CN107643227A - The measurement apparatus and method of fluid density and viscosity based on QCM - Google Patents
The measurement apparatus and method of fluid density and viscosity based on QCM Download PDFInfo
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- CN107643227A CN107643227A CN201710939696.8A CN201710939696A CN107643227A CN 107643227 A CN107643227 A CN 107643227A CN 201710939696 A CN201710939696 A CN 201710939696A CN 107643227 A CN107643227 A CN 107643227A
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- 230000001360 synchronised effect Effects 0.000 claims abstract description 36
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- 238000006243 chemical reaction Methods 0.000 claims abstract description 12
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Abstract
The invention discloses a kind of fluid density based on QCM and the measurement apparatus and method of viscosity, device includes sinusoidal drive unit, QCM sensing units, synchronous detection unit, analog-digital converter, digital signal processor and computer, and sinusoidal drive unit is used to produce sine sweep signal;QCM sensing units are driven by sine sweep signal, and for sensing liquid, the density of liquid and viscosity information are converted into ac voltage signal;Synchronous detection unit is used to being converted to the ac voltage signal that QCM sensing units export into the d. c. voltage signal corresponding to the change of QCM conductances;Analog-digital converter is used to carry out analog-to-digital conversion to d. c. voltage signal;Digital signal processor is used to extract the series resonance frequency under the conductance peaks and the peak value of data signal;Computer is used for the density and viscosity for digital signal processor output be calculated liquid.Apparatus of the present invention small volume, integrated level are high, and measurement process is simple, and measurement result is accurate.
Description
Technical field
The present invention relates to sensor detection field, and in particular to fluid density and viscosity based on QCM
Measurement apparatus and method.
Background technology
Density and viscosity are two most basic physical attributes of liquid, are led in analytical chemistry, biomedicine, environmental project etc.
Domain has great importance.QCM (quartz crystal microbalance, QCM) can be used for measuring liquid
The physical attribute of body, such as the density and viscosity of liquid, the physical attribute of testing liquid can be converted into measurable frequency by it
Signal or conductance signal.
At present, based on the analytical instrument of qcm sensor in bio-molecular interaction, high polymer material absorption, germ inspection
The application in the fields such as survey, electrochemical deposition analysis and Air hygienic quality detection is very extensive, but applies it to liquid category
Property fields of measurement it is also seldom.1993, Martin et al. changed to obtain the close of liquid by two qcm sensor resonant frequencies
Degree and viscosity, one of electrode surface is smooth, and the product term of density and viscosity to liquid has response, another electrode surface
Provided with microflute, response is outer except having to the product term of the density of liquid and viscosity, is also added to only relevant with the density of liquid
Item has response.Due to having carried out Approximate Equivalent to the qcm sensor frequency contributions of two different structures, measurement error is relatively
Greatly, test process is also more complicated.2011, Itoh et al. proposed a kind of using single qcm sensor combination admittance analysis
Method measures the density and viscosity of liquid, but the data that needs measure are more, and data analysis process is highly difficult, while measures
Network Analyzer used is bulky in journey, expensive, is unfavorable for applying in actual production.
The content of the invention
Technical problem solved by the invention is to provide a kind of fluid density and viscosity based on QCM
Measurement apparatus and method, device volume is small, integrated level is high, and measurement process is simple, and measurement result is accurate.
The technical solution for realizing the object of the invention is:The survey of fluid density and viscosity based on QCM
Measure device, including sinusoidal drive unit, QCM sensing units, synchronous detection unit, analog-digital converter, digital signal processor and
Computer, wherein:
Sinusoidal drive unit is used to produce sine sweep signal, and is transported to synchronous detection unit and QCM sensing units;
The sine sweep signal that QCM sensing units are exported by sinusoidal drive unit drives, for sensing liquid, by liquid
Density and viscosity information be converted into ac voltage signal, and be transported to synchronous detection unit;
Synchronous detection unit is used to handle the output signal of sinusoidal driver element and QCM sensing units, and QCM is passed
The ac voltage signal of sense unit output is converted to the d. c. voltage signal corresponding to the change of QCM conductances, and is transported to modulus and turns
Parallel operation;
The d. c. voltage signal that analog-digital converter exports to synchronous detection unit carries out analog-to-digital conversion, and data signal is defeated
It is sent to digital signal processor;
Digital signal processor is used to produce needed for the frequency control word and analog-digital converter needed for sinusoidal drive unit
Sequential is gathered, extracts the series resonance frequency under the conductance peaks and the peak value of data signal, and be transported to computer;
The series resonance frequency that computer is used under the conductance peaks and the peak value to digital signal processor output is carried out
Calculate, obtain the density and viscosity of liquid.
