1

High Resolution Micro-Optical Wall Shear Stress Sensor

Ulaş K. Ayaz§, Tindaro Ioppolo

*, Volkan Ötügen

†

Southern Methodist University, Dallas, TX 75275

We report an optical wall shear stress sensor based on the whispering gallery modes (WGM) of a

dielectric sphere. Radial deformations of such spheres, for example caused by shear stress, results in

a shift in the WGMs, thereby allowing one to monitor the effect (shear stress) causing such shifts.

The sensor is composed of a sensing element, which is a movable plate flush to the wall. The sensing

element is attached to a lever on one end, and the other end is in contact with the sphere. Thus, the

shear force felt by the sensing element is transmitted to the sphere mechanically through the rotation

of the lever. Previous experimental results with these spheres showed force resolutions as good as

~10-10

N, which for a sensing element of ~650 m2, would be equivalent to a few hundred Pa

resolution. In this paper, we experimentally investigate an WGM based shear stress sensor that is

composed of a PDMS sphere with base-to-curing-agent mixing ratio of 40:1 and a sensing element of

~650 m2. The sensor is first calibrated statically and then the performance characteristics of the

sensor (sensitivity to normal pressure, dynamic range and frequency response) are tested. The

calibration of the sensor is then validated by testing the sensor in a 2-D Poiseuille's flow.

I. Introduction The measurement of wall shear stress has been one of the challenges of fluid mechanics research. Significant

progress has been made in wall shear

stress measurement techniques, but still

further developments are needed. In

particular, reliable, low-noise, high

resolution sensors applicable to a wide

range of flows are needed 1,2

. Most of

the currently used sensors, such as hot-

wire/film-based anemometry 3, heat

flux gages 4, surface acoustic wave

sensors 5 and laser based velocity

sensors 6,7,8

, oil film interferometry 9,

are indirect approaches where the wall

shear stress is determined from the

measurement of another flow property.

Further, a new class of MEMS-based

sensors have been proposed recently

(thermal 10,11

, floating element 12

and

optical wall shear sensor 13

) to measure

the shear stress indirectly. Of these,

thermal sensors are simple to fabricate

but they are based on heat transfer

analogy, and their calibration can be

§

Graduate student, Mechanical Engineering Department * Post Doctoral Associate, Mechanical Engineering Dept.

† Professor, Mechanical & Aerospace Engineering Dept., AIAA Associate Fellow

Figure 1. Schematic of WGM sensor

49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition4 - 7 January 2011, Orlando, Florida

AIAA 2011-337

Copyright © 2011 by Volkan Ötügen. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

2

difficult. Optical MEMS (MOEMS) sensors based on laser Doppler anemometry are promising, however

generating sufficiently small measurement volumes for high Reynolds number applications can be challenging. A

direct measurement method is the floating element sensor which is based on the measurement of the deflection of a

floating element that is flush with the flow. Capacitive 12,13,14

, piezoresistive 15,16

, differential optical shutter and

fringe moiré 17

techniques have been developed to measure the displacement of the floating element. Some of

these techniques are quite promising but they are still work in progress, as such, some of the MEMS and MOEMS

approaches described above may suffer from electromagnetic noise interference, tunnel vibration, and undesirable

flow through gaps.

The micro-optical sensor presented here is based on WGM resonators and is capable of measurements resolved

in time and space with a large dynamic range. It promises to overcome some of the drawbacks of the current skin

friction measurement techniques. The signal output is optical, which makes the sensor essentially immune to

electromagnetic interference. The mechanical principle is similar to the floating element technique in that the force

exerted by the flow on a small surface element flush with the wall is measured. However, whereas the typical

floating element sensor requires considerable movement/deflection to measure the force exerted by the flow, the

present sensor requires movements only in the order of nanometers for measurement. Thus, the present sensor

basically has no moving parts.

