1) The authors developed new models for quartz-enhanced photoacoustic spectroscopy (QEPAS) sensors that account for viscous damping effects in order to enable numerical optimization of sensor design. 2) Their viscous damping model describes how fluid viscosity attenuates acoustic pressure waves and dampens the resonant mechanical deformation of the quartz tuning fork in QEPAS sensors. 3) Preliminary experimental validation showed good agreement between the model and measurements of acoustic signal strength as a function of laser beam position, though discrepancies occurred at larger distances due to unmodeled QEPAS-ROTADE interaction effects.

1. Modeling and Design Optimization of
Quartz-Enhanced PhotoAcoustic Spectroscopy
(QEPAS) Sensors
J. Zweck(1) , S. Minkoff(1) , F. Tittel(2) , A. Kosterev(2) ,
N. Petra(3) , M. Barouti(1) , and J. Doty(2)
(1)
Department of Mathematics and Statistics, UMBC
(2)
Department of Electrical and Computer Engineering, Rice U.
(3)
Institute for Computational and Engineering Sciences, U.T. Austin
March 2012
J. Zweck (UMBC) QEPAS March 2012 1/5

2. Project Motivation
Microresonator (MR) tubes amplify the QEPAS signal by a factor
of about 30.
But alignment cost of laser, MR and quartz tuning fork (QTF) is
prohibitive (≈$2,500 per sensor).
Possible Solution
Omit MR and numerically optimize QEPAS signal strength as a
function of QEPAS geometry.
Potential for 50% assembly cost savings.
More generally, we are developing better models for
QEPAS—with or without a MR—and using them to
numerically optimize QEPAS design (increase S/N).
J. Zweck (UMBC) QEPAS March 2012 2/5

3. Viscous Damping Model for QEPAS
Existing QEPAS models require experimentally measured
values of Q-factor (bad for numerical design optimization).
The Q-factor is primarily determined by viscous damping due to
motion of QTF in air.
We propose a viscous damping model for QEPAS that will allow
us to numerically optimize QEPAS geometry.
Mechanism for Viscous Damping
Fluid viscosity attenuates acoustic pressure wave
Hence pressure-driven displacement of QTF is damped
Model based on a system of partial differential equations
that couples acoustic pressure wave and heat diffusion in
gas with resonant mechanical deformation of QTF.
J. Zweck (UMBC) QEPAS March 2012 3/5

4. Experimental Validation of Models
7
10
Theory
1 Experiment
Normalized signal strength
0.8
Normalized Amplitude
6
10
0.6
0.4 5
10
0.2
4
0 10
0 1 2 3 4 5 0 0.4 0.8
Beam Position (mm) z (mm)
Normalized amplitude of piezoelectric signal as a function of
vertical position of laser beam.
Left: QEPAS without MR tubes or viscous damping
Right: ROTADE (Resonant OptoThermoAcoustic DEtection).
The discrepancy for z > 0.25 mm is due to QEPAS-ROTADE
interaction, which we did not model (yet!)
J. Zweck (UMBC) QEPAS March 2012 4/5

5. Preliminary Design Optimization Result
(ROTADE)
Left: Standard QTF; Right: Optimized QTF with 20× signal
strength
Caveat: Optimization proceedure assumed Q-factor
independent of QTF geometry (not realistic).
Goal: Do more realistic design optimization using new viscous
damping model for QEPAS.
J. Zweck (UMBC) QEPAS March 2012 5/5