The QCM sensing units include resistance R, buffer amplifier Buf, qcm sensor and controllable impedance L0, resistance R's
One end connects sinusoidal drive unit, resistance R other end connection buffer amplifier Buf positive input, buffer amplifier Buf
Inverting input connection buffer amplifier Buf output end, buffer amplifier Buf output end connection synchronous detection unit,
Qcm sensor and controllable impedance L0One end connection buffer amplifier Buf positive input, other end ground connection after parallel connection.
The qcm sensor includes quartz crystal and is arranged on the electrode of quartz crystal upper and lower surface, the upper surface electricity
Some straight-line grooves are uniformly distributed on extremely, the direction of straight-line groove is vertical with the shear displacemant direction of quartz crystal, and the ridge of straight-line groove is high
Degree scope is h=(0.8~1.2) μm, and ridge width is that the distance between a=(4.0~5.0) μm, adjacent straight-line groove is b=(4.0
~5.0) μm.
The sinusoidal drive unit includes digital frequency synthesizer and the first low pass filter, and the first low pass filter is seven
Rank ellipse lowpass filter, cut-off frequency areStop-band frequency is 2fs, wherein fsFor the series resonance frequency of qcm sensor
Rate.
The synchronous detection unit includes multiplier and the second low pass filter, and the second low pass filter is that second order salung is triumphant
Low pass filter, cut-off frequency 10KHz.
The measuring method of fluid density and viscosity based on QCM, comprises the following steps:
Step 1, sinusoidal drive unit produce sine sweep signal under the control of digital signal processor, and driving QCM is passed
Feel cell operation;
Step 2, in the case where being not added with fluid load, QCM sensing units detect liquid physical attribute, export no liquid
Ac voltage signal U during load1;
Step 3, synchronous detection unit are by ac voltage signal U1With sine sweep signal multiplication, and the result of multiplication is entered
Row filtering process, obtain the d. c. voltage signal V of corresponding QCM conductances change1;
Step 4, analog-digital converter under the control of digital signal processor to step 3 in synchronous detection unit export it is straight
Flow voltage signal V1Analog-to-digital conversion is carried out, digital signal processor extracts conductance peaks G from the data signal after conversion1And this
Series resonance frequency f under peak values1;
Step 5:Qcm sensor is immersed in Newtonian liquid, makes qcm sensor upper surface electrode contact liq, lower surface
Not contact liq, the detection of QCM sensing units have liquid physical attribute during fluid load, and output has alternating current during fluid load
Press signal U2;
Step 6, synchronous detection unit are by ac voltage signal U2With sine sweep signal multiplication, and the result of multiplication is entered
Row filtering process, obtain the d. c. voltage signal V of QCM conductances change2;
Step 7:The d. c. voltage signal V that analog-digital converter exports to synchronous detection unit in step 62Modulus is carried out to turn
Change, digital signal processor extracts the conductance peaks G of digits after conversion signal2With the series resonance frequency f under the peak values2;
Step 8:Series resonance frequency and conductance peaks of the computer according to qcm sensor when contacting and not in contact with liquid
Calculate the density and viscosity of Newtonian liquid to be measured.
The specific formula of the density and viscosity that calculate Newtonian liquid to be measured is:
In formula, ρ is density, and η is viscosity, Δ fs=fs2-fs1Offset for series resonance frequency, R2=(G1-G2)/G1G2For
Dynamic electric resistor changes, k1It is that frequency changes the sensitivity coefficient relevant with fluid density, k2It is that frequency change couples with liquid viscosity
The relevant sensitivity coefficient of effect, k3It is that dynamic electric resistor changes the sensitivity coefficient relevant with liquid viscosity coupling effect.
Compared with prior art, its remarkable advantage is the present invention:(1) by establishing QCM series resonance frequencys and dynamic electric
Contacting to solve the density of liquid and viscosity between resistance, measurement process is simple, practical;(2) compensate for controllable impedance
Direct capacitance C0Influence to series resonance frequency, make test result more accurate;(3) in QCM sensing units only with
One plus groove qcm sensor, device volume is small, integrated level is high;(4) calculating of density and viscosity is carried out on computers, not only
Can in real time, Real time displaying measurement result, and be also convenient for carrying out post analysis and processing to data.
