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Measuring Liquid Viscosity Using Acoustic Absorption.

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. Motivation. Food industry rheometers rely on boundary layers.

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Measuring Liquid Viscosity Using Acoustic Absorption.

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  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. • 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.

  3. 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

  4. 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.

  5. Measuring complex acoustic speed with a tube. • Measure impedances of driving piston (Zm0) and end piston (ZmL). • Measure “total tube impedance” Slender tube Piston speed Exciting force uL(w) F(w) Zm0 ZmL Longitudinal waves Piston impedance Piston impedance

  6. Total tube impedance F/uL Piston speed Exciting force uL(w) • Pressure amplitude at position x and wavenumber k is F(w) Zm0 ZmL L = tube length, m AandBare constants from boundary conditions • Boundary conditions: • F = pressure at (x=0) times piston area + speed at (x=0) times Zm0 • Pressure at (x=L) times piston area = speed at (x=L) times ZmL.

  7. Obtaining complex acoustic speed • Total tube impedance F/uL = total tube impedance, N/(m/s2) Zm0, ZmL = piston impedance in-vacuo, N/(m/s2) S = piston area, m2 r = liquid density, kg/m3 L = tube length, m w = frequency, rad/s Measured Known • Solve for complex acoustic speed c.

  8. Obtaining viscosity from complex c • From complex acoustic speed c, obtain relaxation time t using • From relaxation time t , obtain absorption coefficient a using c = real speed, m/s • Viscosity h can be related to absorption coefficient a. r = density, kg/m3 a = tube radius, m (Exact relationship to be determined)

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

  10. Results so far: Accelerances 60 0 dB = 1 m/s2/N • Piston in-vacuo • Tube with water, theoretical. -20 500 0 Hz • Tube with water, experimental. 25 -5 0 Hz 100

  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 From modal analysis • f is mode shape, w is natural frequency. z is damping.

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

  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.

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