Pierre et al.
Proceedings of Meetings on Acoustics Volume 19, 2013
http://acousticalsociety.org/
ICA 2013 Montreal Montreal, Canada 2 - 7 June 2013 Physical Acoustics Session 2pPA: Material Characterization 2pPA7. Shaving foam: A complex system for acoustic wave propagation Juliette Pierre*, Valentin Leroy, Arnaud Saint-Jalmes, Benjamin Dollet, Imen Ben Salem, Jerôme Crassous, Reine-Marie Guillermic, Wiebke Drenckhan and Florence Elias *Corresponding author's address: Institut de Physique de Rennes UMR CNRS 6251 - University Rennes 1, Campus Beaulieu, Rennes, 35042 Rennes Cedex, Rennes, France,
[email protected] While liquid foams have applications in an increasing number of industrial areas (food, cosmetic or petroleum industry), it remains difficult to non-invasively probe their structure and/or composition. Since the propagation of acoustic waves is very sensitive to parameters such that the liquid fraction, the bubble size distribution, or even the nature of the liquid phase, acoustic spectroscopy could be a very powerful tool to determine the structure and/or composition of liquid foams. In this context, we present an investigation of the acoustic properties of a useful and common foam, often considered as a model system: shaving foam. Phase velocity and attenuation of acoustic waves in a commercial shaving foam (Gillette) were measured over a broad frequency range (0.5 to 600 kHz), using four different experimental setups: an impedance tube (0.5-6 kHz), an acousto-optic setup based on Diffusive Wave Spectroscopy (0.4-10 kHz), and two transmission setups with narrow-band (40 kHz) and broad-band (60-600 kHz) transducers. We present the results and discuss the advantages and shortcomings of each setup in terms of a potential spectroscopy technique. Published by the Acoustical Society of America through the American Institute of Physics
© 2013 Acoustical Society of America [DOI: 10.1121/1.4800701] Received 22 Jan 2013; published 2 Jun 2013 Proceedings of Meetings on Acoustics, Vol. 19, 045044 (2013)
Page 1
Pierre et al.
I NTRODUCTION Liquid foams consist of discrete and closely packed gas bubbles dispersed in a liquid phase with a typical liquid volume fraction ranging from 0.1% up to about 30% of the volume. The films that separate the bubbles are stabilised by interfacially active agents (such as surfactants, proteins, polymers or particles). The presence of a continuous liquid network makes foams a complex material, at the borderline between the solid and the liquid state, having simultaneously elastic, plastic and viscous properties. Moreover, the constant evolution in time of liquid foams adds to the complexity of the system. While liquid foams have applications in an increasing number of industrial areas (food, cosmetic or petroleum industry), it remains difficult to non-invasively probe their structure and/or composition. Propagation of acoustic waves in a foam is very sensitive to parameters such as the liquid fraction, the bubble size distribution, and even potentially the chemical formulation of the foaming liquid. Acoustic spectroscopy could thus be a very powerful tool to determine the structure and/or composition of liquid foams. Acoustic measurements in liquid foams are not straightforward. Contrary to other multiphase systems (as bubbly liquids or suspension of particles for examples), acoustic measurements in liquid foams, in the literature, are not numerous [1, 2, 3] and do not cover a range of frequencies broad enough to measure a dispersion of the acoustical properties, the key feature for extracting the size distribution. In this article we present four different setups used for measuring the acoustic velocity and attenuation in a liquid foam. Each setup differs either by the frequency range over which it operates, or by the conditioning which it imposes to the foam. The conditioning of the foam is a crucial point because it may disturb the acoustic propagation or modify the time evolution of the foam. As an example and to highlight the potentiality of the different experimental techniques we present an investigation of the acoustic properties of a useful and common foam, often considered as a model system: a shaving foam.
E XPERIMENTAL SETUPS A commercial shaving foam (Gillette) was used in the four setups. Gillette foam is readily available and offers a good stability. It has been extensively studied in rheological studies and is commonly considered as a model system. Gillette foam presents a typical volume fraction between 6% and 9%, with almost no drainage and a slow coarsening. Coarsening without drainage is an advantage because the evolution in time can be directly link to the bubbles radii. For a Gillette foam coarsening in the open air the average bubble size is of the order of 15 µm initially and grows slowly with time as showed in figure 1.
Bubble mean radius (μm)
150
100
50
0 1
10
50 150 500 Time (min)
2000
F IGURE 1: A typical time evolution of the average bubble size in a Gillette foam.
Proceedings of Meetings on Acoustics, Vol. 19, 045044 (2013)
Page 2
Pierre et al.