Brief description of the drawings
Fig. 1 is the structural representation of the measurement apparatus of fluid density and viscosity based on QCM.
Fig. 2 is the circuit diagram of the QCM sensing units with inductance compensation function.
Fig. 3 is the structural representation for adding groove qcm sensor, wherein figure (a) is front electrode front view, (b) is front electricity
The sectional view of pole.
Fig. 4 is to add the equivalent circuit diagram after groove qcm sensor single-contact liquid.
Fig. 5 is the schematic diagram of the change of qcm sensor series resonance frequency and dynamic electric resistor change.
Embodiment
With reference to the accompanying drawings and detailed description, the present invention program is described further.
Fig. 1 is the structural representation of the measurement apparatus of fluid density based on QCM and viscosity, device bag
Sinusoidal drive unit, QCM sensing units, synchronous detection unit, analog-digital converter, digital signal processor and computer are included, its
In:Sinusoidal drive unit is used to produce sine sweep signal, and is transported to synchronous detection unit and QCM sensing units;QCM is sensed
The sine sweep signal that unit is exported by sinusoidal drive unit drives, and for sensing liquid, the density of liquid and viscosity are believed
Breath is converted into ac voltage signal, and is transported to synchronous detection unit;Synchronous detection unit is used for sinusoidal driver element and QCM
The output signal of sensing unit is handled, and the ac voltage signal that QCM sensing units export is converted to corresponding to QCM conductances
The d. c. voltage signal of change, and it is transported to analog-digital converter;The DC voltage that analog-digital converter exports to synchronous detection unit
Signal carries out analog-to-digital conversion, and data signal is transported into digital signal processor;Digital signal processor is used to produce sine
The collection sequential needed for frequency control word and analog-digital converter needed for driver element, extract the conductance peaks of data signal and be somebody's turn to do
Series resonance frequency under peak value, and it is transported to computer;Computer is used for the conductance peaks to digital signal processor output
Calculated with the series resonance frequency under the peak value, obtain the density and viscosity of liquid.
Fig. 2 is the circuit diagram of the QCM sensing units with inductance compensation function, and QCM sensing units include resistance R, buffering
Amplifier Buf, qcm sensor and controllable impedance L0, resistance R one end connection sinusoidal drive unit, resistance R other end connection
Buffer amplifier Buf positive input, buffer amplifier Buf inverting input connection buffer amplifier Buf output end,
Buffer amplifier Buf output end connection synchronous detection unit, qcm sensor and controllable impedance L0Connection buffering in one end after parallel connection
Amplifier Buf positive input, other end ground connection.When quartz crystal is operated under series resonance, crystal will show impedance
Characteristic, it is equivalent to dynamic electric resistor, and dynamic electric resistor can significantly increase when crystal is in liquid phase environment, under this situation,
Due to the influence of quartz crystal direct capacitance, cause phase drift so that the series resonance frequency measured and connecting for reality are humorous
Vibration frequency has larger deviation.In one controllable impedance L of qcm sensor both ends parallel connection0, controllable impedance is according to series resonance frequency
The change of rate turns to L0=1/ (4 π2fs 2C0), the phase drift that direct capacitance is brought under liquid phase environment can be compensated, makes measurement number
Improved according to the degree of accuracy.
Fig. 3 is the structural representation for adding groove qcm sensor, wherein figure (a) is front electrode front view, (b) is front electricity
The sectional view of pole.According to the size of the series resonance frequency of qcm sensor used, first in quartz-crystal by way of electro-deposition
The upper and lower surface of body plates the gold that a layer thickness is d=(0.1~0.2) μm, as electrode.Then, on upper surface electrode again
Equally distributed straight-line groove is set by way of photoetching, the direction of straight-line groove is vertical with the shear displacemant direction of quartz crystal,
The ridge altitude range of straight-line groove is h=(0.8~1.2) μm, and ridge width is a=(4.0~5.0) μm, between adjacent straight-line groove
Distance is b=(4.0~5.0) μm, and the design of groove should make qcm sensor obtain maximum mass loading effect.
