte fluid. The source of vibration is switched on and off and the decay in amplitude of the vibration is monitored. The method is particularly useful for the measurement of process conditions in remote locations in real time.

Description

TITLE OF THE INVENTION
MICROMECHANICAL TRANSIENT SENSOR FOR MEASURING VISCOSITY AND DENSITY OF A FLUID STATEMENT OF GOVERNMENT RIGHTS
The U.S. Government has rights in this invention pursuant to Contract Number DE- AC05-00OR22725 between the U.S. Department of Energy and UT-Battelle, LLC.
FIELD OF THE INVENTION This invention relates to apparatus and methods for the accurate determination of viscosity, density or both of very small volumes of fluids.
BACKGROUND OF THE INVENTION The atomic force microscope (AFM) was first demonstrated by Binnig and co-workers at IBM in Switzerland. In the AFM, the tip of a flexible cantilever stylus is rastered over the surface of a sample and the movement of the tip of the cantilever is monitored as a measure of minute forces characteristic of surfaces are the atomic level. Demonstration of this principle led to rapid development of microcantilevers [(Albrecht et al., J. Vac. Sci. Technol, 8, 3386 (1990)] The concept of micromechanical and microelectromechanical detection devices has been developed for a number of analytical uses. Wachter et al., U.S. Patent No. 5,445,008 describes the use of vibrated microcantilevers having a chemical coating as a detector for the presence of specific chemical entities. Thundat, et al. in Appliance
Manufacturer, April 1997, 57 (1997) and Microscale Thermophysical Engineering 1, 185 (1997) describe developments of the microelectromechanical sensors (MEMS) for the measurement of chemicals and physical phenomena including the use of sensors to determine concentrations of glycerol in water based on viscosity. U.S. Patent No. 5,719,342 to Thundat et al., addresses additional methods for analysis using MEMS devices particularly directed to induced stress in the microcantilever.
U.S. Patent No. 5,130,257 to Bear et al., discloses a viscosity sensor fabricated using a surface transverse wave device for use in the measurement of viscosity.
Oden et al., Appl. Phys. Lett., 68, 3814 (1996) discloses method for the measurement of viscosity using microfabricated cantilevers in a confined medium. The frequency of vibration of an isolated vibrating cantilever is measured in different solutions. US. Patent No. 5,494,639 to Grzegorzewski discloses a disposable biosensor which uses a vibrating member beneath a cell to accurately measure blood coagulation time as a function of viscosity . The foregoing methods are attempts to find an alternative to the instruments most currently used to measure viscosity of both liquids and gases. These are instruments which perform the analysis by a comparison with a "control fluid." For this reason, measurements are still routinely done using instruments such as the Redwood viscometer, the Couette or rotational concentric-cylinder viscometer (MacMichael or Stormer viscometer), the Rotating Sphere viscometer, the Sayboult Falling Body viscometer, the Vibrating String viscosity meter and the thickness-sheer mode resonators. All of these methods require comparatively large volumes and bulky equipment. The need remains for a small reliable and inexpensive instrument which can measure the viscosity or specific density of small amounts of a liquid or gas and which can be used in difficult-to-access locations.
SUMMARY OF THE INVENTION It is an object of this invention to provide a microminiaturized instrument for the measurement of viscosity and density in liquids and gases. It is a further object of this invention to provide such an instrument which is reliable and inexpensive in comparison with other instrumentation available.
It is a further object to provide a means for profiling the viscosity in a non- inhomogeneous fluid.
It is a further object of this invention to provide means for detecting viscosity and density of very small sample volumes of fluids; to determine viscosity and density of fluids in small confined spaces; to determine kinetics of chemical, biological, and physical reactions by measuring viscosity and density; and, to determine the completeness of chemical, biological, and physical reactions by measuring the viscosity and density.
These and other objects are met by using microcantilevers having typical dimensions of 50-200 μ m in length, 10-40 μ m in width, and 0.3-3 μ m in thickness. When such a microcantilever is driven into resonance, the resonance frequency, amplitude and Q-value varies with the viscosity and the density of the medium surrounding the cantilever. More particularly, according to this invention, the cantilever is excited into resonance by an external means for a finite amount of time until a stable resonance amplitude is established. After that period, the external excitation is switched off and the transient behavior (decay) of the vibration is recorded. The resonance frequency, amplitude and Q factor are determined from the transient spectrum. The decay in amplitude of vibration can be used to determine the density of the material. Numerous methods for measuring the vibration of the cantilever are available and a multiplicity of cantilevers can be used for the determination of a wide range of densities. BRIEF DESCRIPTION OF THE DRAWINGS
Fig. 1 is a schematic diagram illustrating the components of this invention. Fig. 2 is an illustration of the signal which is used to discern the viscosity and density of a fluid medium.
