Ultrasonic spectroscopy for particle sizing and characterisation of liquidbased systems Mel Holmes, Malcolm J. Povey, Elena Simone, Valerie Pinfield*, Oliver Harlen, Tom Hazlehurst. School of Food Science and Nutrition, University of Leeds *Chemical Engineering Department, Loughborough University Abstract Ultrasound, by definition primarily consists of longitudinal pressure waves having frequency exceeding 16 kHz which oscillate the particles in the media through which they propagate e.g. gases, liquids, solids and complex media such as emulsions. By evaluating the wave speed and attenuation within the material in response to a range of frequencies of the incident field, many properties may be estimated e.g. compressibility, elasticity, viscosity and also insight into chemical structure and concentration effects of mixtures. In the case of emulsions, that is a fluid system in which droplets (10 nm 1 mm) of one or more immiscible fluids dispersed in a continuous phase these are usually opaque in appearance and pose a problem in order to ascertain the particle size distribution using conventional optical techniques since significant dilution is required. Ultrasound spectroscopy in this respect enables accurate determination of the particle size distribution and associated volume fraction and furthermore permits kinetic evaluation in processes such as coalescence and flocculation which may occur. In addition, ultrasound methods are non-invasive, non-destructive and may be applied to concentrated systems and evaluate changes in phase state, dissolution and crystallisation. Here we present the theoretical descriptions and experimental methods which are utilised for acoustic spectroscopy and highlight current research challenges and activities in liquid-based systems. Sound waves key features Sound is a travelling wave which is an oscillation of pressure transmitted through a solid, liquid, or gas Ultrasound above human audible range Analogy: slinky

Velocity, frequency, wavelength, attenuation, continuous standing waves spatial/temporal variation, pulses M. J. W. Povey, Ultrasonic Techniques for Fluids Characterisation (Academic Press, 1997) Summary definitions Pressure distribution at an instant in time P(x) Acoustic wave Amplitude A0 Position Wavelength Amplitude A0 Pressure at one position P(t) Time Period T 1 Wave frequency (Hz or s ) f T Wave attenuation (dB cm-1) 2 K

i wavelengt h attenuatio n Sound speed -1 decrease in amplitude with penetration depth x Wave number Wave speed (ms-1) Ae x v f v 2 Ultrasound in food systems Advantages Economical Can be used real-time Can be used on optically opaque and solid materials

Non-destructive and non-invasive Disadvantages May require sophisticated analyses Scattering and temperature may affect measurements Uses Material properties analysis density, compressibility, viscosity Monitor creaming/sedimentation processes Crystallisation/solubility processes Phase changes i.e. Solid-liquid etc Particle sizing concentrated systems Microscopy Types of waves Longitudinal-compressional wave Transverse wave Pulses Invariably consist of wave packets multiple frequencies distributed around a primary characteristic frequency http://www.acs.psu.edu/drussell/Demos/waves/wavemotion.html Low power ultrasound velocity measurement Ultrasound velocity meter (UVM) - Pulsed system Immersed in temperature bath

Stirred to ensure no temperature variation Frequency: 2.5 MHz transducer Closed system: no evaporation Fixed volume radius 40 mm Test range of concentrations Control rate of heating/cooling Averaged (n=10) time of flight UVM Velocity ms-1 = 80 mm/ 54 s = 1481.48 ms-1 Speed of sound Material v (ms-1) iron lead 5170 The speed of sound depends on the bond strength and separations between molecules/atoms. It can be determined from (Newton): v

2160 1 - is the density of the medium water 1464 is the compressibility, a measure of how easily the system is compressed under a force oxygen 316 air 331 Isothermal and adiabatic thermodynamic considerations Isothermal compressibility

1 V V P T 1600 1500 550 1400 500 1300 450 1200 1100 400 350 300 0 v

1 600 C D e n s ity / [k g /m 3 ] Velocity / [m/s] C Is o th e rm a l c o m p re s s ib ility / [1 /P a ] Velocity of sound in water 10 20 30 40 50 60 70 80 Temperature / CC

