Ultrasonic characterisation of solid-liquid suspensions

Ultrasonics 36 ( 1998) 467 -470

Ultrasonic characterisation

of solid-liquid suspensions

Abstract

Results on ultrasonic attenuation in suspensions of alumina powder in water at high concentration (40% vol.) are presented. When high concentrations of solid material in the host liquid are desired, it is very important to keep the solid particles well separated (deflocculated). This property is achieved by using a dispersant. whose concentration is critical for obtaining a good particle separation. The purpose of our study was to identify weak structural differences which occur between suspensions with direrent degrees of deflocculation. obtained by slightly varying the quantity ofdispersant around the critical value: such differences are difficult to be seen with other methods or devices (optical, Acoustosizer) at high concentration. In this aim the attenuation coefficient of ultrasonic waves travelling through the samples has been determined by using an ultrasonic method. This method. based on techniques used for electric network analysis. allows us to achieve the absorption curve of the suspension under test. To this purpose. a plane ultrasonic wave. whose frequency is linearly swept, is generated inside the liquid by a piezoelectric transducer, acting as a transmitter. and received by a second transducer. frontally placed and aligned on the same axis. The transfer function of the system is proportional to the ratio of the acoustic pressure at the receiver and at the transmitter and depends on the spectral response of the transducers and on the acoustic path inside the liquid. The measurement of the system response is provided by a swept frequency network analyser. From the ratio of the transfer functions H and H, measured at two positions separated by ;I distance Ad the absorption coefficient x is obtained as a function of the frequency through the simple relation LX=-( I .4t/)log(H~H,,). In the frequency range in which the measurements have been carried out ( l-20 MHz) we observed small but significant differences between attenuation dependence on frequency in suspensions with the same basic composition but with slightly different particle size distributions: indeed weakly flocculated suspensions presented lower attenuation than well deflocculated suspensions. In order to decide which mechanism is responsible for attenuation dependence in our experiments. we calculated the attenuation values for different mechanisms: thermal conduction, multiple scattering and viscous drag. Good agreement was obtained with a hydrodynamic model (Harker et al.. C’ltrusonic~s 29 ( 1991 ) 427) mainly based on viscous losses. Moreover this model is also able to reproduce the dependence of attenuation on slight variations in particle size distributions. as observed in our experiments. c 1998 Elsevier Science B.V. ,G~wrwt/\:

Attenuation:

Suspensions

1. Introduction

Sound attenuation by suspensions of small particles has been the subject of numerous studies [l-15]. An exhaustive paper by Allegra and Hawley [ 1] constitutes the basis for most recent studies on this subject. This argument belongs to the more general field of wave propagation in inhomogeneous media, which received enormous attention due to the multitude of concerned aspects; indeed different phenomena can be involved, starting with attenuation produced by viscous and thermal transport phenomena up to scattering or multiple

* Corresponding

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scattering of waves on inhomogeneities. including phenomena of classical wave localization. Therefore the problem has been treated with very different approaches but, fortunately, when comparing experiment with theory in order to extract useful information about the propagation medium, one can neglect some aspects and favour others. For example, while at wavelengths comparable with the inhomogeneities scattering losses can be predominant, at great wavelengths these are negligible and only other mechanisms are present. It has been shown [I] that at great wavelengths the absorption of sound in suspensions is due to viscous and thermal transport processes occurring at the interface of the inhomogeneities. as well as to the intrinsic absorption in the materials.

G. Guidarelli et al. / Ultrasonics 36 (1998) 467-470

468

There are several applications in which it is desirable to measure the size of solid particles suspended in a fluid by using ultrasound attenuation. Some other methods (optical) and devices (Acoustosizer) are available but they generally fail when a high concentration of particles is involved. This paper presents experimental measurements of attenuation in highly concentrated suspensions of alumina in water. Few samples with different particle size have been examined and different models have been used to explain the results.