In the past few years, several optical sensor concepts have been proposed exploiting the WGM shifts of

microspheres. They include protein adsorption18,19

, trace gas detection20

, impurity detection in liquids 21

, structural

health monitoring of composite materials 22,

detection of electric field 23

, magnetic field 24, 25

and temperature26, 27

as

well as mechanical sensing, such as pressure 28

and force 29,30

. The technique we present here is an extension of the

WGM-based force sensor reported earlier 29,30

. The central element is the dielectric microsphere whose optical

mode (WGM) shifts are monitored to determine the force exerted on it by the surface (sensing) element. Several

individual sensors were built and tested to validate them under steady and unsteady conditions. Each sensor had a

surface element (plate) of 1mm x 1mm or smaller.

II. WGM Sensor Concept

The sensing is based on tracking the shifts in optical modes (WGM) of a dielectric sphere caused by applied

force. The optical modes of the sphere are excited by coupling light from a tunable laser into the sphere using a

tapered optical fiber as illustrated in Fig. 1. Light from a tunable laser is carried through an optical fiber with a

section that is stripped and tapered to about ~10 m diameter. A photodiode placed on the opposite end of the fiber

monitors the transmitted light intensity. The tapered section of the fiber serves as an input/output port for the

microsphere. When the laser frequency is tuned over a small range, the WGMs are observed as narrow dips in the

transmission spectrum through the fiber. The position of each WGM in the transmission spectrum depends on the

morphology (i.e. size, shape) of the sphere. The WGM linewidths, , can be extremely narrow thereby allowing

for the detection of even very small perturbations of the sphere’s morphology. Thus, any force applied to the

sphere that causes a detectable shift in WGM can be measured by monitoring the transmission spectrum through

the fiber.

WGMs of microspheres can be explained by ray optics. Laser light coupled at a grazing angle into the

microsphere will experience a total internal reflection, provided that the index of refraction of the sphere is greater

than that of the surrounding medium. The light will circumnavigate the interior surface of the sphere and a

resonance (WGM) will be observed when the round trip distance traveled is an integer multiple of the light

wavelength. Therefore, a first order approximation to the optical path inside the sphere would give the resonance

wavelengths as

lan 0

2 (1)

where no and a are the sphere’s refractive index and radius, is the vacuum wavelength of laser and l is an

integer representing the circumferential mode number. The above condition is valid for a >>. A minute change in

the size or the refractive index of the microsphere will lead to a shift in the resonance wavelength as

a

da

n

dnd

0

0

. (2)

3

By monitoring the WGM shifts, any effect that leads to a radial deformation or change in the refractive index

can be measured. For example, force applied to the sphere will lead to a change in both its radius and its refractive

index. However, previous investigations have shown that (dno/no) >> (da/a) when a uniaxial force is applied to the

sphere along the polar direction 30

. Thus, only the radial deformation needs to be considered for the measurement

of force.

One of the features that makes the WGM-based sensors attractive is the extremely large optical quality factors

(Q= /) associated with the spheres. Larger Q values lead to higher measurement resolution of the WGM shift

() and the physical parameter causing the shift. For example, Q values approaching the material loss limit of 1010

have been reported 31

with fused silica micro-spheres. These exceptionally large Q values cannot be reached by

planar interferometric systems such as Fabry-Perot instruments and brag gratings (which render Q values typically

in the order of 100). In the present, we obtain optical Q values between 106 and 10

7 with polymeric spheres of

diameters in the range between 200µm and 1 mm.

III. Sensor Details

A. Sensor Design A schematic and photographs of the wall shear stress sensor are shown in Figs. 2 and 3, respectively. The

cylindrical sensor cavity fits into a hole on test section wall with its outside surface flush to the wall. The top

surface of the cylindrical cavity is made of

~1 mm thick aluminum. The active

components of the sensor cavity are the

PDMS microsphere, a 125 µm silica beam

that acts as a lever, and a flat plate that

serves as the sensing surface. The silica

beam is connected to the 0.8 by 0.8 mm

square sensing plate on one end and to a

back plate (0.4 by 0.4 mm) on the other

with loctite epoxy. The back plate

compresses the microsphere against the

backstop with the force transmitted

through the beam. Both plates are made of

brass with a nominal thickness of ~25m.

