Post on 09-May-2018
MATHEMATICAL MODELING FOR THE NEXT GENERATIONOF TRACE GAS SENSORS
Susan E. MinkoffThanks to: Noemi Petra, John Zweck, Michael Reid (UMBC),
Anatoliy Kosterev, Frank Tittel, James. H. Doty III, and David Thomazy (Rice University)
MIRTHE Goals: To develop trace gas sensors usingtwo new technologies:
• Quantum Cascade Lasers (QCL’s) – see ex-hibit by Claire Gmachl (Princeton)
• Quartz-Enhanced PhotoAcoustic Spec-troscopy (QEPAS) developed by Kosterevand Tittel at Rice University.
NSF ENGINEERING RESEARCHCENTER: MID–INFRARED TECH-
NOLOGIES FOR HEALTH ANDTHE ENVIRONMENT (MIRTHE)
• Non-invasive disease diagnosis (e.g., liverdisease and lung cancer) using breath bio-markers.
• Environmental and industrial monitoring us-ing networks of sensors (e.g., monitoring ofatmospheric carbon dioxide levels).
• Homeland security (e.g., chemical weapondetection at airports, train stations, etc).
APPLICATIONS
• In 1888 Alexander Graham Bell discoveredthe photoacoustic effect:
∗ Specifically that periodic absorption oflight by matter produces sound.
∗ He used this phenomenon to develop awireless communication device.
• Since light is only absorbed by the gas at par-ticular wavelengths the photoacoustic effectcan detect trace gases.
• In the 1970’s PAS was used to detect nitricoxide in the stratosphere which was proof ofozone depletion by man-made chemicals.
PHOTOACOUSTIC SPECTROSCOPY (PAS)
QEPAS Sensors detect the sound produced in PAS us-ing a quartz tuning fork (like the one in your watch)to amplify and detect the sound wave.
QEPAS
• Greater sensitivity due to the strong absorp-tion by simple molecules in the infrared spec-trum and the power of QCL’s.
• Rugged and small in size → portable
• Cost Effective → can be deployed in sensornetworks.
Left: Actual QEPAS sensor device. Right: Schematic diagram ofQEPAS device for simulation.
ADVANTAGES OF QEPAS WITHQCL’S OVER PREVIOUS TECHNIQUES
Goals:
• Increase physical understanding of QEPAS,
• Optimize design of sensors.
Outline of Model
• The interaction of the laser and the trace gasgenerates a sound wave which we model us-ing a forced acoustic wave equation.
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0.1
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r (mm)
Am
plitu
de (
mP
a)
f = 32.8 kHz (Exact)f = 32.8 kHz (Approx.)f = 4.25 kHz
Simulated acoustic pressure wave as a function of radial distancefrom laser beam.
• The sound wave excites a vibration of the quartz tuning fork.
Left: The displacement of the 32.8 kHz tuning fork. The red andblue colors show the maximum and minimum displacement, re-spectively. Right: The first principal stress. The stress is largest(red) where the tines of the tuning fork meet the base.
• The photoelectric effect in quartz converts this vibration to anelectric current whose strength is proportional to the concen-tration of the trace gas.
A MATHEMATICAL MODELFOR QEPAS SENSORS
Left: Mathematical Modeling Group (John Zweck, Noemi Petra,Susan Minkoff). Right: Experimental Group (Lei Dong, AnatoliyKosterev, Jim Doty, Christian Zaugg; Not shown: Frank Tittel andDavid Thomazy).
PROJECT PARTICIPANTS
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Beam Position (mm)
Nor
mal
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nal
TheoryExp 450 TorrExp 60 Torr
Normalized amplitude of the piezoelectric current as a function ofthe vertical position of the laser beam for a QEPAS sensor with a32.8 kHz tuning fork.
• We used experiments and computer simulation to find the po-sition that produces the largest current.
• These results validate the model and confirm the optimalplacement of the laser beam.
SENSOR OPTIMIZATION
• The heat generated by absorption of light canbe directly detected using a tuning fork.
• ROTADE and QEPAS are complementarytechniques operating in different pressureregimes.
• Experiments and simulations show that thelaser must be positioned close to the walls ofthe tuning fork and near the base of the tines.
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Source position (mm)
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tren
gth
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Source position (mm)
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Left: The normalized experimental signal strength vs the positionof the laser beam. Right: the numerically computed signal strengthvs laser position.
Experimental Results. Left: tuning fork image depicting transmit-ted power and signal as a function of beam position for 300 torr ofpure CO2 . Observed signal primarily due to photoacoustic effect.Right: tuning fork (in black) shows the signal due to ROTADE asa function of beam position at a reduced pressure of 20 torr of pureCO2 .
• We plan to use the models to improve performance of bothmethods by optimizing the geometry of the tuning fork.
RESONANT OPTOTHERMOA-COUSTIC DETECTION (ROTADE)
This research was funded by the National Science Foundation un-der Grant No. EEC-0540832.
ACKNOWLEDGEMENT