Fig. 4 is to add the equivalent circuit diagram after groove qcm sensor single-contact liquid, when smooth qcm sensor connects with liquid
When touching operation, due to the sticky coupling effect of liquid, the equivalent circuit of qcm sensor can increase on dynamic arm represents that kinetic energy is deposited
The dynamic inductance L of storage2With the dynamic electric resistor R for representing function loss2.When plane of crystal is coarse or electrode surface is added with regular pattern
Straight-line groove when, the device can also capture a certain amount of liquid, and this captured liquid shows as desirable quality and contributes one
Individual surface density quality, this mass loading effect do not change the oscillation amplitude of crystal, do not cause the energy loss of crystal yet, and it draws
Rise additional resonant frequencies skew, only rely upon density and independent of viscosity, so only causing in the equivalent circuit of crystal
Inductance L3Change.
Fig. 5 is the schematic diagram of the change of qcm sensor series resonance frequency and dynamic electric resistor change.Wherein, curve 1 is QCM
Sensor is not added with conductance plots during fluid load, and curve 2 adds conductance plots during fluid load, two electricity for qcm sensor
The series resonance frequency when peak value of lead curve is not added with fluid load corresponding to qcm sensor and adds fluid load, and peak difference
That value represents is due to dynamic electric resistor R caused by the sticky coupling effect of liquid2Change.
Using above-mentioned measurement apparatus measurement liquid density and viscosity, its general principle be using quartz crystal contact and
Series resonance frequency change, dynamic electric resistor change and the liquid viscosity coupling effect and quality of plane of crystal are born during not in contact with liquid
The relation between effect is carried, passes through numerical measuring twice, it is established that fluid density and viscosity and frequency change and dynamic electric resistive
Corresponding relation between change, the density and viscosity of liquid are calculated respectively, specifically comprises the following steps:
First, by digital signal processor, into Direct Digital Frequency Synthesizers, write frequency control word, control are direct
Digital frequency synthesizer produces sine sweep signal, and sweep voltage value is Ui=Asin [2 π (f+ Δ f) t], wherein A is frequency sweep electricity
The amplitude of pressure, initial frequency when f is frequency sweep, Δ f are step frequency.If for example, qcm sensor used in measurement apparatus
Series resonance frequency fs=5MHz, then it is 5MHz ± 0.1MHz that should control swept frequency range.
Then, the swept-frequency signal is input to QCM sensing units to drive qcm sensor resonance, is not added with fluid load
With add two kinds of feelings of fluid load (when adding fluid load, qcm sensor upper surface electrode contact liq, lower surface not contact liq)
The ac voltage signal exported under condition after QCM sensing units isWithWherein, B1And B2For the alternating current for being not added with fluid load with being exported when adding fluid load
Press signal amplitude,WithTo be not added with fluid load and plus the phase of ac voltage signal that exports during fluid load.
Next need to handle the ac voltage signal of QCM sensing units output, measure the series connection of qcm sensor
Resonant frequency and dynamic electric resistor.Ac voltage signal changes into the direct current corresponding to conductance amplitude after synchronized detection unit processing
Voltage signal.
The series resonance frequency of groove qcm sensor is added to be expressed as when not loading liquid:
Wherein, L1For zero load when dynamic inductance, C1For zero load when dynamic capacity.
The series resonance frequency of groove qcm sensor is added to be expressed as after single-contact liquid:
Wherein, L1For zero load when dynamic inductance, L2To represent the dynamic inductance of sticky coupling effect, L under fluid load3
To represent the dynamic inductance of mass loading effect, C under fluid load1For zero load when dynamic capacity.
Then plus groove qcm sensor is gone here and there caused by the sticky coupling effect and mass loading effect collective effect of liquid
Connection resonant frequency, which becomes, to be turned to:
Wherein, ρ is fluid density, and η is liquid viscosity, k1It is that frequency changes the sensitivity coefficient relevant with fluid density, k2
It is that frequency changes the sensitivity coefficient relevant with liquid viscosity coupling effect.
Section 2-k in above-mentioned (3) formula2(ρη)1/2The frequency shift (FS) of expression is caused by the sticky coupling response of liquid
, it corresponds to dynamic inductance L2.Meanwhile it can be seen from the utility theory under QCM liquid-phase conditions and to Fig. 4 analysis, by
In the sticky coupling effect of liquid, it not only causes dynamic inductance L2Change, also cause qcm sensor dynamic electric resistor R2Change
Change, (ρ η)1/2With the dynamic electric resistor R of qcm sensor2Between equally exist linear relationship:
R2=k3(ρη)1/2 (4)
Wherein, k3It is that dynamic electric resistor changes the sensitivity coefficient relevant with liquid viscosity coupling effect.