1000 Volumetric mechanism 900 Max velocity C 800 90 100 Low temperature 0.3 m/s ~ 0.1 C Probe molecular interactions Attenuation Ideal material Real material A( x) A0 A( x) A0 exp x In the ideal case, the wave energy and amplitude remain constant In reality some energy leaks away, e.g. due to fluid viscosity The wave amplitude attenuates (decays) exponentially with distance x and quantified by log ratio of initial amplitude (dB cm-1) Attenuation coefficient (varies from material to material) Frequency dependent Dynamics of sound waves

Obey the same general dynamics as all waves, e.g. light, water waves. Transmission Reflection Refraction Diffraction Absorption/Attenuation Scattering Viscosity/heating-friction (/f 2) /1014 (dB m1 Hz2) in water /f 2) /1014 (/f 2) /1014 (dB m1 Hz2) in waterd B m1 Hz2) Velocity and attenuation in water 1600 60 1550 50 Velocity

f(x) = NaN x^NaN R = NaN Attenuation (/f 2) /1014 (dB m1 Hz2) in waterUltrasizer) / (/f 2) /1014 (dB m1 Hz2) in waterdB m1 ) in distilled water 40 1600 30 1400 1400 20 1200 1350 10 1500 Polynomial (Velocity) Attenuation 1450 1300

0 20 40 T/C 60 80 0 100 Attenuation / (/f 2) /1014 (dB m1 Hz2) in waterdB m1 ) v/(m s1) Velocity v/ms-1 and attenuation (/f 2) /1014 (dB m1 Hz2) in water/f 2) /1014 (/f 2) /1014 (dB m1 Hz2) in waterdB m1 Hz2) in water 10 f(x) = 0.09 x^2.03 R = 1 C 1000 800 600 400 200 0

0 20 40 60 f / MHz 80 100 120 Velocity in some common liquids Acetic acid (19.6oC) Acetone (25oC) Alcohol, ethyl (ethanol) (25oC) Alcohol, methyl (25oC) Alcohol, propyl Castor oil Chloroform (25oC) Ethylene glycol (25oC) Glycerol (glycerine) (25oC) Heptane Hexane n-Hexanol (25oC) Oil (castor) (25oC) Oil (lubricating) (25oC) n-Propanol (25oC)

Water (20oC) Water, sea 3.5% salinity (20oC) Velocity (ms) 1173 1170 1144 1103 1205 1474 984 1660 1920 1138 1203 1303 1490 1461 1207 1482 1522 Molecular models sound speed in n-alkanes and 1-alcohols. Povey et al Compressibility of 1-alcohols OH 1-alcohols Urick n-alkanes Urick

1300 CH2 a a a a CH3 1.6E-09 Schaafs measured Urick Silicon Silicon prediction -1 C om pressibilty in P a Ultrasound velocity (m/s) 1500 1.2E-09

1100 900 8E-10 4E-10 0 5 10 15 Carbon number 20 0 2 4 6 8 10 12 14 16 Carbon or silicon number Concentration detection f(x) = 0 R = 0 Difference in Ultrasonic velocity of various saccharides versus different molality concentrations at 37C 16 14 f(x) = 99.38 x R = 1

Li ne ar (X yl os e) 12 10 Velocity/ [m/s] X yl os e 8 6 4 2 0 0 0.02 0.04 0.06 0.08

0.1 Molality / [moles /kg] 0.12 0.14 0.16 Liquid mixtures Wood equation the composite material behaves like a single material Inwhose mixtures, measurement of the sound can tell us of the density and compressibility is the speed volume-average the two concentrations. components: Important for assessing fermentation, emulsions, sugar content in juices 1

( 1 ) mix 2 1 where v Speed of sound in mixture of two denoted 1and 2 materials, ( 1 ) mix mix mix 2 1 = volume fraction of material 2 in material 1

Monitoring of fermentation Ethanol-water mixture There is a large variation of the speed of sound with volume fraction We can measure the speed of sound accurately, usually to within 0.1 ms -1 Real-time, non-invasive and non-destructive Mixtures air water There is a large variation of the speed of sound with volume fraction 1500 1400 1300 1200 1100 1000 900 800 700 600 500 400 300 200 100 0 1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E-01 1.0E+00