The silica beam is attached to the bottom

corner of the cavity wall as shown in Fig. 2

with a PDMS 10:1 base-to-curing agent

mixing ratio. The attachment point also

serves as the pivot about which the

silica/plate system rotates. The sensing

plate is aligned flush with the wind tunnel wall with its outer side exposed to the flow. As the silica/plate system

pivots about the attachment point, it transmits the shear force experienced by the plate to the microsphere slightly

deforming it (dr/r) and causing a shift in the sphere WGM. A 60-µm latex membrane covers the gap of about 200

µm between the sensing element and the wall to prevent flow through the cavity.

Figure 2. Side view (left) and front view (right) of the shear stress

sensor

Figure 3. Top (left) and bottom (right) photographs of the shear

stress sensor

4

B. Calibration Previous studies have shown that for a given sphere material, the sphere size determines the calibration factor

relating WGM shift to applied force 29,30

. For the shear stress sensor, however, the effect of the additional

components (the lever, the polymeric base at the pivoting point, latex membrane, etc) will each have an effect on

sensor calibration.

Figure 4 shows a schematic of the static calibration setup.

A cantilever beam mounted on a translational stage is used to

exert the force on the sensing surface. The beam is a silica fiber

with a length and diameter of 60 mm and 0.125 mm,

respectively. One end of the beam is attached to a micro-

translation stage while the other end (which is flattened to have a

larger surface area) is in contact with the microsphere. A

Michelson interferometer is used to measure the deflection of

the beam (with a resolution of ~ 65 nm). The force exerted on

the sensor by the deflected beam can be calculated as:

ukFbeam

(3)

where

3

4

64

3

L

DEkbeam

(4)

F is the force exerted on the sensor by

the beam and u, D, E and L are the tip

deflection, diameter, Young's modulus and

length of the beam, respectively. Figure 5

shows a typical calibration result for a PDMS

sphere with 40:1 base-to-curing-agent mixing

ratio. The sphere diameter for this case is

~700 m. The shear stress is obtained by

dividing the applied force by the sensing

surface area. The plot of Fig. 5 is essentially

linear in the range of calibration and the

sensitivity is simply d/d. Along with the

optical quality factor, sensitivity determines

the measurement resolution. If we assume

that the minimum measurable WGM shift is

∆λ= λ/Q, the measurement resolution is:

1

dd

Q

(5)

For a Q-factor of 107, the resolution for

the sensor of Fig. 5 is ~10-2

Pa. The measurement resolution can be increased by using PDMS spheres with larger

base-to-curing agent ratios which yield smaller Young's moduli. For example, Fig. 6 shows the calibration plot of

Figure 4. Experimental setup for

static calibration

d/d = 15.145 pm/Pa

0

2

4

6

8

10

12

14

16

18

20

0 0.5 1 1.5

WG

M S

hif

t, p

m

Shear Stress, Pa

Figure 5. Static calibration of sensor with a 40:1 mixing

ratio PDMS sphere of diameter ~ 700 µm

d/d = 230.87 pm/Pa

0

20

40

60

80

100

120

140

0 0.2 0.4 0.6 0.8

WG

M s

hif

t, p

m

Shear stress, Pa

Figure 6. Static calibration for shear stress sensor with a 60:1

mixing ratio PDMS sphere of diameter ~ 750 µm

5

a sensor with a 60:1 base-to-curing agent ratio PDMS sphere of diameter ~ 750 m. As shown, a fifteen fold

increase in sensitivity is achieved with this sphere. The corresponding shear stress resolution for this sensor is ~650

Pa.

Although we show here sensor results with only PDMS spheres of 40:1 and 60:1 mixing ratios, other dielectric

spheres with similar optical characteristics (such as silica, PMMA etc.) can also be used for this type of sensor. By

changing the sphere diameter and material, a wide range of measurement range and resolution can thus be obtained.