Therefore, can be by measuring qcm sensor dynamic electric resistor R2Change and series resonance frequency skew try to achieve liquid
Density and viscosity.And dynamic electric resistor R2Change can be determined by measuring the conductance peaks under series resonance frequency, its
Corresponding to the DC voltage maximum exported after the processing of synchronized detection unit, pass through multiplier and second order Sa on hardware circuit
The triumphant low pass filter of human relations is realized.Its basic process is:
In the case where being not added with fluid load, it is assumed that a certain moment sinusoidal drive signals are Ui=Asin (2 π fiT), then QCM
The output signal of sensor isWherein, fiFor driving frequency now,For now alternating voltage
The phase of signal.Multiplying is done to drive signal and output signal by the multiplier in synchronous detection unit
After cut-off frequency is the 10KHz triumphant low pass filter of second order salung, high-frequency signal is filtered out, is obtained under frequency sweep
DC voltage value, i.e. conductance amplitude, which become, to be turned to
In the case where adding fluid load, synchronous detection unit is similar to the processing procedure for exporting AC signal.
It is recognised that under series resonance frequency, qcm sensor is equivalent to a pure resistance for analysis to Fig. 5, does not add
Before carrier fluid body, the dynamic electric resistor of qcm sensor is R1=1/G1, after loading liquid, qcm sensor is in new series resonance frequency
Under dynamic electric resistor be R1+R2=1/G2, turned to so while dynamic electric resistor caused by the sticky coupling effect of liquid becomes
After synchronized detection unit processing, series resonance frequency change and dynamic electric resistor change can be tried to achieve.Now, it is digital
The DC voltage value of signal processor control analog-to-digital conversion device collection synchronous detection unit output, and data signal is sent to number
Data processing, maximum DC voltage value and frequency values in extraction frequency sweep output, i.e. qcm sensor are carried out in word signal processor
Conductance peaks and the peak value under series resonance frequency be sent in computer and store.Liquid is not added with measuring qcm sensor
Conductance peaks G during load1With the series resonance frequency f under the peak values1With conductance peaks when qcm sensor plus fluid load
G2With the series resonance frequency f under the peak values2Afterwards, the series resonance frequency shifted by delta of qcm sensor is calculated by computer
fsChange R with dynamic electric resistor2, it is possible to try to achieve the density and viscosity of Newtonian liquid.
The density that liquid is tried to achieve by equation (3) and (4) is:
(8) formula substitution (4) formula can be tried to achieve into the viscosity of liquid is:
Wherein, k1It is that frequency changes the sensitivity coefficient relevant with fluid density, k2It is that frequency change couples with liquid viscosity
The relevant sensitivity coefficient of effect, k3It is that dynamic electric resistor changes the sensitivity coefficient relevant with liquid viscosity coupling effect.ΔfsWith
R2It is the series resonance frequency change of qcm sensor when not loading and load liquid and the dynamic electric resistive under series resonance frequency
Change.
Claims (7)
1. the measurement apparatus of fluid density and viscosity based on QCM, it is characterised in that including sinusoidal drive list
Member, QCM sensing units, synchronous detection unit, analog-digital converter, digital signal processor and computer, wherein:
Sinusoidal drive unit is used to produce sine sweep signal, and is transported to synchronous detection unit and QCM sensing units;
The sine sweep signal that QCM sensing units are exported by sinusoidal drive unit drives, for sensing liquid, by the close of liquid
Degree and viscosity information are converted into ac voltage signal, and are transported to synchronous detection unit;
Synchronous detection unit is used to handle the output signal of sinusoidal driver element and QCM sensing units, QCM is sensed single
The ac voltage signal of member output is converted to the d. c. voltage signal corresponding to the change of QCM conductances, and is transported to analog-digital converter;
The d. c. voltage signal that analog-digital converter exports to synchronous detection unit carries out analog-to-digital conversion, and data signal is transported to
Digital signal processor;
Digital signal processor is used to produce the collection needed for the frequency control word and analog-digital converter needed for sinusoidal drive unit
Sequential, the series resonance frequency under the conductance peaks and the peak value of data signal is extracted, and be transported to computer;
The series resonance frequency that computer is used under the conductance peaks and the peak value to digital signal processor output calculates,
Obtain the density and viscosity of liquid.
