Dia 1

1
Ultrasound 2006
Application of the Biot-Allard model to the
non-contact ultrasonic characterization of bread
crumb.
L. Boeckx1, B.Lagrain², E.Wilderjans², J.
Delcour2 ,W. Lauriks1. 1 Laboratory of Acoustics
and Thermal Physics, Catholic University Leuven,
Belgium. 2 Laboratory of Food chemistry,
Catholic University Leuven, Belgium.
Laboratory for Acoustics and Thermal Physics,
K.U.Leuven
2
Outline/introduction
Ultrasound 2006
Applicability of the Biot-Allard model to the
non-contact ultrasonic characterization of bread
crumb
Porous materials

• Solid phase
• Fluid

Characterization of Porous materials/ Sound
absorbing foams
1 mm
Laboratory for Acoustics and Thermal Physics,
K.U.Leuven
3
Outline/introduction
Ultrasound 2006
Applicability of the Biot-Allard model to the
non-contact ultrasonic characterization of bread
crumb.

Laboratory for Acoustics and Thermal Physics,
K.U.Leuven
4
Biot-Allard Model
Ultrasound 2006

• Fluid density
• Flow resistivity
• Porosity
• Tortuosity
• Viscous length
• Thermal length
• Solid density
• Youngs modulus
• Shear modulus

Frame movement ? Poro-elastic
x
Wave propagation through material
2 longitudinal waves and 1 transversal
wave through both solid and fluid phase
Rigid frame approximation
1 longitudinal wave through the fluid
Laboratory for Acoustics and Thermal Physics,
K.U.Leuven
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Biot-Allard Model
Ultrasound 2006

• Fluid density
• Flow resistivity
• Porosity
• Tortuosity
• Viscous length
• Thermal length
• Solid density
• Youngs modulus
• Shear modulus

Rigid Frame approximation
Wave propagation through material 1 longitudinal
wave through fluid
- J.F.Allard, Rev. Scientific Instruments,
65,754-755, (1994) - P. Leclaire, J. Appl. Phys.,
80(4), 2009-2012, 1996 -Fellah, Z.E.A, JASA,
2003
Ultrasonic measurements
Laboratory for Acoustics and Thermal Physics,
K.U.Leuven
6
Biot-Allard Model
Ultrasound 2006

• Fluid density
• Flow resistivity
• Porosity
• Tortuosity
• Viscous length
• Thermal length

Rigid Frame approximation
Wave propagation through material 1 longitudinal
wave through fluid
Laboratory for Acoustics and Thermal Physics,
K.U.Leuven
7
Biot-Allard Model
Ultrasound 2006
Energy dissipation

