Measuring Liquid Viscosity Using Acoustic Absorption.

Presentation to NRL

by ASEE Summer Faculty Fellow candidate

Hartono Sumali

Purdue UniversityMarch 26, 2001

http://pasture.ecn.purdue.edu/~sumali/research/tube1.pdf

Motivation

Food industry rheometers rely on boundary layers. Fail to work with solid-liquid slip (mayonnaise

etc). Fail to obtain zero-shear viscosity. Cannot be used on-line.

Acoustic waves attenuate with liquid absorption.

Possible Approaches

Attenuation over distance Simple fundamental phenomenon

Requires long aparatus.

Reflection coefficient Ultrasonics have shown success. Empirical/

calibration. Three-dimensional nature complicates

fundamental analysis

)(12

12)()( xxexPxP

Approaches pursued so far

Longitudinal waves in tubes Low-frequency in narrow tube allows simple 1-D

analysis.

Fluid loading of plate vibration. Simple device.

Measuring complex acoustic speed with a tube.

Measure impedances of driving piston (Zm0) and end piston (ZmL).

Measure “total tube impedance”

F() uL()Exciting force Piston speed

Piston impedanceZm0

Piston impedanceZmL

Slender tube

Longitudinal waves

)(

)()(

Lu

FH

Total tube impedance F/uL

Pressure amplitude at position x and wavenumber k is

F() uL()Exciting force Piston speed

Zm0 ZmL

))(exp())(exp()( xLjkxLjkxp BA L = tube length, mA and B are constants from boundary conditions Boundary conditions:

1) F = pressure at (x=0) times piston area + speed at (x=0) times Zm0

2) Pressure at (x=L) times piston area = speed at (x=L) times ZmL.

Obtaining complex acoustic speed

Total tube impedance

F

u L

Z m0 Z mL cosc

L

1iZ mL

S cZ m0 S c

sinc

L

F/uL = total tube impedance, N/(m/s2)Zm0, ZmL = piston impedance in-vacuo, N/(m/s2)S = piston area, m2

= liquid density, kg/m3

L = tube length, m = frequency, rad/s

Measured

Known

Solve for complex acoustic speed c.

Obtaining viscosity from complex c

From relaxation time , obtain absorption coefficient using

jc 1c

2/1

2

2

1

11

2

1

c

= density, kg/m3

a = tube radius, m

2

1

ac

Viscosity can be related to absorption coefficient .

(Exact relationship to be determined)

From complex acoustic speed c, obtain relaxation time using

c = real speed, m/s

Experimental Aparatus

F/uL is obtained using FFT analyzer.

Accelerometer

Force from shaker or hammer.Mesured with force transducer

Piston with spring beam

Results so far: Accelerances0 dB = 1 m/s2/N Piston in-vacuo

-20

60

0 Hz 500

-5

25

Hz0 100

Tube with water, theoretical. Tube with water, experimental.

Measuring viscosity using plates Box is filled with liquid. Accelerance obtained with force transducer and

accelerometer.

Analytical model of plate

Plate deflection w at point (x,y) is summation of modal responses

M

mmm yxpyxw

1

),()(),,(

p is modal coordinate from

)(),()(

)(

)(

)(tf

yxt

t

t

t

φp

p

p

p 0

Z

I02

n

is mode shape, is natural frequency. is damping.

n2

12

2

0

0

M

Z

0

0

2

2

1 1

M M

From modal analysis

0 10 20 30 40 50 60-30

-25

-20

-15

-10

-5

0

5

10

15

20

Frequency, Hz

dB

, 0

dB

=1

m/s

2/N

Z 1.5*Z2*Z

Results with plate: Accelerance with difference liquid viscosities

Theoretical Experimental

-10

-5

0

5

10

15

20

0 20 40 60

Frequency (Hz)

Ma

gn

itu

de

(d

B)

Water

0.5% CMC

1% CMC

Liquid viscosity or concentration of Carboxy-Methyl Cellulose (CMC) :High, medium, low

-10

20

Hz

60-30

20

Hz 60

Relationship between damping and viscosity

From first mode data

0

2

4

6

8

10

12

14

16

5 7 9

Frequency (Hz)

Mag

nit

ud

e (d

B)

Water

0.5% CMC

1% CMC

0

50

100

150

200

250

300

Fluid

Vis

cosi

ty (

mP

a*s)

3

3.5

4

4.5

5

5.5

Acc

eler

ance

(m

/s^

2/N

)

Water 0.5% CMC 1% CMC

0 10 20 30 40 50 60-30

-25

-20

-15

-10

-5

0

5

10

15

20

Frequency, Hz

dB

, 0

dB

=1

m/s

2/N

Z 1.5*Z2*Z

Conclusions so far

Higher viscosity results in higher damping. Absorption coefficient appears to have an

important role in relating viscosity to vibration responses of liquid-filled structures.

Much work is yet to be done to develop a method to masure viscosity using acoustic waves.