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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

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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.

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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

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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.

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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

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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.

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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.

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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

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

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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.

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

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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

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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

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Relationship between damping and viscosity From first mode data

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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.

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