Fig. 3(a) shows a square wave signal used to excite a cantilever; Fig. 3(b) shows the corresponding transient response of a cantilever.
Fig. 4 is a trace of the transient response of a cantilever. DETAILED DESCRIPTION OF THE INVENTION
A MEMS device can be constructed using available or easily fabricated components. The microcantilevers used are commercially available from several sources, and may include those conventionally used in scanning force microscopy. Alternatively, the microcantilever may be prepared from various ceramics metals and semiconductor materials by methods well known to those familiar with the fabrication of microelectronic devices and according to the method of the aforementioned Albrecht et al. reference. Likewise, a mounting block with an inventive piezoelectric exciting device is commercially available, as is a mounting stage for the cantilever and laboratory base. Detection methods may be optical beam deflection, interference, capacitance, piezoresistance, or electron tunneling. On the basis of familiarity, we prefer optical methods such as those described in the Wachter et al. patent, although one or more of the other methods described above may be suitable for liquids with a high degree of opacity or density. The technique involve exciting the cantilever into resonance frequency by an external means such as a piezoelectric crystal or by electrostatic means, or electromagnetic, or photoinduced, or the like as are known in the art. The microcantilevers can also be excited using a photothermal technique where the light source is used in a pulse mode to impart energy to the cantilever. Microcantilevers can also be excited using acoustic waves. It may take many pulses to excite the microcantilevers into resonance. Because the square pulses contain all the Fourier components, a cantilever of any natural resonance frequency can be excited using square pulse excitation. The form of the excitation amplitude can be periodic at or near the resonant frequency of the cantilever and can be pure harmonic, square, or other arbitrary waveform. A pure harmonic waveform to induce the maximum amplitude resonance of the cantilever may be used. An impulse or rectangular pulse can also be used. Once the cantilever is excited into resonance, the excitation source is switched off and the transient behavior of the microcantilever deflection is recorded. In the case of rectangular pulses, the transient response occurs at the beginning and at the end of the pulse. The cantilever resonance amplitude drops off exponentially with time. From the zero crossing of the deflection, the resonance frequency (crossing per unite time) can easily be found. The Q-factor can be determined from decay curve of the amplitude (from the logarithmic decrement).
The mathematical expression for viscosity and density of the fluid can be derived as follows. Let L, W, and T be the length, width, and thickness of the cantilever. The density of the cantilever is taken as pc. The cantilever resonates in vacuum with a resonance frequency, ω0 (2πf°) and a quality factor Q0. The finite Q-factor in vacuum is mainly due to internal energy loss. However, when operated in a fluid, the resonance frequency and Q-factor change due to energy loss due to viscosity. The equation of motion of the cantilever in a medium can be written as:
*§?♦(*.♦*)!♦( ♦»,) =o (1)
where E is the Young's modulus, I is the moment of inertia, b0 is the intrinsic damping of the cantilever, M0 is the mass per unit length of the cantilever, Mf us the induced mass (mass of fluid moving along with the cantilever per unit length), and u is the cantilever displacement at distance x from the fixed end of the cantilever.