Voume fraction of air in water V elocity / 10-3m s-1 S p e e d o f s o u n d / m s -1 Non-invasive detection Definition: Brown heart Due to Boron deficiency 0.44 0.4 0.36 0.32 f(x) = 0.01 x + 0.26 R = 0.67 0.28 0.24 0.2 Pearson correlation r = 0 1 2 3 4 5 6 7

8 Browness index 0.82 9 10 50m Colloids and Emulsions Emulsion is a fluid system in which one or more immiscible (i.e. normally non-mixable) liquids is/are dispersed into a continuous phase liquid in the form of droplets Colloids particles uniformly dispersed in a fluid Sizes in the range nm - m In foods; Increased shelf-life Sensory profile Controlled release Crystallisation processes Important in dairy industry Crystallization Evaporation

Cooling heating T.L. Threlfall and S.J. Coles, Cryst Eng Comm. 18, 369 (2016). 45 T e m p e ra tu re /C C 40 35 2000 6. Dissolution of crystal solids 5. Sound velocity rises with rising temperature and changing crystal solids 1980 7. Temperature dependence of speed of sound in solution 4. Crystal solids in

equilibrium with saturated solution 1960 1940 Temperature Velocity 30 25 20 0 1. Cycl e5 indu ction 500 perio d 3. Temperature rise due to crystal growth exothermic 8. Cycle 6 induction period

1920 1900 1880 2. Nucleation 1000 1500 Time /s 1860 2000 2500 1840 3000 V e lo c ity o f s o u n d /m s -1 Crystallisation and dissolution Amylopectin 70-80% highly branched, degraded by enzymes easily Native Potato Starch (NPS) approximately 25% amylose

Ultrasound velocity / [m/s] Starch gel and enzyme action (40x magnification) Enzymatic dextrinisation -amylase from Bacillus subtilis Activity: Approx. 165 Bacterial Amylase units per mg One unit will dextrinize 1 mg of starch per minute at pH 6.6 and 30C. Time / [s] Ungelatinised amylase added to gelatinised NPS starch amylase activity breaks down gel Gelatinised cells broken down entirely, Holmes, M J., Southworth, T., Watson, N G., Povey, M J W. Enzyme activity determination using ultrasound. J. Phys.: Conf. Ser 1. 2014, 498, 012003 doi:10.1088/1742-6596/498/1/012003. Phase change - margarine 1650 Solid

Velocity / m s-1 1600 Phase transition 1550 1500 Liquid 1450 I II III 1400 -10 -5 0 5 10

15 20 25 30 35 Temperature / C Ultrasonic Techniques for Fluids Characterization (1997). Malcolm J.W. Povey ISBN: 978-0-12-563730-5 40 45 Emulsion stability Thermodynamically unstable Mathematical model ECAH v is the velocity vector of the fluid (ms-1), T is the temperature (K), g is the ratio of specific heats, t is the thermal conductivity (J s-1 m-1 K-1), is the density (kg m-3), Cp is the specific heat constant pressure (J kg-1 K-1), is the thermal expansivity (K-1), h is the shear viscosity (N s m-1),

is the bulk viscosity (N s m-1). Epstein, P.S. and Carhart, R.R. (1953) The absorption of sound in suspensions and emulsions. I. Water fog in air. Journal of the Acoustical Society of America 25, 553565. Allegra, J.R. and Hawley, S.A. (1972) Attenuation of sound in suspensions and emulsions: Theory and experiments. Journal of the Acoustical Society of America 51, 15451564. 100 Attenuation /dB cm-1 B u lk a n d S h e a r V is c o s ity [P a .s ] Bulk viscosity of fluids Shear Viscosity Bulk Viscosity Bulk Viscosity Xu et al [16] Dukhin and Goetz [10] Litovitz and Davies [4] 8.0E-03 7.0E-03 6.0E-03 f(x) = 0 x^2 R = 1 10 1