C. Normal Pressure Response Shear stress sensors are subject to a normal

pressure due to the pressure difference between the

test section (flow channel) and the surrounding

medium (atmospheric pressure). The sensor's

response to such a pressure could add additional

noise in the measurements. In order to test the

response of the sensor to the normal pressure, we

mounted the sensor on a test chamber where, the

sensing element was subject to the pressure in the

chamber. The microsphere used for this test had

~700 m and it was made of PDMS 40:1 base to

curing agent mixing ratio. The pressure inside the

chamber was changed and the corresponding

WGM shifts were observed. The WGM shifts with

respect to the changes in the normal pressure are shown in Fig. 7.

As it is seen in the figure, the sensor does not respond to the changes in the normal pressure. The random

scatter in the data is most likely due to the vibration of the test section as it was subject to the normal pressure.

D. Dynamic Range

The dynamic range of the sensor is defined as the ratio of maximum to minimum shear stress it can measure.

In the proposed sensor, since WGMs of the dielectric microsphere essentially defines this ratio, we setup an

experiment to measure the dynamic range

of the microsphere. Figure 8 illustrates

the setup for this experiment. Basically,

a PDMS microsphere of 60:1 base to

curing agent mixing ratio and ~900 m

diameter is placed between two infinitely

stiff metallic plates, one of which is

attached to 1-D translation stage whereas

the other remained fixed in position. A

Michelson interferometer is used to

measure the distance the translational

stage moved. The translation stage is

moved forward for ~ 200 m and then it

was moved back. The WGM shifts

during the loading and unloading process

of the sphere are given in Fig. 9. Note

that the data in Fig. 2 represents a slight

scatter (< 2%).

The dynamic range of the sphere is

calculated as:

max

(6)

Figure 8. Experimental setup for dynamic range

measurements

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0 20 40 60 80

WG

M s

hif

t, p

m

Normal Pressure, Pa

Figure 7. Sensor response to applied normal Pressure

6

Where max is the

maximum applied shear

stress and is the

minimum resolvable shear

stress. Previously, we

have shown that the

WGMs are linear with

respect to the radial

deformation 29,30

,

therefore, we can rewrite

the Eq. (6) as:

L

L

max

(7)

With Q-factor given

as:

L

DQ

(8) where Lmax is the maximum distance

the translation stage has moved and L is

the minimum resolvable displacement, and

D is the diameter of the sphere. Thus, the

minimum resolvable distance is given as

Q

RL

(9)

Assuming a Q~107, the data in Fig. 9

would result in a dynamic range as high as

~5x105, >100 dB.

E. Frequency Response Dynamic calibrations have also been

carried out to determine the frequency

response of the sensors. The setup for

dynamic calibrations is a variation of

the static setup shown in Fig 4. The

long optical fiber beam is replaced by

a short, rigid beam that is connected

to a piezoelectric actuator. The

actuator is driven at a range

frequencies while the displacement

amplitude is kept constant. Several

measurements (typically, 5 to 8) are

made at each frequency, and the

corresponding WGM shifts are

plotted against frequency as shown in

Figs. 10 and 11 for PDMS spheres of

60:1 and 40:1 mixing ratios,

respectively.

0123456789

0 200 400 600 800

WG

M s

hif

t, p

m

Frequency, Hz

Figure 10. Frequency response for WGM shear stress sensor

with a PDMS sphere (60:1 mixing ratio, ~750 m diameter)

0

1

2

3

4

5

6

0 1000 2000 3000 4000

WG

M S

hif

t, p

m

Frequency, Hz

Figure 11. Results of the frequency response for WGM shear stress

sensor with a PDMS sphere (40:1 mixing ratio, ~700 m diameter)

Figure 9. The WGM shifts with respect to the displacement

of the translational stage. (Sphere diameter ~900 m)

7

For the 60:1 mixing ratio sphere, the natural frequency of the sensor is around ~300 Hz. Therefore, the

sensor's performance is limited to a bandwidth < 300 Hz. The sphere with 40:1 mixing ratio, on the other hand,

possesses a fairly flat frequency response

up to ~3.5 kHz. Thus, as it is typical of a

sensor that has any mechanical

components, the present sensor presents

a tradeoff between bandwidth and

sensitivity.