• Viscous effects
• Thermal effects
• Structural damping

Materials
Foams, ceramic materials, bone and tissue, Snow
layers, ocean floors, grass plains
Bread crumb ???
Which parameters ????
Laboratory for Acoustics and Thermal Physics,
K.U.Leuven
8
Biot-Allard Model
Ultrasound 2006
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K.U.Leuven
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Phase velocity
Ultrasound 2006
Tortuosity or structural form factor
Time signals
Porous absorbers
Slice of White Bread
J.F.Allard, Rev. Scientific Instruments,
65,754-755, (1994)
Laboratory for Acoustics and Thermal Physics,
K.U.Leuven
10
Tortuosity
Ultrasound 2006
Tortuosity or structural form factor
Phase Velocity
Porous absorbers
Slice of White Bread
J.F.Allard, Rev. Scientific Instruments,
65,754-755, (1994)
Laboratory for Acoustics and Thermal Physics,
K.U.Leuven
11
Tortuosity
Ultrasound 2006
EB bread supplemented with Alpha amylase
TB toast bread
Laboratory for Acoustics and Thermal Physics,
K.U.Leuven
12
Tortuosity
Ultrasound 2006
EB bread supplemented with Alpha amylase
Attenuation (dB/m)
fd
Frequency (kHz)
Laboratory for Acoustics and Thermal Physics,
K.U.Leuven
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Viscous and thermal length
Ultrasound 2006
Characteristic lengths
Viscous characteristic length
Thermal characteristic length
Measurement Setup
Porous absorbers 10-500 µm
P. Leclaire, J. Appl. Phys., 80(4), 2009-2012,
1996
Laboratory for Acoustics and Thermal Physics,
K.U.Leuven
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Viscous and thermal length
Ultrasound 2006
Characteristic lengths
Viscous characteristic length
Thermal characteristic length
Time signals
Porous absorbers 10-500 µm
P. Leclaire, J. Appl. Phys., 80(4), 2009-2012,
1996
Laboratory for Acoustics and Thermal Physics,
K.U.Leuven
15
Viscous and thermal length
Ultrasound 2006
EB bread supplemented with Alpha amylase
TB toast bread
Laboratory for Acoustics and Thermal Physics,
K.U.Leuven
16
Open porosity
Ultrasound 2006
Open porosity
Fellah Z, J.Acoust. Soc. Am.,113, 2424-2432,
(2003)
Laboratory for Acoustics and Thermal Physics,
K.U.Leuven
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Open porosity
Ultrasound 2006
EB bread supplemented with Alpha amylase
TB toast bread
Laboratory for Acoustics and Thermal Physics,
K.U.Leuven
18
Summary
Ultrasound 2006
Acoustics
Validation at low frequencies using impedance
tube/ Kundts tube
DIA
Laboratory for Acoustics and Thermal Physics,
K.U.Leuven
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Conclusions/Future Research
Ultrasound 2006
Conclusions

• Biot-allard model can be used for bead crumb
  characterization
• The parametes are related to the geometry of the
  structure
• 2 different bread types were characterized using
  non-contact ultrasonic
• measurement techniques
• Differences in crumb structure could be
  perceived regarding open porosity,
• characteristic lengths and tortuosity
• Cell sizes were estimated using DIA
• Attenuation was solely determined by microcracks
• Parameters were within Literature values (DIA,
  Electron microscopy)

Future research

• Variability study within one bread/ different
  breads of 1 batch
• Significance of the differences in parameters
• Variation of parameters from centre to crust
• Effects of additives
• Changes of crumb structure during time

Laboratory for Acoustics and Thermal Physics,
K.U.Leuven
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Einde
Zie ook

• L. Boeckx, P.Leclaire, P. Khurana, C. Glorieux,
  W.Lauriks, J.F.Allard, Guided
• elastic waves in porous materials saturated by
  air under Lamb conditions,
• Journal of Applied Physics, 97, 094911, (2005).
• L.Boeckx, P.Leclaire, P. Khurana, C. Glorieux,
  W.Lauriks, J.F.Allard, Investigation
• of the phase velocities of guided acoustic waves
  in soft porous layers,
• Journal of Acoustical Society of America, 117
  (2), 545-554, (2005).
• J.F.Allard, M.Henry, L. Boeckx, P. Leclaire,
  W.Lauriks, Acoustical measurement
• of the shear modulus for thin porous layers,
• Journal of Acoustical Society of America, 117(4),
  1737-1743, (2005).
• L. Boeckx, G. Jansens, W.Lauriks, D.G.
  Albert,Modelling acoustic surface waves
• above a snow layer, Acustica, 90, 246-250,
  (2004).

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K.U.Leuven
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Ultrasound 2006
1
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Laboratory for Acoustics and Thermal Physics,
K.U.Leuven
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Ultrasound 2006
Ultrasonic acoustic testing methods
Measurement Setup

• Fast, user friendly measurements
• Non destructive acoustic testing
• Frequency or temporal domain

• High frequency (MHz) burst or pulse through the
  sample
• Material behaves as a equivalent fluid ?
  theoretical simplification

Laboratory for Acoustics and Thermal Physics,
K.U.Leuven
23
Flow resistivity
Ultrasound 2006
Flow resistivity
Laboratory for Acoustics and Thermal Physics,
K.U.Leuven