5.0E-03 4.0E-03 0.1 3.0E-03 1 2.0E-03 1.0E-03 0.0E+00 0 5 10 15 20 25 30 35 40 45

50 10 Frequency /MHz 55 Temperature [C] Ultrasizer 100 Wavenumbers decoupled system Compressional Thermal Shear Attenuation i n 2n 1 An hn kC r Pn cos n 0 i n 2n 1 An j n k C r Pn cos n 0 exterior fields are defined by ( )

interior fields primed quantities ( ). Decay lengths Boundary conditions (BC) Sound hard Dirichlet BC Sound soft Zero-flux BC High to low density reflect Low to high density reflect http://www.acs.psu.edu/drussell/Demos/reflect/reflect.html Boundary conditions (BC) To complete the model we require the following boundary conditions, these are given by (no shear given for brevity) normal velocity- pressure- 0 ' ' n n n

0 ' ', temperature- c 0 c T c T heat flux- C ' 0 T t C T r r r r t t ' t Mathematical model ECAH The pressure and temperature perturbations are given by and it

P ie T e it C T b g where, C ik C2 g 1 t / C p Thermal diffusivity igk C2 , T ik T2 g 1

igk T2 , c kC2 g 1 T kT2 kC2 kT2 Temperature changes dominated by thermal terms. This condition is significant in the heat flux BC and substitution into the normal velocity, pressure and temperature BCs enables calculation of the A0 coefficient. Successive solutions enable similar solutions for the higher order scattering coefficients Far field and effective wave number B e ik C r r , f , r r 1 f ik B

kC Far field Sommerfeld radiation condition 2n 1 A P cos n n n 0 2 3i 1 A0 3 A1 3 3 kC a Foldy (1961) sum of forward scattered fields 2 e B , v m B

excess = total - (1 - )continuous - droplets Far field and effective wave number B Waterman and Truell (WT) (1961) sum of forward and backward scattered fields Developed by Lloyd and Berry (1967) B kC 2 3 f (0) 9 2 1 2 3 4 6 k a 4 k C C a 2 2 f f 0

1 d 2 d f sin 2 d 0 First two terms of Lloyd and Berry give WT and first term Foldy B kC 2 3i 1 3 3 A0 3 A1 kC a Assumptions; Particles are treated as point scatterers and monodispersed Particle fields do not overlap and so do not interact Thermal and shear wave modes decay to zero

Sum of N single droplets converted into volume fraction Emulsions and ultrasound A0 Thermal monopole Breathing mode Difference of wave speeds in continuous and droplet Difference in compressibility Pressuretemperature coupling Emulsions and ultrasound A1 Shear dipole Oscillation of particle when density contrast dominates Ultrasound propagation in emulsions Particle sizing using ultrasound Ultrasizer 500 ml sample frequency range 1-100 MHz Attenuation /dB cm-1 f(x) 100 = NaN x^NaN

R = NaN f(x) = 0 x^2 R = 1 10 Silica in water 1% v/v 1 0.1 1 10 Frequency /MHz Ae x Kf ResoScan permits simultaneous measurements of the ultrasonic velocity and ultrasonic absorption, two sample cells (200 l capacity) in frequency range 7.3-8.4 MHz with temperature precision 0.05C 100 Silicone oil-in-water data Attenuation in 5% monodisperse suspension of silicon oil in water for different droplet sizes Data from Hemar et al (1997) J Phys II, 7 0.02 a=0.23 a=0.30

a=0.34 a=0.76 (Np) 0.015 0.01 0.005 0 0.01 Different droplet sizes 0.1 1 fa 2 (MHz m2) 10 Product attenuation and wavelength / Silicone oil-in-water data Different volume fraction Particle size distribution (PSD)

n SSD [ T f i E f i ] 2 i 1 PSD r 1 x g ln g ln r ln x g 2 ln 2 g exp exp 2 2 2 ln g 2 xg and g are geometric mean and standard deviation predicted by minimizing SSD Merit quality T theory E experiment 1.8 Measured at n frequencies 1.6 1.4 n T E

