**1. Introduction**

212 Acoustic Waves – From Microdevices to Helioseismology

La Rivière, P. J., Zhang, J. & Anastasio, M. A. (2006). Image reconstruction in optoacoustic tomography for dispersive acoustic media, *Optics Letters*. 31(6), 781-783 Lemons, D. S. (2002). An Introduction to Stochatic Processes in Physics, The Johns Hopkins

Nachman, A. I., Smith III, J. F. & Waag, R. C. (1990). An equation for acoustic propagation in inhomogeneous media with relaxation losses, *J.Acoust.Soc.Am*. 88, 1584-1595 Nuster, R., Gratt, S., Passler, K., Grün, H., Berer, T., Burgholzer, P. & Paltauf, G. (2009).

Paltauf, G., Nuster, R., Haltmeier, M. & Burgholzer, P. (2006). Photoacoustic tomography using a Mach-Zehnder interferometer as acoustic line detector, *Appl. Opt.* 46, 3352–3358 Paltauf, G., Nuster, R., Passler, K., Haltmeier, M. & Burgholzer, P. (2008). Optimizing Image

Roitner, H. & Burgholzer, P. (2011). Efficient modeling and compensation of ultrasound attenuation losses in photoacoustic imaging, *Inverse Problems* 27, 015003 Roitner, H., Bauer-Marschallinger, J., Berer, T. & Burgholzer, P. (2011). Experimental

Shutilov, V. A. (1988). *Fundamental Physics of Ultrasound*, Gordon and Breach Science

Stokes, G. G. (1845). On the theories of the internal friction of fluids in motion, and of the equilibrium and motion of elastic solids, *Trans. Cambridge Philos. Soc*. 8, 287-319 Szabo, T. L. (1994). Time domain wave equations for lossy media obeying a frequency

Treeby, B. E. & Cox, B. T. (2010). Modeling power law absorption and dispersion for acoustic propagation using the fractional Laplacian, *J.Acoust. Soc. Am*. 127 , 2741-2748 Treeby, B.E. & Cox, B. T. (2010b). k-wave: Matlab toolbox for the simulation and reconstruction of photoacoustic wave fields, *J. Biomed. Optics* 15(2), 021314-1 - 021314-12 Treeby, B.E., Zhang, E. Z. & Cox, B. T. (2010c). Photoacoustic tomography in absorbing

Uhlenbeck, G. E. & Ornstein, L. S. (1930). On the Theory of Brownian Motion, *Phys. Rev.* 36,

Xu, M. & Wang, L. V. (2006). Photoacoustic imaging in biomedicine, *Review of Scientific* 

Zhang, E. Z., Laufer, J. G., Pedley, R. B. & Beard, P. C. (2009). In vivo high-resolution 3D

photoacoustic imaging of superficial vascular anatomy, *Phys. Med. Biol.* 54, 1035–1046

Wang, L. V. (2008). Prospects of photoacoustic tomography, *Medical Physics* 35, 5758–5767

acoustic media using time reversal, *Inverse Problems* 26, 115003

Widrow, B. & Kollar, I. (2008). *Quantization noise*, Cambridge Books, Cambridge

Trefethen, L. M. (2000). *Spectral Methods in Matlab*, SIAM, Philadelphia

Comparison of optical and piezoelectric integration line detectors, in *Biomedical Optics: Photons Plus Ultrasound: Imagingand Sensing 2009*, edited by A. A. Oraevsky

Resolution in Three-Dimensional Photoacoustic Tomography With Line Detectors, in *Biomedical Optics: Photons Plus Ultrasound: Imaging and Sensing 2008, Proc SPIE,* 

Evaluation of ultrasound attenuation losses in photoacoustic imaging, submitted

University Press

Nyquist, H. (1928). *Phys. Rev*. 32, 110

to *J.Acoust.Soc.Am.*

Publishers

823-41

6856

and L. H. Wang, *Proc. SPIE* 7177, 71770T

Royer, D. & Dieulesaint, E. (2000). *Elastic Waves in Solids I*, Springer

power law, *J.Acoust. Soc. Am.* 96, 491–500

*Instruments*. 77(4), 041101-041122

The evolution in consumer expectations in terms of quality and safety in the agro-industry has led to the need to develop new methods of investigating product quality and the processes involved. Many fields of production still rely too much on the know-how of the operators who, with their experience acquired over time, have become key players in the company. In addition, the manufacturing of quality food products frequently relies on artisanal know-how that is difficult to industrialise and often synonymous of high production losses, therefore prohibitive costs. In contrast, so as to limit costs, the industrial production process is often associated with poorer quality. The objective evaluation of product quality involves the development of methods and sensors adapted to the product or the manufacturing process.