2. Experimental Two types of samples have been prepared by mixing alumina powder ALCOA Al6 SG in proportion of 40% vol. with water. Sample A has been added with 0.2% deflocculant DURAMAX D3021 while Sample B with 1% of the same deflocculant. Sample A is well deflocculated as the quantity of the additive was optimum, but Sample B, which was added with a quantity of deflocculant higher than critical, is slightly flocculated. Particle size distributions have been determined with Acoustosizer from Matec AS. for suspensions up to 25% vol. concentration and extrapolated to 40% vol. suspensions. The attenuation coefficient of ultrasonic waves travelling through the samples has been determined by using an ultrasonic method already developed for investigating the properties of viscous liquids [ 161. The method, based on techniques used for electric network analysis, allows us to achieve the absorption curve of the liquid under test. To this purpose a plane ultrasonic wave, whose frequency is linearly swept, is generated inside the liquid by a piezoelectric transducer, acting as a transmitter, and received by a second transducer, frontally placed

and aligned on the same axis (Fig. 1). Previous measurements of testing have been performed in pure water. Careful alignment of transducers has been done in order to minimize the measurement errors. The measurements have been performed at room temperature (20°C). The whole electroacoustic chain, formed by the transducers and by the liquid between them, is viewed as a two port electric network corresponding to the input of the transmitter and to the output of the receiver. The transfer function of the system is proportional to the ratio of the acoustic pressure at the receiver and at the transmitter and depends on the spectral response of the transducers and on the acoustic path inside the liquid. The measurement of the system response is provided by a swept frequency network analyser. Two steps are required to achieve the absorption curve of the liquid: in the first step the transducers are placed at a given distance d~5 cm apart, and the corresponding transfer function H, is determined and taken as a reference level. In the second step the distance between transducers is changed by a known amount Adz3 mm and the new transfer function H is measured and referred to H,; this normalisation eliminates the weighting effect of the transducers response and allows to get the absorption coefficient E as a function of the frequency through the simple relation a= -( l/Ad)log(H/H,).

3. Results and discussion Particle size distributions for Samples A and B as measured by Acoustosizer are presented in Fig. 2. Size analysis gives d50= 0.282 pm, d,, = 0.126 urn, d+, = 0.633 for Sample A and d,,=O.352 urn, di6=0.21 7 urn, ds4 = 0.571 for Sample B. Fig. 3 shows measured attenuation in the two type of samples. Analysis of the curves evidence that their dependence on frequency follow a power law a-j”‘,

PLOTTER

Size (pm)

Fig,

I. Experimental

set-up; T = transmitter;

R = receiver.

Fig. 2. Particle size distributions for suspensions deflocculated; B = slightly flocculated).

A and B (A=well

G. Guidarrlli 25

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6 15

20

f (MHz) Fig. 3. Attenuation function and B at room temperature.

of frequency

measured

in suspensions

A

with no 1.7 for Sample A and n 2 1.5 for Sample B. It can be observed that Sample B, which has a larger particle size presents a lower attenuation, which is more evident at higher frequencies. Further we tried to understand which loss mechanism is responsible for attenuation values in our experimental findings. First we considered the effects of multiple scattering [ 3,&l 11. With our data, calculated attenuation by using these models was two orders of magnitude lower than the measured one, therefore we concluded that scattering has no influence on loss in our experiment. Furthermore we considered losses due to thermal conduction and viscous drag. In the thermal mechanism, temperature changes produced by an acoustical wave are related to the pressure. This pressureetemperature coupling describes the changes in temperature from the equilibrium value for a sound wave which propagates adiabatically through a medium [ 11. The temperature variations produced by the sound wave in the different components of suspension are generally different, producing heat flow from one substance to another. When this heat flow does not occur in phase with the passage of the sound wave, damping occurs. A similar discussion can be made for viscous drag mechanism, which concerns the relative motion of the suspending particles and host liquid medium, produced by the wave passage. Two quantities have been introduced in order to compare these losses. The first one is the thermal wavelength ii, = d2K,/(p, C,w), where K,, ps, C, are the thermal conductivity, the density and the specific heat of alumina, and (0 is the angular frequency of the wave. The second is the viscous wavelength S, =$%&& where 9 and p, are the viscosity and density of the liquid. It has been shown by different authors that thermal conduction and viscous drag losses present maxima when

