1. Measuring Liquid Viscosity Using Acoustic Absorption. Presentation to NRL by ASEE Summer Faculty Fellow candidate Hartono Sumali Purdue University March 26, 2001 http://pasture.ecn.purdue.edu/~sumali/research/tube1.pdf

2. Motivation Food industry rheometers rely on boundary layers. u Fail to work with solid-liquid slip (mayonnaise etc). u Fail to obtain zero-shear viscosity. u Cannot be used on-line. Acoustic waves attenuate with liquid absorption.

3. Possible Approaches n Attenuation over distance u Simple fundamental phenomenon u Requires long aparatus. n Reflection coefficient u Ultrasonics have shown success. Empirical/ calibration. u Three-dimensional nature complicates fundamental analysis

4. Approaches pursued so far Longitudinal waves in tubes u Low-frequency in narrow tube allows simple 1-D analysis. Fluid loading of plate vibration. u Simple device.

5. Measuring complex acoustic speed with a tube. Measure impedances of driving piston ( Z m0 ) and end piston ( Z mL ). Measure total tube impedance F( ) u L ( ) Exciting force Piston speed Piston impedance Z m0 Piston impedance Z mL Slender tube Longitudinal waves

6. Total tube impedance F/u L Pressure amplitude at position x and wavenumber k is F( ) u L ( ) Exciting force Piston speed Z m0 Z mL L = tube length, m A and B are constants from boundary conditions Boundary conditions: 1) F = pressure at ( x =0) times piston area + speed at ( x =0) times Z m0 2) Pressure at (x=L) times piston area = speed at (x=L) times Z mL.

7. Obtaining complex acoustic speed Total tube impedance F/u L = total tube impedance, N/(m/s 2 ) Z m0, Z mL = piston impedance in-vacuo, N/(m/s 2 ) S = piston area, m 2 = liquid density, kg/m 3 L = tube length, m = frequency, rad/s Measured Known Solve for complex acoustic speed c.

8. Obtaining viscosity from complex c From relaxation time, obtain absorption coefficient using = density, kg/m 3 a = tube radius, m 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

9. Experimental Aparatus F/u L is obtained using FFT analyzer. Accelerometer Force from shaker or hammer. Mesured with force transducer Piston with spring beam

10. Results so far: Accelerances 0 dB = 1 m/s 2 /N Piston in-vacuo -20 60 0Hz 500 -5 25 Hz0100 Tube with water, theoretical. Tube with water, experimental.

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

12. Analytical model of plate Plate deflection w at point ( x, y ) is summation of modal responses p is modal coordinate from is mode shape, is natural frequency. is damping. From modal analysis

13. Results with plate: Accelerance with difference liquid viscosities Theoretical Experimental Liquid viscosity or concentration of Carboxy-Methyl Cellulose (CMC) : High, medium, low -10 20 Hz 60 -30 20 Hz60

14. Relationship between damping and viscosity From first mode data

15. 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.