Broad-band transducers! (60-600kHz)!
Impedance tube (0.5-6kHz)
Acousto-optic setup (0.4-10kHz)
Broad band air transducer: transmitter! 40kHz Transducers!
receivers
Fixed transmitter!
Moving receiver!
Foam cell! CCD
Laser He-Ne
foam
foam Broad band air transducer:! receiver!
F IGURE 2: Simplified schemes of the four different setup.
In this section, we describe briefly the four different setups used for measuring the acoustic properties in liquid foams. The frequency range and the conditioning of the foam are presented. We discuss also the advantages and the limits of these different experimental techniques. Simplified schemes of the different setups are presented figure 2. Impedance Tube. A commercial impedance tube (type 4206, Bruel&Kjaer) was hanged vertically and the shaving foam was poured into the sample holder on 1 to 3 cm height. By analysing the positions and width of the resonances in the foam sample, one can determine the density, sound velocity and sound attenuation. It operates from 0.5 to 6 kHz. The major advantage of this setup is that it is based on a commercial tube directly and readily usable. Acousto-optic setup. The foam is also placed in a tube, but with transparent walls. The foam is excited by a monochromatic compressional wave with a range of frequency depending of acoustic source (at the moment we use a source operating from 400 Hz tol 10 kHz). Then the displacement of the foam induced by the sound wave propagation is measured by an optical technique based on multiple scattering of the light (Diffusing Wave Spectroscopy, DWS) [4]. This technique is very sensitive and gives insight on the acoustic profile close to the wall and not in the bulk. An advantage of this acousto-optic technique is in the study of the problem of the viscous frictions on the wall which may exist in the impedance tube technique. At this stage we have only access to the sound attenuation, but the elaboration of a system to measure a wavelength by scanning vertically is under progress. 40 kHz Transducers. The foam is placed in the open air in between a couple of narrow-band air transducers. By varying the distance between the transducers, one can measure the velocity and attenuation [5]. This setup is readily usable and following the dynamics of the foam with aging is an easy task. The very narrow band of frequency (around 40 kHz) of the transducers is a limitation. Note also that in order to not disturb the foam with the displacement of the receiver very small displacements are realized (< 0.5 mm). Broadband Transducers. The foam is conditioned in a cell with PET (polyethylene terephtalate) wall of 3 µm of thickness. Two broad band air transducers (BATs) are used to explore a frequency range between 60 kHz and 600 kHz. The acoustic velocity and attenuation are deduced from the transmitted signal through the cell and real-time analysis is possible [6]. As a main advantage, the acoustic properties are real-time recorded on a large range of frequency without invasion of the foam. However this technique presents some limitation. Filling the cell to have an homogeneous cell of foam is tricky. To ensure a three dimensional
Proceedings of Meetings on Acoustics, Vol. 19, 045044 (2013)
Page 3
Pierre et al.
configuration of the foam, the thickness of the cell needs to be adapted to the bubble sizes (for shaving foam, the cell was 0.5 mm thick).
R ESULTS
Velocity (m/s)
Density (kg/m3)
Below we present a selection of striking results obtained with these setups, showing that we start to cover a large range of frequency.
80 60 40 20 0
1
2
3
4
5
1
2
3
4
5
4
5
80
60
40 0
Attenuation (m−1)
50 GILLETTE A GILLETTE B
40 30 20 10 0 0
1
2 3 Frequency (kHz)
F IGURE 3: Density, velocity and attenuation measured for two Gillette foams in an impedance tube
Figure 3 shows the density, velocity and attenuation for two shaving foams (Gillette), with approximatively the same liquid fraction Φ = 6 % (independently determined by weight measurements), obtained using the Impedance Tube technique. As expected, the acoustic measurements are similar for the two samples. Interestingly, the measured density gives a good determination of the liquid fraction. The velocity is found to be almost constant with frequency, around 60 m/s, a value higher than the 42 m/s predicted by a simple effective medium model (known as Wood’s model) for this liquid fraction [7]. Attenuation is found very dispersive in this frequency range. One can always wonder about the possible role of the friction on the wall of the tube. The DWS technique may be a good way to answer this question. The DWS measurements show that the foam is sheared close to the wall on a zone of the oder of 1 mm at 1 kHz [4] which gives an attenuation of the order of 3 m−1 according to the Kirchhoff formula [8] in our tube of diameter of 29 mm. Figure 4 shows the time evolution of the phase velocity and the attenuation at 40 kHz (40 kHz Transducers technique) for a Gillette foam of liquid fraction close to 8 %. During the first 30 min the velocity goes from
Proceedings of Meetings on Acoustics, Vol. 19, 045044 (2013)
Page 4
Pierre et al.