36 ( 1WX) 467.-470

469

thermal and viscous wavelengths are approximately equal to the particle’s radius [ 11. Indeed at low frequencies the temperature difference between the particle and the suspending fluid will equilibrate in the time of passage of a sound wave whereas at high frequencies only a small portion of the particle volume near the surface is involved in the thermal conduction process. Only when the thermal wavelength is the same size as that of the suspended particle does the whole particle participate in the loss mechanism [ 11. Also viscous loss is greatest when the viscous wavelength is approximately equal to the particle radius. At low frequencies both the particle and the molecules of the suspending medium can follow the sound wave with small relative motion, while at very high frequencies there is little motion of either the particles or the molecules of the suspending medium [ 11. We calculated the two characteristic lengths for our samples: for the frequency range l-20 MHz we obtained that 6,>>r (where Y is particle radius) while 6, is found to be comparable to Y, therefore we hypothesized that viscous losses should be the dominant loss mechanism in our case. Consequently we used for interpretation of our results a hydrodynamic model based on viscous losses developed by Harker et al. [6,9]. This model gives the dispersion equation for the complex wavevector k which depends on concentration, compressibilities and densities of the two components and on the ratio between the viscous wavelength and the particle size. One solves for the real part of k in order to obtain velocity, while the imaginary part is the attenuation. The attenuation obtained from this model by using our parameters is represented in Fig. 4 as a function of frequency and particle radius. It can be seen that it depends on particle radius and is generally decreasing when r increases, except for very small particle size where a crossover is registered (such a crossover has been observed also in the experimental data, more visible in a logarithmic scale, at approx. 1 MHz). Values of attenuation obtained from this model are close to the measured ones. For example, at 15 MHz calculated and aB z 12 Np cm- 1 and measured x,z14Npcm-’ and r,% 11 Np cm- ‘. We concluded x,gl4.5Npcm-’ that a hydrodynamic model based on viscous drag losses is adequate to be used for predictions of particle size from attenuation measurements in this type of suspension.

4. Conclusions We demonstrated that ultrasonic attenuation measurements can show small structural differences between different suspensions at high values of solid volume fractions, where measurements by other methods fail. A hydrodynamic model based on viscous drag

G. Guidmdli el ul. / Ultrusonic~~36 ( lYY8) 467-470

470

A (Np/cm) 10

Fig. 4. Calculated

attenuation

function

mechanism has been found to be the most appropriate model for predicting particle size from attenuation measurements in alumina-water highly concentrated suspensions.

Acknowledgement The authors gratefully acknowledge ments from Anna Costa.

help in measure-

References [ I ] J.R. Allegra, S.A. Hawley, J. Acoust. Sot. Am. 51 ( 1972) 1545. [2] M.C. Davis, J. Acoust. Sot. Am. 64 ( 1978) 408. [3] L. Tang. J.A. ( 1982) 552.

Kong,

T. Habashi.

J. Acoust.

Sot.

Am.

71

of frequency

and particle

size.

[4] W.M. Madigoski. Proc. Ultrasonics International ‘89. p. 913. [5] A.E. Hay, AS. Schaafsma, J. Acoust. Sot. Am. 85 ( 1989) I 124. [6] A.H. Harker, J.A.G. Temple, J. Phys. D: Appl. Phys. 21 (1988) 1576. [7] R.A. Roy. R.E. Apfel. J. Acoust. Sot. Am. 87 (1990) 2332. [8] Y. Ma, V.K. Varadan, V.V. bradan, J. Acoust. Sot. Am. 87 ( 1990) 1779. [Y] A.H. Harker, P. Schofield, B.P. Stimpson, R.G. Taylor. J.A.G. Temple, Ultrasonics 29 ( 1991 ) 427. [IO] W.H. Schwartz, T.S. Margulis. J. Acoust. Sot. Am. 90 (1991) 3209. [I I] D.J. McClements. J. Acoust. Sot. Am. 91 ( 1991) 849. [ 121 M. Stautberg Grcenwod. J.L. Mai, M.S. Good. J. Acoust. Sot. Am. 94 (1993) 908. [I31 J. Adach, R.C. Chivers. L.W. Anson, J. Acoust. Sot. Am. 93 ( 1993) 3208. [ 141 S. Temkin, J. Acoust. Sot. Am. 100 ( 1996) 825. [ 151 C.S. Hall, J.N. Marsh, M.S. Hughes. J. Mobley. K.D. Wallace. J.G. Miller. G.H. Brandenburger, J. Acoust. Sot. Am. IO1 (1997) 1162. [ 161 G. Guidarelli. It. Pat. RMY5-A000623 720.95.