E i 1 1.2 % volume 100 M % n 2 1 0.8 0.6 0.4 0.2 0 0.1 1 10 D43 size / mm 100

Multiple scattering 1 f ik C 2n 1 Tn Pn cos n 0 e ik C r r , f , r r Far-field Scattered wave is incident on neighbour Primary and secondary waves will scatter Incident field scatters off particle Perturbation solutions In the low frequency potential scattering (LFPST)regions we have kC a<<1 Geometric high frequency kT a>>1 and resonance theory kC a<<1, kT a1 and utilise transformations of the form, ik C r ~ e

n ikC ~ ~ m nm n 0 m 0 ikT ikT r ~ e with similar expressions for the other fields Thermoacoustic Scattering Limits Harlen et al 2001,2003,2010 1. kC a <<1, |kT a|<<1 (low frequency, small particle) thermal boundary layer is large compared to particle size. Find ~ |kT a|2 (Recall |kT a|2 = a2/ is thermal diffusivity)

2. kC a <<1, |kT a| >> 1, (high frequency, large particle) thermal boundary layer is small compared to particle size Find ~ |kT a|-1 3. kC a<<1, |kT a| ~ 1, Maximum attenuation boundary layer thickness is equal to the particle size Perturbation solutions Attenuation per wavelength al / Np m 1.000 0.100 LFPST ECAH Geometric theory General/resonance theory Experimental 5 % v/v 0.010 0.001

0.000 0.1 1.0 10.0 100.0 Product of thermal wavenumber and particle radius kTa Concentrated systems Overlap of thermal fields decrease in measured attenuation for flocculated emulsion higher concentrations empirical theories (Herrmann, McClements) using effective medium model E x c e s s a tte n u a tio n p e r w a v e le n g th Thermal overlap mode conversion 0.100 0.010 0.001

0.03 0.000 Reduced attenuation due to mode conversion of thermal into compressional wave 0.25 2.50 Product of thermal wavenumber and particle radius kTa 25.00 Bispherical geometry We can identify particular numbers which specify a unique bispherical system d>(a1+ a2 ) is the separation of the two spheres Superposition single particles Two spherical droplets kCa<<1, kTa ~1

kT2 0, for r1 , r2 a kT 0, for r1, 2 a 2 r1 eikz r2 2 2 d B1n hn (kT r1 ) Pn (cos 1 ) B2 n hn (kT r2 ) Pn (cos 2 ), for r1 , r2 a n 0 b1, 2 jn (kT r1, 2 ) Pn (cos 1, 2 ), for r1, 2 a n 0 Use addition theorem for spherical waves

hn (kT r2 ) Pn (cos 2 ) C (n0 | l 0 | m0)hl (kT d ) jm (kT r1 ) Pm (cos1 ) l m Thermal overlap Hazlehurst, T.A., Harlen, O.G., Holmes, M.J. & Povey, M.J.W . Multiple scattering in dispersions, for long wavelength thermoacoustic solutions. J. Phys.: Conf. Ser 1. 2014, 5doi:10.1088/1742-6596/498/1/01200. Attenuation Prediction vs Experiment Reduces attenuation at lower frequencies . Mode conversions generalised Luppe et al. (2012) developed Waterman and Truell approach and further by Pinfield (2014) to define generalised transition operator for the far-field f qp 2n 1 qp

Tn Pn cos , n 0 pq Tn r j n k q r Pn cos pq Tn r hn k p r Pn cos Far field interactions between pairwise modes to be expressed e.g. CT Tn TnCC denotes the thermal scattering coefficient (Bn in ECAH Lloyd-Berry equivalent) of the thermal wave T resulting from an incident compressional wave C. An compressional scattering coefficient of the compressional wave C resulting from an incident thermal wave T Models are predicting reduced attenuation due to mode conversion of thermal into compressional wave

Challenge - Bi-disperse Mixtures Larger particles screen smaller particles a= 100nm, b=900nm Two particle theory still over-estimates attenuation Many challenging and interesting theoretical and experimental opportunities to do ! Thank you