2. the measurement apparatus of fluid density and viscosity according to claim 1 based on QCM, its feature
It is, the QCM sensing units include resistance R, buffer amplifier Buf, qcm sensor and controllable impedance L0, resistance R one end
Sinusoidal drive unit is connected, resistance R other end connection buffer amplifier Buf positive input, buffer amplifier Buf's is anti-
Phase input connection buffer amplifier Buf output end, buffer amplifier Buf output end connection synchronous detection unit, QCM are passed
Sensor and controllable impedance L0One end connection buffer amplifier Buf positive input, other end ground connection after parallel connection.
3. the measurement apparatus of fluid density and viscosity according to claim 2 based on QCM, its feature
It is, the qcm sensor includes quartz crystal and is arranged on the electrode of quartz crystal upper and lower surface, on the upper surface electrode
Some straight-line grooves are uniformly distributed, the direction of straight-line groove is vertical with the shear displacemant direction of quartz crystal, the ridge height model of straight-line groove
Enclose for h=(0.8~1.2) μm, ridge width be the distance between a=(4.0~5.0) μm, adjacent straight-line groove be b=(4.0~
5.0)μm。
4. the measurement apparatus of fluid density and viscosity according to claim 1 based on QCM, its feature
It is, the sinusoidal drive unit includes digital frequency synthesizer and the first low pass filter, and the first low pass filter is seven ranks
Ellipse lowpass filter, cut-off frequency areStop-band frequency is 2fs, wherein fsFor the series resonance frequency of qcm sensor
Rate.
5. the measurement apparatus of fluid density and viscosity according to claim 1 based on QCM, its feature
It is, the synchronous detection unit includes multiplier and the second low pass filter, and the second low pass filter is that second order salung is triumphant low
Bandpass filter, cut-off frequency 10KHz.
6. the measuring method of fluid density and viscosity based on QCM, it is characterised in that comprise the following steps:
Step 1, sinusoidal drive unit produce sine sweep signal under the control of digital signal processor, and driving QCM sensings are single
Member work;
Step 2, in the case where being not added with fluid load, QCM sensing units detect liquid physical attribute, output no liquid load
When ac voltage signal U1;
Step 3, synchronous detection unit are by ac voltage signal U1With sine sweep signal multiplication, and the result of multiplication is filtered
Ripple processing, obtain the d. c. voltage signal V of corresponding QCM conductances change1;
Step 4, analog-digital converter under the control of digital signal processor to step 3 in synchronous detection unit export direct current
Press signal V1Analog-to-digital conversion is carried out, digital signal processor extracts conductance peaks G from the data signal after conversion1With the peak value
Under series resonance frequency fs1;
Step 5:Qcm sensor is immersed in Newtonian liquid, makes qcm sensor upper surface electrode contact liq, lower surface does not connect
Liquid is touched, the detection of QCM sensing units has liquid physical attribute during fluid load, and output has alternating voltage letter during fluid load
Number U2;
Step 6, synchronous detection unit are by ac voltage signal U2With sine sweep signal multiplication, and the result of multiplication is filtered
Ripple processing, obtains the d. c. voltage signal V of QCM conductances change2;
Step 7:The d. c. voltage signal V that analog-digital converter exports to synchronous detection unit in step 62Carry out analog-to-digital conversion, numeral
Signal processor extracts the conductance peaks G of digits after conversion signal2With the series resonance frequency f under the peak values2;
Step 8:Computer calculates according to qcm sensor in contact and series resonance frequency during not in contact with liquid and conductance peaks
The density and viscosity of Newtonian liquid to be measured.
7. the measuring method of QCM fluid density according to claim 6 and viscosity, it is characterised in that step
The density of rapid 8 calculating Newtonian liquid to be measured and the specific formula of viscosity are:
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</mrow>
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<mi>&eta;</mi>
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In formula, ρ is density, and η is viscosity, Δ fs=fs2-fs1Offset for series resonance frequency, R2=(G1-G2)/G1G2For dynamic electric
Resistive, k1It is that frequency changes the sensitivity coefficient relevant with fluid density, k2It is that frequency change has with liquid viscosity coupling effect
The sensitivity coefficient of pass, k3It is that dynamic electric resistor changes the sensitivity coefficient relevant with liquid viscosity coupling effect.
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CN201710939696.8A CN107643227B (en) | 2017-10-11 | 2017-10-11 | Device and method for measuring density and viscosity of liquid based on quartz crystal microbalance |
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