100
2.5 ï1
Attenuation (mm )
3
Velocity (m/s)
110
90 80 70 60 50 0
2 1.5 1 0.5
40
80 Time (min)
120
0 0
160
40
80 Time (min)
120
160
F IGURE 4: Time evolution of the phase velocity and attenuation of an acoustic wave at 40kHz propagating through a Gillette foam.
65 m/s to a maximum of 85 m/s and goes back down at 65 m/s. On the same period of time, the attenuation is decreasing. Between 30 and 120 min, the phase velocity decreases from 65 m/s to 60 m/s, and the attenuation increases slowly from 0.2 mm−1 to 1.2 mm−1 . The velocities measured at 40 kHz are still above the velocity predicted by the model of Wood. Close to 150 min, the attenuation and the velocity increases drastically. In the absence of drainage the time evolution can be related to the bubble size. For an acoustic propagation at 40 kHz, the single bubble resonance is for a radius of 72 µm [9], which is consistent with a maximum of attenuation at 150 minutes (see figure 1).
10
80 0min (r =13.1μm) 0
70
15min (r0=17μm)
8
60
Attenuation (mm−1)
Velocity (m/s)
60min (r0=20.8μm) 120min (r0=24μm)
50 40
4
2
30 20 50
6
100 150 200 Frequency (kHz)
250
0 50
100 150 200 Frequency (kHz)
250
F IGURE 5: Gillette foam: velocity v and attenuation α in frequency for different bubble size (i.e. different ages).
Figure 5 shows the frequency dependence of the phase velocity and the attenuation at different time (i.e. different bubbles radii) extracted from the Broadband Transducers technique. The phase velocity starts above Wood velocity but reaches values inferiors to Wood velocity. The smaller value of velocity recorded is 25 m/s. The attenuation shows a strong dependence to both time and the frequency.
Proceedings of Meetings on Acoustics, Vol. 19, 045044 (2013)
Page 5
Pierre et al.
C ONCLUSION We have shown that we are able to measure acoustic properties in a liquid foam on a very large range of frequencies: from low frequencies to ultrasonic regime. The results extracted from the four different techniques are consistent. The coherence between results shows that our different techniques do not disturb the acoustic response of liquid foams. We have highlight that we are able to observe the bubble resonance, which may be used to determine the bubbles size in the foam. As an important result, we have showed that Wood model cannot describe the sound velocity measured in a Gillette foam. An idea to explain this peculiar sound velocity is to invoke a large visco-elasticity of the films [2]. It would mean that measuring the acoustic velocity in a foam could give insight in its chemical composition.
ACKNOWLEDGMENTS Support from the French Agence Nationale de la Recherche (project SAMOUSSE, ANR-11-BS09-001) is gratefully acknowledged. The authors thank the GDR “Mousses et Émulsions” for its stimulating scientific environment.
R EFERENCES [1] Z. M. Orenbakh and G. A. Shushkov, “Acoustical characteristics of water-air foams”, Sov. Phys. Acoust. 39, 63–66 (1993). [2] N. Mujica and S. Fauve, “Sound velocity and absorption in a coarsening foam”, Physical Review E 66, 021404 (2002). [3] D. Daugelaite, “Time dependent studies of foam stability using image analysis”, Ph.D. thesis, Electrical Resistivity and Ultrasound, PhD thesis, University of Manitoba (2011). [4] M. Erpelding, R. M. Guillermic, B. Dollet, A. Saint-Jalmes, and J. Crassous, “Investigating acousticinduced deformations in a foam using multiple light scattering”, Physical Review E 82, 021409 (2010). [5] I. B. Salem, R. M. Guillermic, C. Sample, V. Leroy, A. Saint-Jalmes, and B. Dollet, “Propagation of ultrasound in aqueous foams: bubble size dependence and resonance effects”, Soft Matter 9, 1194–1202 (2013). [6] J. Pierre, F. Elias, and V. Leroy, “A technique for measuring velocity and attenuation of ultrasound in liquid foams”, Ultrasonics 53, 622–629 (2013). [7] A. B. Wood, A textbook of sound (Bell and Sons, London) (1944). [8] T. Rossing, Springer Handbook of Acoustics (Springer Verlag) (2007). [9] M. Minnaert, “On musical air-bubbles and the sounds of running water”, Philosophical Magazine 16, 235– 248 (1933).
Proceedings of Meetings on Acoustics, Vol. 19, 045044 (2013)
Page 6