The moment of inertia of a rectangular cantilever is given by:
/ = (2)
12
where W is the width and T is the thickness of the cantilever. The intrinsic damping b0 can be determined from the resonance characteristics of the cantilever in vacuum (w0 and Q0. The intrinsic damping, b0, can be written as:
. <Ocp WT
where w0 and Q0 are the resonance frequency and the quality factor, respectively of the cantilever in vacuum, the damping due to viscosity of the fluid is given by:
Figure imgf000005_0001
Where w is the angular frequency and Rk is the Reynold's number of the fluid defined as:
Figure imgf000005_0002
The mass per unit length, Mc = pcWT:
Mc = pcWT (6)
The induced Mf equals:
)pctou 1 +
(7)
Solution for the equation of motion is complex quantity. The angular resonance frequency is given by:
Figure imgf000006_0001
Equation 8 is a complex number of form, X + iY. The measured angular frequency is:
ω rial = 7 (9)
And the full width at 2.05 of the maximum angular frequency is:
Aω = Y (10)
The Q-factor can be expressed as Q = ω/Δω , defining
M* = 2(Mc+Mf) and b* = (bc+ bf) in Eq.1,
and b* = —\ -?— | with C= 3.522EUL4
Figure imgf000006_0002
Therefore, Mj and bf can now be written as:
Figure imgf000007_0001
bf =ϊ-bc (12)
Using Eq. 4, Reynold's number can now be expressed as:
Figure imgf000007_0002
Now Rx can be calculated using the resonance frequency, Q-factor, and the amplitude of vibration in vacuum and in the medium, the length, width, and the thickness of the cantilever as well as the density of the cantilever material is known apriori. Once the Reynold's number and Mf are known, the density and the viscosity of the medium can be calculated as follows:
Density of the medium can be written as:
Figure imgf000007_0003
The viscosity of the medium is given by:
Figure imgf000007_0004
Initially the cantilever is calibrated in vacuum or a fluid with known properties for determining its intrinsic resonance properties. Later the cantilever can be resonated in unknown fluids. Or the cantilever can be calibrated in vacuum and a fluid of known viscosity and density to determine the relative changes in viscosity and density with respect to a fluid of known viscosity and density.
Another advantage is that this technique is the speed by which measurements can be carried out. The typical time involved is in the range of sub milliseconds to sub microseconds. As can be seen from the derivation of equation (15) the method has two inherent advantages. The cantilever can be recalibrated as needed by testing in a vacuum or a fluid of known properties. Any drift in the instrument can be immediately identified. In addition, different cantilevers can be compared to each other so that there is no instrumental error resulting from the fabrication of the devices. A second advantage is that, for a given device, comparisons between fluids can be readily made. As noted earlier, for most industrial uses, it is not the absolute viscosity but the viscosity relative to another fluid which is important. A third advantage is magnetic excitation. Magnetic excitation can be achieved by attaching a magnetic particle or evaporating a magnetic film such as Cr or Co or their alloys to the apex of the cantilever. For process control, this device quickly senses the direction and the magnitude of any change in viscosity. Since viscosity is affected by temperature, the device may be used to identify a process or operational change before a bulk viscosity or density change could be quickly measured. Because cantilevers can be readily fabricated in one- or two- dimensional arrays, inhomogeneities of viscosity or density in the monitored fluid can be sensed. Individual cantilevers in the arrays sense physical properties in their immediate vicinity. For example, a one-dimensional array could be placed in a fluid stream, such as a pipe, to measure any inhomogeneities or gradients in viscosity or density of the fluid flow. Microcantilevers can be excited and their movement measured in a variety of manners.
Excitation may be by piezoelectric, piezoresistive methods, by capacitive, photothermal, electrostatic, or acoustic techniques. Movement of the cantilever is preferably measured by reflection of light from the tip of the microcantilever but may also be measured piezoelectricly, piezoresistively, and by the methods disclosed in U.S. Patent Nos. 5,440,008 and 5,719,324. An exemplary device for measuring viscosity and density is shown in Fig. 1. An oscillator circuit 1 generates a square wave signal 2 which energizes a device 4 such as a piezoelectric transducer to cause a cantilever 3 to resonate. The resonance is detected, in the example, by shinning a light from laser diode 5 onto the tip of cantilever 3. The reflected light impinges upon position sensitive diode 6. The signal from PSD 6 is amplified (7) and analyzed at amplitude measuring circuit 8. The display of the result form the measurement is shown in Fig. 2 as a plot of amplitude versus time for the decay of resonance when the stimulation is interrupted. Fig. 3 illustrates the relationship between the square wave signal and cantilever response.
The method of this invention may be used to determine many physical parameters and for process and quality control. The sensors are very small and may be located in remote and even hazardous locations. Viscosity/specific density provides a good indication of the completeness of a chemical reaction and provides a nearly instantaneous indication of when a process stream condition changes. Leaks, especially gas leaks, are quickly identified at the source.
The devices are also useful in kinetic studies, especially using shock tubes to study reaction process. Because this method is based on relative changes in the successive amplitudes rather than absolute amplitudes, this method can be used for measuring viscosity and density in noisy environments. However, when used in severely interfering noise environments, a reference cantilever can be used to avoid transients caused by noises. For example, acoustic noises in the environments can produce transient motion of a cantilever. Using a reference cantilever the noise contribution from the transient can be filtered using wavelet or Fourier transform analysis. The same approach can be used for other interference such as noise introduced by temperature variation.
The invention will be described in terms of an example which illustrates the operation of the invention. The example is not limitative of the invention and modifications obvious to those with skill in this art are included within the scope of applicants' invention.
Example 1
A microcantilever may be fabricated to specify length, width and thickness. The microcantilever is attached, at its base, to a piezoelectric device which is energized by a square wave generator. The microcantilever may be first characterized in a vacuum to determine the resonance frequency and Q-factor by observing the transient response of the cantilever. This is the calibration of the cantilever.
The chamber is then opened to admit a gas, pure nitrogen, and allowed to equilibrate at a pressure of 760mm of Hg. The decay curve of the microcantilever is determined as before and plotted as illustrated in Fig. 4. It is noted that the absolute magnitude of the amplitude is not critical, only the decrement. The experiment was repeated using Argon and He. The logarithmic decrement of the amplitude σ is given by equation (16). The value of Q can be determined from the decay curve of the amplitude. The value of the resonance frequency can be determined from the center crossing of the decay curve. The logarithmic decrement of the amplitude δ is given by
Figure imgf000009_0001
where A(n+1) and A„ are successive amplitudes. The Q factor is given as Q = π/δ. Density and viscosity of some gases:
Gas p (kg/m3) η (μPa-s)
Air 1.29 18.6
N2 1.25 17.9
02 1.43 20.8
Ar 1.78 22.9
CO 1.25 17.8
CH4 0.71 11.2
H2 0.0899 9.0
Experimental results obtained from transient techniques for density and viscosity closely follows published values. This technique was also extended to liquids.

Claims

What is claimed is:
1. A method for the determination of viscosity and density of a fluid comprising: a) providing at least one microcantilever, a means to vibrate said at least one microcantilever, and a means to detect the motion of said at least one microcantilever; b) calibrating said at least one microcantilever by observing the decay in vibration of said cantilever when said vibratory means is terminated using a vacuum or a known fluid as a standard; c) measuring the decay of vibration of the at least one cantilever in an unknown fluid; and d) calculating the viscosity or density gravity of the unknown by reference to the standard.
2. A method according to claim 1 wherein the fluid is a gas.
3. A method according to claim 2 wherein the gas is a pure, ideal gas.
4. A method according to claim 2 wherein the gas is a mixture of gasses.
5. A method according to claim 1 wherein the fluid is a liquid.
6. A method according to claim 5 wherein the liquid is a neat liquid.
7. A method according to claim 5 wherein the liquid is a mixture.
8. A method according to claim 1 wherein the means to vibrate said at least one microcantilever is selected from the group consisting of piezoelectric crystals, electromechanical devices, acoustic waves, magnetic, electrical, photothermal sources and photoinduction devices.
9. A method according to claim 8 wherein the means to vibrate is operated in a selected from the group consisting of pure harmonic, impulse or rectangular pulse mode.
10. A method according to claim 9 wherein the means to vibrate is operated in a rectangular excitation mode.
11. A method according to claim 1 wherein the means to detect motion of said at least one microcantilever is the microcantilever is selected from the group consisting of photo-optic detectors, piezoresistive detectors, piezoelectric detectors, capacitive detectors and electron tunneling.
12. A method for the determination of the completeness of a chemical reaction comprising observing the change in the viscosity of the solution or mixture using the method according to claim 1.
13. A method for determining the presence of inhomogentetics and gradients in a flowing fluid comprising observing the viscosity or density using a method according to claim 1.
14. A method for investigating the kinetics of a chemical reaction based upon variation of viscosity and density.
15. A method according to claim 1 wherein the at least one microcantilever is an array of microcantilevers arranged in a pattern.
16. A method according to claim 15 wherein said pattern is selected from the group consisting of one-dimensional and two-dimensional patterns.
17. A method according to claim 15 wherein said array of cantilever is used to map variations in viscosity and density of a fluid.
18. A method according to claim 17 wherein the fluid is a flowing fluid.
19. A method according to claim 1 further comprising at least one reference cantilever.
PCT/US2000/026287 1999-09-23 2000-09-22 Micromechanical transient sensor for measuring viscosity and density of a fluid WO2001022056A1 (en)

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