IV. Experiments

A schematic of the two-dimensional

wind tunnel is shown in Fig. 12. In order

to achieve a two-dimensional flow in the

mid section, the cross-section of the

wind tunnel has a large aspect ratio; the

height and span of the channel are 4.76 ±

0.05 mm and 160 mm, respectively

yielding an aspect ratio of AR ~33. The

test section is far enough from the

entrance (800 mm) so that the flow in the

test region is fully developed for nearly

the full range of flow rates considered.

A set of six pressure taps are located inside the wind tunnel at the mid-point to measure the streamwise distribution

of the wall pressure. The pressure taps are placed on the wall opposite to the wall shear sensor, and have a diameter

of ~100m to minimize flow

perturbations and spatial

integration effects in the measured

pressure. Each tap is connected to a

Scanivalve which is attached to

pressure transducer as shown. At

the outlet of the tunnel, a fan

operates in the suction mode to

drive the air flow inside the

channel. The fan is controlled by a

dc motor and its rpm can be varied

continuously allowing for

measurements at different flow

rates. For a fully developed one-

dimensional isothermal flow, the

shear stress at the wall can be

calculated from

dx

xdPh

2

(10)

where h is the channel height and dP/dx

is the streamwise gradient of pressure in the

fully developed flow region. In these

experiments, the shear stress calculated by

Eq. (10) is compared to the shear stress

measured by the optical sensor. Figure 13,

shows the results of a typical experiment

Figure 12. Test facility for the steady flow studies

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

-0.5

0.5

1.5

2.5

3.5

4.5

5.5

0.00 5.00 10.00 15.00 20.00 25.00

She

ar S

tre

ss, P

a

WG

M s

hif

ts,

pm

Time, seconds

WGM sensor

Calculated shear stress

Fig ure 13. Steady flow test results for the WGM shear stress sensor

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 0.1 0.2 0.3 0.4

Wa

ll s

hea

r st

ress

, P

a (

WG

M

sen

sor)

Wall shear stress, Pa (Calculated)

Figure 14. Comparison of WGM sensor results to those

calculated from pressure drop

8

where the flow rate is first increased and then decreased over a long period of time. The figure presents both the

shear stress calculated from Eq (10) and the WGM shifts registered from the optical sensor. Figure 14 compares the

results directly obtained by the WGM sensor and those inferred from the pressure gradients. (The WGM shifts are

converted to shear stress using the calibration curve of Fig 5). The solid line in Fig 11 represents perfect

coincidence of two data sets. Clearly, there is strong agreement between the two measurements and, further, the

sensor shows no hysteresis effects.

V. Conclusion

An optical wall shear stress sensor based on whispering gallery modes of a spherical resonator has been

demonstrated. In situ calibration as well as the frequency response of the sensor have been investigated. Shear

stress resolutions of the order of 10-2

Pa have been demonstrated when a 700 µm diameter PDMS sphere with 40:1

base-to-curing agent mixing ratio is used. This resolution is further improved to ~650 Pa if a 60:1 mixing ratio

PDMS sphere is used. However, frequency response tests show that, while using a softer material for sphere

improves the resolution of the sensor, at the same time there is a corresponding reduction in the sensor bandwidth.

The sensor is linear even when the sphere deformation is on the order of hundreds of microns promising to have

extremely high dynamic range.

Acknowledgements

We acknowledge the support from the National Science Foundation through grant CBET-0809240 with Dr.

Henning Winter as program director and the Air Force Office of Scientific Research through STTR contract FA

9550-10-C-0091 with Dr. John Schmisseur as program manager.

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