Indeed, beneath an apparent simplicity, agro-industry products have complex physical properties linked to elasticity, viscosity and plasticity. One of the major difficulties lies in the complexity of the processes which depend on numerous physical parameters. The matter is subjected to numerous mechanical, thermal or chemical treatments thus migrating towards viscoelastic or even plastic properties that are more difficult to quantify.

The originality of the approach adopted consists in the study and set up of an ultrasonic measuring device associated with its electronic environment in order to reply to a specific need due to the complexity of the physico-chemical phenomena involved. A global approach to this problem is very tricky as the physical properties of the media evolve significantly throughout processing.

We thus focused on the development of sensors and methods of characterisation dedicated to different phases of the industrial processes. Two very closely linked aspects were therefore studied targeting product characterisation and process control.

Work has been carried out to develop acoustic and ultrasonic instrumentation designed to monitor the change in state of the matter (liquid-gel transition and product cohesion), then to monitor the evolution of its elastic properties. The process control applications concern the development of a very low frequency, non-destructive monitoring method to reply to the specificities of the physical properties of the matter.

In this document, we report the scientific approach highlighting the design of the ultrasonic sources which dispenses with classic design through the choice of specific resonance modes for the sensors. Their design aims at promoting low frequency resonance in a relatively small scale composite structure. This sensor technology was adapted according to the

Low Frequency Acoustic Devices for Viscoelastic Complex Media Characterization 215

The processes can also evolve over time. This is the case with heat exchangers for which the performance varies over time due to fouling. Only preventive maintenance leading to additional production costs can ensure stable performances of the process over time. The development of sensors integrated in the process to provide information on the evolution of

This work presents a selection of studies which have led to the development of low frequency acoustic sensors specifically adapted to monitor changes in the physical state of complex media and the process: fragile gel, highly heterogeneous or highly absorbent

• A low frequency acoustic sensor adapted to the characterization of complex products using an omni-directional source in the case of media undergoing a change in physical

• complex heterogeneous medium: transition from a suspension of particles in a

• A very low frequency acoustic sensor used to monitor the response of a medium subjected to mechanical vibrations. Such technology is designed to study the processing phenomena of a highly absorbent product such as bread dough during fermentation. Finally, the identification of the needs and constraints imposed by certain environments (temperature, hygiene, attenuation...) have led to the combination of these types of technology to monitor a process (e.g. fouling of plate heat exchangers, search for an optimum point in the kneading phase...). By taking into account the coupling of the sensor with its environment this technique can, in certain cases, exploit the noise emitted by the

In this work, we chose to illustrate the potential of low frequency acoustic methods on applications from the agri-foodstuffs sector. These same states can also be found in the pharmaceutical and cosmetics industries, the aviation industry, the medical field as well as

• Definition and/or optimisation of the appropriate method and a sensor meeting the

**3. Sensors suitable for studying media of which the physical properties** 

The analysis of the different stages in the formation of macromolecular networks is of major importance, since understanding the structure and properties (physical or chemical) of gels requires the understanding of the process of organization. In many physical, chemical or biological processes, the union of small separate elements to form aggregates of different sizes and further macroscopic phases makes connectivity an essential characteristic of this

the performance remains essential.

Several cases were studied:

state;

media, media with complex rheological behaviour...

process itself, as in kneading for example.

• Analysis of the product and/or process

in material chemistry.

**evolve over time** 

various constraints : • Analytical study • Numerical modelling • Experimental validation of the sensor

• Validation of the application

• continuous homogeneous medium: sol-gel transition,

The methodology implemented can be divided into several phases:

**3.1 Monitoring changes in the physical state of the matter** 

liquid to a cohesive visco-elasto-plastic solid.

frequency chosen to study the change in physical state of the media and to monitor the evolution of the acoustic properties of products that are often heterogeneous.

Several approaches were used to optimise this technology: an analytical approach to determine the sensor's first vibratory mode which was consolidated by a numerical study, then confirmed and validated experimentally.

The application is based on two points:

